@article{2stageTMLE,
	title        = {{Blurring cluster randomized trials and observational studies: Two-Stage TMLE for subsampling, missingness, and few independent units}},
	author       = {Nugent, Joshua R and Marquez, Carina and Charlebois, Edwin D and Abbott, Rachel and Balzer, Laura B, for the SEARCH COLLABORATION},
	year         = 2023,
	month        = {08},
	journal      = {Biostatistics},
	volume       = 25,
	number       = 3,
	pages        = {599--616},
	doi          = {10.1093/biostatistics/kxad015},
	issn         = {1465-4644},
	url          = {https://doi.org/10.1093/biostatistics/kxad015},
	abstract     = {{Cluster randomized trials (CRTs) often enroll large numbers of participants; yet due to resource constraints, only a subset of participants may be selected for outcome assessment, and those sampled may not be representative of all cluster members. Missing data also present a challenge: if sampled individuals with measured outcomes are dissimilar from those with missing outcomes, unadjusted estimates of arm-specific endpoints and the intervention effect may be biased. Further, CRTs often enroll and randomize few clusters, limiting statistical power and raising concerns about finite sample performance. Motivated by SEARCH-TB, a CRT aimed at reducing incident tuberculosis infection, we demonstrate interlocking methods to handle these challenges. First, we extend Two-Stage targeted minimum loss-based estimation to account for three sources of missingness: (i) subsampling; (ii) measurement of baseline status among those sampled; and (iii) measurement of final status among those in the incidence cohort (persons known to be at risk at baseline). Second, we critically evaluate the assumptions under which subunits of the cluster can be considered the conditionally independent unit, improving precision and statistical power but also causing the CRT to behave like an observational study. Our application to SEARCH-TB highlights the real-world impact of different assumptions on measurement and dependence; estimates relying on unrealistic assumptions suggested the intervention increased the incidence of TB infection by 18\\\% (risk ratio [RR]=1.18, 95\\\% confidence interval [CI]: 0.85--1.63), while estimates accounting for the sampling scheme, missingness, and within community dependence found the intervention decreased the incident TB by 27\\\% (RR=0.73, 95\\\% CI: 0.57--0.92).}},
	eprint       = {https://academic.oup.com/biostatistics/article-pdf/25/3/599/58538070/kxad015.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/biostatistics/kxad015}
}
@article{AAP,
	title        = {On Noise Abduction for Answering Counterfactual Queries: A Practical Outlook},
	author       = {Saptarshi Saha and Utpal Garain},
	year         = 2022,
	journal      = {Transactions on Machine Learning Research},
	issn         = {2835-8856},
	url          = {https://openreview.net/forum?id=4FU8Jz1Oyj},
	bdsk-url-1   = {https://openreview.net/forum?id=4FU8Jz1Oyj}
}
@article{ADHDNorway,
	title        = {The {ADHD} deficit in school performance across sex and parental education: A prospective sibling-comparison register study of 344,152 Norwegian adolescents},
	author       = {Sunde, Hans  and Kleppest\o{}, Thomas and Gustavson, Kristin and Nordmo, Magnus and Reme, Bj\o{}rn-Atle and Torvik, Fartein},
	year         = 2022,
	journal      = {JCPP Advances},
	volume       = 2,
	number       = 1,
	pages        = {e12064},
	doi          = {https://doi.org/10.1002/jcv2.12064},
	url          = {https://acamh.onlinelibrary.wiley.com/doi/abs/10.1002/jcv2.12064},
	keywords     = {ADHD, register data, school performance, sex differences, socioeconomic status},
	eprint       = {https://acamh.onlinelibrary.wiley.com/doi/pdf/10.1002/jcv2.12064},
	abstract     = {Abstract Background Attention-Deficit Hyperactivity Disorder (ADHD) is associated with impaired school performance, but the impact of ADHD may vary across sex, family background, and school subjects. By using prospective population-wide register data, we describe impairment in academic performance related to ADHD across different school subjects and investigate how this impairment differ across sex and parental education. Methods We examined grades and Grade Point Averages (GPA) at age \sim{}16 among 344,152 Norwegian children born between 1997 and 2002. We linked grades with diagnoses from publicly funded general practitioners and with demographic information. Associations between ADHD diagnosed between age 10 and 16 and school performance were estimated with linear models, including sibling-models which control for unobserved variables shared within families. Results Children with ADHD (4.0\%) had -1.11 standard deviations lower GPAs compared to children without ADHD. This difference remained substantial after adjusting for demographic factors (-0.87), comorbid mental disorders (-0.82), early school performance (-0.54), and when comparing full siblings (-0.60). The relative ADHD deficit was 22\% larger for girls than for boys and 39\% larger for children with highly educated parents than for children of parents without completed high school, but the absolute deficit was smaller. Conclusion The ADHD deficit in school performance was large and not easily attributable to other factors. Because the ADHD deficit was large in all school subjects, interventions should ideally address factors that affect school performance broadly, although targeting theoretical subjects specifically may be most effective given limited resources.}
}
@article{AIPW2017,
	title        = {{Inverse-Probability-Weighted Estimation for Monotone and Nonmonotone Missing Data}},
	author       = {Sun, BaoLuo and Perkins, Neil and Cole, Stephen and Harel, Ofer and Mitchell, Emily and Schisterman, Enrique and Tchetgen Tchetgen, Eric},
	year         = 2017,
	month        = 11,
	journal      = {American Journal of Epidemiology},
	volume       = 187,
	number       = 3,
	pages        = {585--591},
	doi          = {10.1093/aje/kwx350},
	issn         = {0002-9262},
	url          = {https://doi.org/10.1093/aje/kwx350},
	abstract     = {{Missing data is a common occurrence in epidemiologic research. In this paper, 3 data sets with induced missing values from the Collaborative Perinatal Project, a multisite US study conducted from 1959 to 1974, are provided as examples of prototypical epidemiologic studies with missing data. Our goal was to estimate the association of maternal smoking behavior with spontaneous abortion while adjusting for numerous confounders. At the same time, we did not necessarily wish to evaluate the joint distribution among potentially unobserved covariates, which is seldom the subject of substantive scientific interest. The inverse probability weighting (IPW) approach preserves the semiparametric structure of the underlying model of substantive interest and clearly separates the model of substantive interest from the model used to account for the missing data. However, IPW often will not result in valid inference if the missing-data pattern is nonmonotone, even if the data are missing at random. We describe a recently proposed approach to modeling nonmonotone missing-data mechanisms under missingness at random to use in constructing the weights in IPW complete-case estimation, and we illustrate the approach using 3 data sets described in a companion article (Am J Epidemiol. 2018;187(3):568--575).}},
	eprint       = {https://academic.oup.com/aje/article-pdf/187/3/585/24134641/kwx350tchetgenwebmaterialfinal.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/aje/kwx350}
}
@book{allWasserman,
	title        = {All of Nonparametric Statistics (Springer Texts in Statistics)},
	author       = {Wasserman, Larry},
	year         = 2006,
	publisher    = {Springer-Verlag},
	address      = {Berlin, Heidelberg},
	isbn         = {0387251456}
}
@book{Anastasios,
	title        = {Dynamic Treatment Regimes: Statistical Methods for Precision Medicine},
	author       = {Anastasios Tsiatis and Marie Davidian and Shannon Holloway and Eric Laber},
	year         = 2019,
	publisher    = {Chapman and Hall/CRC},
	address      = {New York, NY, USA},
	doi          = {10.1201/9780429192692},
	isbn         = 9780429192692,
	url          = {https://doi.org/10.1201/9780429192692},
	edition      = 1,
	bdsk-url-1   = {https://doi.org/10.1201/9780429192692}
}
@manual{apa2022dsmvtr,
	title        = {Diagnostic and Statistical Manual of Mental Disorders, Fifth edition, text revision},
	author       = {{American Psychiatric Association}},
	year         = 2022,
	publisher    = {American Psychiatric Association Publishing, Washington DC},
	shortauthor  = {{Apa}}
}
@article{app1,
	title        = {Collaborative targeted maximum likelihood for time to event data},
	author       = {Stitelman, Ori and {van der Laan}, Mark},
	year         = 2010,
	journal      = {The International Journal of Biostatistics},
	publisher    = {De Gruyter},
	volume       = 6,
	number       = 1
}
@inproceedings{app2,
	title        = {Collaborative targeted maximum likelihood estimation to assess causal effects in observational studies},
	author       = {Gruber, Susan and {van der Laan}, Mark},
	year         = 2018,
	booktitle    = {Biopharmaceutical Applied Statistics Symposium: Volume 2 Biostatistical Analysis of Clinical Trials},
	pages        = {1--23},
	organization = {Springer}
}
@article{app3,
	title        = {Finding quantitative trait loci genes with collaborative targeted maximum likelihood learning},
	author       = {Wang, Hui and Rose, Sherri and {van der Laan}, Mark},
	year         = 2011,
	journal      = {Statistics \& probability letters},
	publisher    = {Elsevier},
	volume       = 81,
	number       = 7,
	pages        = {792--796}
}
@article{attrition,
	title        = {Attrition Bias Related to Missing Outcome Data: A Longitudinal Simulation Study},
	author       = {Lewin, Antoine and Brondeel, Ruben and Benmarhnia, Tarik and Thomas, Fr{\'e}d{\'e}rique and Chaix, Basile},
	year         = 2018,
	journal      = {Epidemiology},
	volume       = 29,
	number       = 1
}
@article{Australia,
	title        = {Differential loss of participants does not necessarily cause selection bias},
	author       = {Kristie Carter and Fiona Imlach-Gunasekara and Sarah  McKenzie and Tony Blakely},
	year         = 2012,
	journal      = {Australian and New Zealand Journal of Public Health},
	volume       = 36,
	number       = 3,
	pages        = {218--222},
	doi          = {https://doi.org/10.1111/j.1753-6405.2012.00867.x},
	issn         = {1326-0200},
	url          = {https://www.sciencedirect.com/science/article/pii/S1326020023016631},
	abstract     = {Background: Most research is affected by differential participation, where individuals who do not participate have different characteristics to those who do. This is often assumed to induce selection bias. However, selection bias only occurs if the exposure-outcome association differs for participants compared to non-participants. We empirically demonstrate that selection bias does not necessarily occur when participation varies in a study. Methods: We used data from three waves of the longitudinal Survey of Family, Income and Employment (SoFIE). We examined baseline associations of labour market activity and education with self-rated health using logistic regression in five participation samples: A) the original sample at year one (n=22,260); B) those remaining in the sample (n=18,360); C) those (at year 3) consenting to data linkage (n=14,350); D) drop outs over three years (n=3,895); and E) those who dropped out or did not consent (n=7,905). Results: Loss to follow-up was more likely among lower socioeconomic groups and those with poorer health. However, for labour market activity and education, the odds of reporting fair/poor health were similar across all samples. Comparisons of the mutually exclusive samples (C and E) showed no difference in the odds ratios after adjustment for sociodemographic (participation) variables. Thus, there was little evidence of selection bias. Conclusions: Differential loss to follow-up (drop out) need not lead to selection bias in the association between exposure (labour market activity and education) and outcome (self-rated health).},
	keywords     = {selection bias, non-response, survey data},
	bdsk-url-1   = {https://www.sciencedirect.com/science/article/pii/S1326020023016631},
	bdsk-url-2   = {https://doi.org/10.1111/j.1753-6405.2012.00867.x}
}
@incollection{Balke1994a,
	title        = {Counterfactual Probabilities: Computational Methods, Bounds and Applications},
	author       = {Alexander Balke and Judea Pearl},
	year         = 1994,
	booktitle    = {Uncertainty in Artificial Intelligence},
	publisher    = {Morgan Kaufmann},
	address      = {San Francisco (CA)},
	pages        = {46--54},
	doi          = {https://doi.org/10.1016/B978-1-55860-332-5.50011-0},
	isbn         = {978-1-55860-332-5},
	url          = {https://www.sciencedirect.com/science/article/pii/B9781558603325500110},
	abstract     = {Evaluation of counterfactual queries (e.g., ``If A were true, would C have been true?'') is important to fault diagnosis, planning, and determination of liability. In this paper we present methods for computing the probabilities of such queries using the formulation proposed in [Balke and Pearl, 1994], where the antecedent of the query is interpreted as an external action that forces the proposition A to be true. When a prior probability is available on the causal mechanisms governing the domain, counterfactual probabilities can be evaluated precisely. However, when causal knowledge is specified as conditional probabilities on the observables, only bounds can computed. This paper develops techniques for evaluating these bounds, and demonstrates their use in two applications: (1) the determination of treatment efficacy from studies in which subjects may choose their own treatment, and (2) the determination of liability in product-safety litigation.},
	editor       = {Ramon Lopez {de Mantaras} and David Poole},
	bdsk-url-1   = {https://www.sciencedirect.com/science/article/pii/B9781558603325500110},
	bdsk-url-2   = {https://doi.org/10.1016/B978-1-55860-332-5.50011-0}
}
@inproceedings{Balke1994b,
	title        = {Probabilistic evaluation of counterfactual queries},
	author       = {Balke, Alexander and Pearl, Judea},
	year         = 1994,
	booktitle    = {Proceedings of the Twelfth National Conference on Artificial Intelligence (Vol. 1)},
	location     = {Seattle, Washington, USA},
	publisher    = {American Association for Artificial Intelligence},
	address      = {Usa},
	series       = {Aaai '94},
	pages        = {230--237},
	isbn         = {0262611023},
	numpages     = 8
}
@article{Balke1997,
	title        = {Bounds on Treatment Effects From Studies With Imperfect Compliance},
	author       = {Alexander Balke and Judea Pearl},
	year         = 1997,
	journal      = {Journal of the American Statistical Association},
	publisher    = {[American Statistical Association, Taylor \& Francis, Ltd.]},
	volume       = 92,
	number       = 439,
	pages        = {1171--1176},
	issn         = {01621459},
	url          = {http://www.jstor.org/stable/2965583},
	urldate      = {2024-02-04},
	abstract     = {This article establishes nonparametric formulas that can be used to bound the average treatment effect in experimental studies in which treatment assignment is random but subject compliance is imperfect. The bounds provided are the tightest possible, given the distribution of assignments, treatments, and responses. The formulas show that even with high rates of noncompliance, experimental data can yield useful and sometimes accurate information on the average effect of a treatment on the population.},
	bdsk-url-1   = {http://www.jstor.org/stable/2965583}
}
@article{Balke97,
	title        = {Bounds on Treatment Effects from Studies with Imperfect Compliance},
	author       = {Alexander Balke and Judea Pearl},
	year         = 1997,
	journal      = {Journal of the American Statistical Association},
	publisher    = {Taylor and Francis},
	volume       = 92,
	number       = 439,
	pages        = {1171--1176},
	doi          = {10.1080/01621459.1997.10474074},
	url          = {https://doi.org/10.1080/01621459.1997.10474074},
	eprint       = {https://doi.org/10.1080/01621459.1997.10474074},
	bdsk-url-1   = {https://doi.org/10.1080/01621459.1997.10474074}
}
@article{ballis2021long,
	title        = {The long-run impacts of special education},
	author       = {Ballis, Briana and Heath, Katelyn},
	year         = 2021,
	journal      = {American Economic Journal: Economic Policy},
	publisher    = {American Economic Association 2014 Broadway, Suite 305, Nashville, TN 37203-2425},
	volume       = 13,
	number       = 4,
	pages        = {72--111}
}
@article{Bang,
	title        = {Doubly Robust Estimation in Missing Data and Causal Inference Models},
	author       = {Bang, Heejung and Robins, James},
	year         = 2005,
	month        = 12,
	journal      = {Biometrics},
	volume       = 61,
	number       = 4,
	pages        = {962--973},
	doi          = {10.1111/j.1541-0420.2005.00377.x},
	issn         = {0006-341x},
	url          = {https://doi.org/10.1111/j.1541-0420.2005.00377.x},
	abstract     = {The goal of this article is to construct doubly robust (DR) estimators in ignorable missing data and causal inference models. In a missing data model, an estimator is DR if it remains consistent when either (but not necessarily both) a model for the missingness mechanism or a model for the distribution of the complete data is correctly specified. Because with observational data one can never be sure that either a missingness model or a complete data model is correct, perhaps the best that can be hoped for is to find a DR estimator. DR estimators, in contrast to standard likelihood-based or (nonaugmented) inverse probability-weighted estimators, give the analyst two chances, instead of only one, to make a valid inference. In a causal inference model, an estimator is DR if it remains consistent when either a model for the treatment assignment mechanism or a model for the distribution of the counterfactual data is correctly specified. Because with observational data one can never be sure that a model for the treatment assignment mechanism or a model for the counterfactual data is correct, inference based on DR estimators should improve upon previous approaches. Indeed, we present the results of simulation studies which demonstrate that the finite sample performance of DR estimators is as impressive as theory would predict. The proposed method is applied to a cardiovascular clinical trial.},
	eprint       = {https://academic.oup.com/biometrics/article-pdf/61/4/962/51974493/biometrics_61_4_962.pdf}
}
@article{Bareinboim_Tian_2015,
	title        = {Recovering Causal Effects from Selection Bias},
	author       = {Bareinboim, Elias and Tian, Jin},
	year         = 2015,
	month        = 3,
	journal      = {Proceedings of the AAAI Conference on Artificial Intelligence},
	volume       = 29,
	number       = 1,
	doi          = {10.1609/aaai.v29i1.9679},
	url          = {https://ojs.aaai.org/index.php/AAAI/article/view/9679},
	abstractnote = {Controlling for selection and confounding biases are two of the most challenging problems that appear in data analysis in the empirical sciences as well as in artificial intelligence tasks. The combination of previously studied methods for each of these biases in isolation is not directly applicable to certain non-trivial cases in which selection and confounding biases are simultaneously present. In this paper, we tackle these instances non-parametrically and in full generality. We provide graphical and algorithmic conditions for recoverability of interventional distributions for when selection and confounding biases are both present. Our treatment completely characterizes the class of causal effects that are recoverable in {M}arkovian models, and is suffi- cient for Semi-{M}arkovian models.},
	bdsk-url-1   = {https://ojs.aaai.org/index.php/AAAI/article/view/9679},
	bdsk-url-2   = {https://doi.org/10.1609/aaai.v29i1.9679}
}
@article{Bareinboim_Tian_Pearl_2014,
	title        = {Recovering from Selection Bias in Causal and Statistical Inference},
	author       = {Bareinboim, Elias and Tian, Jin and Pearl, Judea},
	year         = 2014,
	month        = 6,
	journal      = {Proceedings of the AAAI Conference on Artificial Intelligence},
	volume       = 28,
	number       = 1,
	doi          = {10.1609/aaai.v28i1.9074},
	url          = {https://ojs.aaai.org/index.php/AAAI/article/view/9074},
	abstractnote = {Selection bias is caused by preferential exclusion of units from the samples and represents a major obstacle to valid causal and statistical inferences; it cannot be removed by randomized experiments and can rarely be detected in either experimental or observational studies. In this paper, we provide complete graphical and algorithmic conditions for recovering conditional probabilities from selection biased data. We also provide graphical conditions for recoverability when unbiased data is available over a subset of the variables. Finally, we provide a graphical condition that generalizes the backdoor criterion and serves to recover causal effects when the data is collected under preferential selection},
	bdsk-url-1   = {https://ojs.aaai.org/index.php/AAAI/article/view/9074},
	bdsk-url-2   = {https://doi.org/10.1609/aaai.v28i1.9074}
}
@inproceedings{Bareinboim12,
	title        = {Controlling Selection Bias in Causal Inference},
	author       = {Bareinboim, Elias and Pearl, Judea},
	year         = 2012,
	month        = 4,
	booktitle    = {Proceedings of the Fifteenth International Conference on Artificial Intelligence and Statistics},
	publisher    = {Pmlr},
	address      = {La Palma, Canary Islands},
	series       = {Proceedings of Machine Learning Research},
	volume       = 22,
	pages        = {100--108},
	url          = {https://proceedings.mlr.press/v22/bareinboim12.html},
	abstract     = {Selection bias, caused by preferential exclusion of samples from the data, is a major obstacle to valid causal and statistical inferences; it cannot be removed by randomized experiments and can hardly be detected  in either experimental or observational studies. This paper highlights several graphical and algebraic methods capable of mitigating and sometimes eliminating this bias. These nonparametric methods generalize previously reported results, and identify the type of knowledge that is needed for reasoning in the presence of selection bias.  Specifically,  we derive a general condition together with a procedure for  deciding recoverability of the odds ratio (OR) from s-biased data. We show that recoverability  is feasible if and only if our condition holds.  We further offer a new method of controlling selection bias using instrumental variables that permits the  recovery of other effect measures besides OR.},
	editor       = {Lawrence, Neil D. and Girolami, Mark},
	pdf          = {http://proceedings.mlr.press/v22/bareinboim12/bareinboim12.pdf},
	bdsk-url-1   = {https://proceedings.mlr.press/v22/bareinboim12.html}
}
@inbook{BareinboimHierarchy2022,
	title        = {On {P}earl's Hierarchy and the foundations of causal inference},
	author       = {Bareinboim, Elias and Correa, Juan and Ibeling, Duligur and Icard, Thomas},
	year         = 2022,
	booktitle    = {Probabilistic and Causal Inference: The Works of {J}udea {P}earl},
	publisher    = {Association for Computing Machinery},
	address      = {New York, NY, USA},
	pages        = {507--556},
	isbn         = 9781450395861,
	url          = {https://doi.org/10.1145/3501714.3501743},
	edition      = 1,
	numpages     = 50,
	bdsk-url-1   = {https://doi.org/10.1145/3501714.3501743}
}
@article{bayesianSB,
	title        = {Correcting for sample selection bias in {B}ayesian distributional regression models},
	author       = {Paul F.V. Wiemann and Nadja Klein and Thomas Kneib},
	year         = 2022,
	journal      = {Computational Statistics and Data Analysis},
	volume       = 168,
	pages        = 107382,
	doi          = {https://doi.org/10.1016/j.csda.2021.107382},
	issn         = {0167-9473},
	url          = {https://www.sciencedirect.com/science/article/pii/S0167947321002164},
	abstract     = {In the presence of non-randomly selected samples, many statistical models, including standard regression models, can fail. In particular, without accounting for the underlying selection process estimates might be biased. Sample selection models can correct this bias when an informative selection process governs the availability of the outcome of interest. A copula based approach is presented for correcting the sample selection bias in Bayesian structured additive distributional regression models. This framework relaxes the distributional assumption on the response of the linear or the generalized linear model and models all distributional parameters as functions of the covariates. Covariate effects are not limited to being purely linear and other effect types, such as smooth functional effects, are available. As a consequence, the approach presented provides increased flexibility with respect to the dependence structure, the available predictor specifications and the choice of the marginal distributions compared to Heckman's classic sample selection model. To facilitate estimation in such a complex model, a fully Bayesian approach based on {M}arkov chain Monte Carlo simulations is developed and the presented methodology is empirically evaluated. Furthermore, the introduced approach is compared to a frequentist competitor and an application on a data set from psychological judge-advisor research is presented.},
	keywords     = {Bayesian distributional regression, Copula, Data augmentation, {M}arkov chain Monte Carlo, Sample selection, Semi-parametric predictors},
	bdsk-url-1   = {https://www.sciencedirect.com/science/article/pii/S0167947321002164},
	bdsk-url-2   = {https://doi.org/10.1016/j.csda.2021.107382}
}
@inproceedings{beckers2022causal,
	title        = {Causal explanations and {XAI}},
	author       = {Beckers, Sander},
	year         = 2022,
	booktitle    = {Conference on Causal Learning and Reasoning},
	pages        = {90--109},
	organization = {Pmlr}
}
@book{BellmanDP,
	title        = {{Dynamic Programming}},
	author       = {Bellman, Richard},
	year         = 1957,
	publisher    = {Dover Publications},
	isbn         = 9780486428093,
	abstract     = {An introduction to the mathematical theory of multistage decision processes, this text takes a "functional equation" approach to the discovery of optimum policies. Written by a leading developer of such policies, it presents a series of methods, uniqueness and existence theorems, and examples for solving the relevant equations. The text examines existence and uniqueness theorems, the optimal inventory equation, bottleneck problems in multistage production processes, a new formalism in the calculus of variation, strategies behind multistage games, and {M}arkovian decision processes. Each chapter concludes with a problem set that Eric V. Denardo of Yale University, in his informative new introduction, calls "a rich lode of applications and research topics." 1957 edition. 37 figures.},
	added-at     = {2011-08-17t16:08:47.000+0200},
	biburl       = {https://www.bibsonomy.org/bibtex/29cdd821222218ded252c8ba5cd712666/pcbouman},
	interhash    = {acf948462171ca060064a7ded257a792},
	intrahash    = {9cdd821222218ded252c8ba5cd712666},
	keywords     = {book dynamic programming},
	timestamp    = {2011-08-18t09:10:27.000+0200}
}
@inproceedings{Bhattacharya2020,
	title        = {Identification In Missing Data Models Represented By Directed Acyclic Graphs},
	author       = {Bhattacharya, Rohit and Nabi, Razieh and Shpitser, Ilya and Robins, James},
	year         = 2020,
	month        = 7,
	booktitle    = {Proceedings of The 35th Uncertainty in Artificial Intelligence Conference},
	publisher    = {Pmlr},
	series       = {Proceedings of Machine Learning Research},
	volume       = 115,
	pages        = {1149--1158},
	url          = {https://proceedings.mlr.press/v115/bhattacharya20b.html},
	abstract     = {Missing data is a pervasive problem in data analyses, resulting in datasets that contain censored realizations of a target distribution. Many approaches to inference on the target distribution using censored observed data, rely on missing data models represented as a factorization with respect to a directed acyclic graph. In this paper we consider the identifiability of the target distribution within this class of models, and show that the most general identification strategies proposed so far retain a significant gap in that they fail to identify a wide class of identifiable distributions. To address this gap, we propose a new algorithm that significantly generalizes the types of manipulations used in the ID algorithm [14, 16], developed in the context of causal inference, in order to obtain identification.},
	editor       = {Adams, Ryan P. and Gogate, Vibhav},
	pdf          = {http://proceedings.mlr.press/v115/bhattacharya20b/bhattacharya20b.pdf},
	bdsk-url-1   = {https://proceedings.mlr.press/v115/bhattacharya20b.html}
}
@article{bibaut2017data,
	title        = {Data-adaptive smoothing for optimal-rate estimation of possibly non-regular parameters},
	author       = {Bibaut, Aur{\'e}lien and {van der Laan}, Mark},
	year         = 2017,
	journal      = {arXiv e-prints},
	pages        = {arXiv--1706}
}
@book{bickel1998,
	title        = {Efficient and adaptive estimation for semiparametric models},
	author       = {Bickel, P. and Klaassen, C. and Ritov, Y. and Wellner, J.},
	year         = 1993,
	publisher    = {Springer New York},
	volume       = 4,
	isbn         = 9780387984735,
	lccn         = 92033799
}
@article{biele2019bias,
	title        = {Bias from self selection and loss to follow-up in prospective cohort studies},
	author       = {Biele, Guido and Gustavson, Kristin and Czajkowski, Nikolai and Nilsen, Roy and Reichborn-Kjennerud, Ted and Magnus, Per and Stoltenberg, Camilla and Aase, Heidi},
	year         = 2019,
	journal      = {European Journal of Epidemiology},
	publisher    = {Springer},
	volume       = 34,
	number       = 10,
	pages        = {927--938},
	doi          = {10.1007/s10654-019-00550-1},
	note         = {Pmid: 31451995},
	bdsk-url-1   = {https://doi.org/10.1007/s10654-019-00550-1}
}
@article{bikoro2020incidence,
	title        = {Incidence and predictors of loss to follow-up among human immunodeficiency virus-infected adult patients on anti-retroviral therapy at Hadiya zone public hospitals, southern Ethiopia: a retrospective cohort study},
	author       = {Bikoro, Belachew and Oljira, Lemessa and Gobena, Tesfaye and Erkalo, Desta},
	year         = 2020,
	journal      = {Journal of Public Health},
	publisher    = {Springer},
	pages        = {1--12}
}
@article{bioRL,
	title        = {Reinforcement Learning in Modern Biostatistics: Constructing Optimal Adaptive Interventions},
	author       = {Deliu, Nina and Williams, Joseph Jay and Chakraborty, Bibhas},
	year         = 2024,
	journal      = {International Statistical Review},
	doi          = {https://doi.org/10.1111/insr.12583},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1111/insr.12583},
	keywords     = {dynamic treatment regimes, just-in-time adaptive interventions, mobile health, multi-armed bandits, artificial intelligence, machine learning, reinforcement learning, optimal policy learning},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/insr.12583},
	abstract     = {Summary In recent years, reinforcement learning (RL) has acquired a prominent position in health-related sequential decision-making problems, gaining traction as a valuable tool for delivering adaptive interventions (AIs). However, in part due to a poor synergy between the methodological and the applied communities, its real-life application is still limited and its potential is still to be realised. To address this gap, our work provides the first unified technical survey on RL methods, complemented with case studies, for constructing various types of AIs in healthcare. In particular, using the common methodological umbrella of RL, we bridge two seemingly different AI domains, dynamic treatment regimes and just-in-time adaptive interventions in mobile health, highlighting similarities and differences between them and discussing the implications of using RL. Open problems and considerations for future research directions are outlined. Finally, we leverage our experience in designing case studies in both areas to showcase the significant collaborative opportunities between statistical, RL and healthcare researchers in advancing AIs.}
}
@inproceedings{BoutilierCSI,
	title        = {Context-specific independence in Bayesian networks},
	author       = {Boutilier, Craig and Friedman, Nir and Goldszmidt, Moises and Koller, Daphne},
	year         = 1996,
	booktitle    = {Proceedings of the Twelfth International Conference on Uncertainty in Artificial Intelligence},
	location     = {Portland, OR},
	publisher    = {Morgan Kaufmann Publishers Inc.},
	address      = {San Francisco, CA, USA},
	series       = {Uai'96},
	pages        = {115–123},
	isbn         = {155860412x},
	abstract     = {Bayesian networks provide a language for qualitatively representing the conditional independence properties of a distribution, This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms. It is well-known, however, that there are certain independencies that we cannot capture qualitatively within the Bayesian network structure: independencies that hold only in certain contexts, i.e., given a specific assignment of values to certain variables, In this paper, we propose a formal notion of context-specific independence (CSI), based on regularities in the conditional probability tables (CPTs) at a node. We present a technique, analogous to (and based on) d-separation, for determining when such independence holds in a given network. We then focus on a particular qualitative representation scheme--tree-structured CPTs-- for capturing CSI. We suggest ways in which this representation can be used to support effective inference algorithms, in particular, we present a structural decomposition of the resulting network which can improve the performance of clustering algorithms, and an alternative algorithm based on outset conditioning.},
	numpages     = 9
}
@article{Brikell2021,
	title        = {Insights into attention-deficit/hyperactivity disorder from recent genetic studies},
	author       = {Brikell, Isabell and Burton, Christie and Mota, Nina and Martin, Joanna},
	year         = 2021,
	journal      = {Psychological Medicine},
	volume       = 51,
	number       = 13,
	pages        = {2274–2286},
	doi          = {10.1017/s0033291721000982}
}
@inproceedings{Brito2002,
	title        = {Generalized Instrumental Variables},
	author       = {Brito, Carlos and Pearl, Judea},
	year         = 2002,
	booktitle    = {Proceedings of the Eighteenth Conference on Uncertainty in Artificial Intelligence},
	location     = {Alberta, Canada},
	publisher    = {Morgan Kaufmann Publishers Inc.},
	address      = {San Francisco, CA, USA},
	series       = {Uai'02},
	pages        = {85--93},
	isbn         = 1558608974,
	abstract     = {This paper concerns the assessment of direct causal effects from a combination of: (i) nonexperimental data, and (ii) qualitative domain knowledge. Domain knowledge is encoded in the form of a directed acyclic graph (DAG), in which all interactions are assumed linear, and some variables are presumed to be unobserved. We provide a generalization of the well-known method of Instrumental Variables, which allows its application to models with few conditional independeces.},
	numpages     = 9
}
@article{causaleffect,
	title        = {Identifying Causal Effects with the {R} Package causaleffect},
	author       = {Tikka, Santtu and Karvanen, Juha},
	year         = 2017,
	journal      = {Journal of Statistical Software},
	volume       = 76,
	number       = 12,
	pages        = {1–30},
	doi          = {10.18637/jss.v076.i12},
	url          = {https://www.jstatsoft.org/index.php/jss/article/view/v076i12},
	abstract     = {Do-calculus is concerned with estimating the interventional distribution of an action from the observed joint probability distribution of the variables in a given causal structure. All identifiable causal effects can be derived using the rules of do-calculus, but the rules themselves do not give any direct indication whether the effect in question is identifiable or not. Shpitser and Pearl (2006b) constructed an algorithm for identifying joint interventional distributions in causal models, which contain unobserved variables and induce directed acyclic graphs. This algorithm can be seen as a repeated application of the rules of do-calculus and known properties of probabilities, and it ultimately either derives an expression for the causal distribution, or fails to identify the effect, in which case the effect is non-identifiable. In this paper, the R package causaleffect is presented, which provides an implementation of this algorithm. Functionality of causaleffect is also demonstrated through examples.}
}
@article{causalMissing,
	title        = {Causal Inference: A Missing Data Perspective},
	author       = {Peng Ding and Fan Li},
	year         = 2018,
	journal      = {Statistical Science},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 33,
	number       = 2,
	pages        = {214 -- 237},
	doi          = {10.1214/18-sts645},
	url          = {https://doi.org/10.1214/18-STS645},
	keywords     = {Assignment mechanism, ignorability, imputation, missing data mechanism, observational studies, potential outcome, propensity score, Randomization, weighting}
}
@article{cdt,
	title        = {{Counterfactual Decision Theory}},
	author       = {Hedden, Brian},
	year         = 2023,
	month        = {04},
	journal      = {Mind},
	volume       = 132,
	number       = 527,
	pages        = {730--761},
	doi          = {10.1093/mind/fzac060},
	issn         = {0026-4423},
	url          = {https://doi.org/10.1093/mind/fzac060},
	abstract     = {{I defend counterfactual decision theory, which says that you should evaluate an action in terms of which outcomes would likely obtain were you to perform it. Counterfactual decision theory has traditionally been subsumed under causal decision theory as a particular formulation of the latter. This is a mistake. Counterfactual decision theory is importantly different from, and superior to, causal decision theory, properly so called. Causation and counterfactuals come apart in three kinds of cases. In cases of overdetermination, an action can cause a good outcome without the latter counterfactually depending on the former. In cases of constitution, an action can constitute a good outcome rather than causing it. And in cases of determinism, either the laws or the past counterfactually depend on your action, even though your action cannot cause the laws or the past to be different. In each of these cases, it is counterfactual decision theory which gives the right verdict, and for the right reasons.}},
	eprint       = {https://academic.oup.com/mind/article-pdf/132/527/730/50968752/fzac060.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/mind/fzac060}
}
@article{censoringTMLE,
	title        = {One-step targeted maximum likelihood estimation for time-to-event outcomes},
	author       = {Cai, Weixin and {van der Laan}, Mark},
	year         = 2020,
	journal      = {Biometrics},
	volume       = 76,
	number       = 3,
	pages        = {722--733},
	doi          = {https://doi.org/10.1111/biom.13172},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1111/biom.13172},
	abstract     = {Abstract Researchers in observational survival analysis are interested in not only estimating survival curve nonparametrically but also having statistical inference for the parameter. We consider right-censored failure time data where we observe n independent and identically distributed observations of a vector random variable consisting of baseline covariates, a binary treatment at baseline, a survival time subject to right censoring, and the censoring indicator. We assume the baseline covariates are allowed to affect the treatment and censoring so that an estimator that ignores covariate information would be inconsistent. The goal is to use these data to estimate the counterfactual average survival curve of the population if all subjects are assigned the same treatment at baseline. Existing observational survival analysis methods do not result in monotone survival curve estimators, which is undesirable and may lose efficiency by not constraining the shape of the estimator using the prior knowledge of the estimand. In this paper, we present a one-step Targeted Maximum Likelihood Estimator (TMLE) for estimating the counterfactual average survival curve. We show that this new TMLE can be executed via recursion in small local updates. We demonstrate the finite sample performance of this one-step TMLE in simulations and an application to a monoclonal gammopathy data.},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/biom.13172},
	keywords     = {causal inference, censored data, machine learning, survival analysis, survival curve, targeted maximum likelihood estimation},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.1111/biom.13172},
	bdsk-url-2   = {https://doi.org/10.1111/biom.13172}
}
@article{chakraborty2010,
	title        = {Inference for Nonregular Parameters in Optimal Dynamic Treatment Regimes},
	author       = {Chakraborty, Bibhas and Strecher, Victor and Murphy, Susan},
	year         = 2010,
	journal      = {Statistical Methods in Medical Research},
	publisher    = {SAGE Publications Sage UK: London, England},
	volume       = 19,
	number       = 3,
	pages        = {317--343}
}
@article{Cinelli,
	title        = {Generalizing experimental results by leveraging knowledge of mechanisms},
	author       = {Cinelli, Carlos and Pearl, Judea},
	year         = 2021,
	journal      = {European Journal of Epidemiology},
	volume       = 36,
	number       = 2,
	pages        = {149--164},
	doi          = {10.1007/s10654-020-00687-4},
	isbn         = {1573-7284},
	url          = {https://doi.org/10.1007/s10654-020-00687-4},
	abstract     = {We show how experimental results can be generalized across diverse populations by leveraging knowledge of local mechanisms that produce the outcome of interest, only some of which may differ in the target domain. We use structural causal models and a refined version of selection diagrams to represent such knowledge, and to decide whether it entails the invariance of probabilities of causation across populations, which then enables generalization. We further provide: (i) bounds for the target effect when some of these conditions are violated; (ii) new identification results for probabilities of causation and the transported causal effect when trials from multiple source domains are available; as well as (iii) a Bayesian approach for estimating the transported causal effect from finite samples. We illustrate these methods both with simulated data and with a real example that transports the effects of Vitamin A supplementation on childhood mortality across different regions.},
	date         = {2021/02/01},
	date-added   = {2024-05-20 21:40:24 -0500},
	date-modified = {2024-05-20 21:40:24 -0500},
	id           = {Cinelli2021},
	bdsk-url-1   = {https://doi.org/10.1007/s10654-020-00687-4}
}
@article{cinelliControls,
	title        = {A Crash Course in Good and Bad Controls},
	author       = {Carlos Cinelli and Andrew Forney and Judea Pearl},
	year         = 2024,
	journal      = {Sociological Methods and Research},
	volume       = 53,
	number       = 3,
	pages        = {1071--1104},
	doi          = {10.1177/00491241221099552},
	url          = {https://doi.org/10.1177/00491241221099552},
	abstract     = {Many students of statistics and econometrics express frustration with the way a problem known as ``bad control'' is treated in the traditional literature. The issue arises when the addition of a variable to a regression equation produces an unintended discrepancy between the regression coefficient and the effect that the coefficient is intended to represent. Avoiding such discrepancies presents a challenge to all analysts in the data intensive sciences. This note describes graphical tools for understanding, visualizing, and resolving the problem through a series of illustrative examples. By making this ``crash course'' accessible to instructors and practitioners, we hope to avail these tools to a broader community of scientists concerned with the causal interpretation of regression models.},
	eprint       = {https://doi.org/10.1177/00491241221099552},
	bdsk-url-1   = {https://doi.org/10.1177/00491241221099552}
}
@article{climate,
	title        = {Causal Counterfactual Theory for the Attribution of Weather and Climate-Related Events},
	author       = {Alexis Hannart and Judea Pearl and Friederike Otto and Philippe Naveau and Michael Ghil},
	year         = 2016,
	journal      = {Bulletin of the American Meteorological Society},
	publisher    = {American Meteorological Society},
	address      = {Boston MA, USA},
	volume       = 97,
	number       = 1,
	pages        = {99--110},
	doi          = {10.1175/bams-d-14-00034.1},
	url          = {https://journals.ametsoc.org/view/journals/bams/97/1/bams-d-14-00034.1.xml},
	bdsk-url-1   = {https://journals.ametsoc.org/view/journals/bams/97/1/bams-d-14-00034.1.xml},
	bdsk-url-2   = {https://doi.org/10.1175/BAMS-D-14-00034.1}
}
@inproceedings{clustered,
	title        = {Causal effect identification in cluster {DAGs}},
	author       = {Anand, Tara and Ribeiro, Adele and Tian, Jin and Bareinboim, Elias},
	year         = 2023,
	booktitle    = {Proceedings of the AAAI Conference on Artificial Intelligence},
	volume       = 37,
	number       = 10,
	pages        = {12172--12179}
}
@article{collaborative2010,
	title        = {Collaborative double robust targeted maximum likelihood estimation},
	author       = {{van der Laan}, Mark  and Gruber, Susan},
	year         = 2010,
	journal      = {The international journal of biostatistics},
	publisher    = {De Gruyter},
	volume       = 6,
	number       = 1
}
@article{colliderStratification,
	title        = {{Selection Bias Requires Selection: The Case of Collider Stratification Bias}},
	author       = {Lu, Haidong and Gonsalves, Gregg and Westreich, Daniel},
	year         = 2023,
	month        = 11,
	journal      = {American Journal of Epidemiology},
	volume       = 193,
	number       = 3,
	pages        = {407--409},
	doi          = {10.1093/aje/kwad213},
	issn         = {0002-9262},
	url          = {https://doi.org/10.1093/aje/kwad213},
	abstract     = {{In epidemiology, collider stratification bias, the bias resulting from conditioning on a common effect of two causes, is oftentimes considered a type of selection bias, regardless of the conditioning methods employed. In this commentary, we distinguish between two types of collider stratification bias: collider restriction bias due to restricting to one level of a collider (or a descendant of a collider) and collider adjustment bias through inclusion of a collider (or a descendant of a collider) in a regression model. We argue that categorizing collider adjustment bias as a form of selection bias may lead to semantic confusion, as adjustment for a collider in a regression model does not involve selecting a sample for analysis. Instead, we propose that collider adjustment bias can be better viewed as a type of overadjustment bias. We further provide two distinct causal diagram structures to distinguish collider restriction bias and collider adjustment bias. We hope that such a terminological distinction can facilitate easier and clearer communication.}},
	eprint       = {https://academic.oup.com/aje/article-pdf/193/3/407/56865501/kwad213.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/aje/kwad213}
}
@article{ColnetJosse,
	title        = {Causal effect on a target population: A sensitivity analysis to handle missing covariates},
	author       = {B\'{e}n\'{e}dicte Colnet and Julie Josse and Ga\"{e}l Varoquaux and Erwan Scornet},
	year         = 2022,
	journal      = {Journal of Causal Inference},
	volume       = 10,
	number       = 1,
	pages        = {372--414},
	doi          = {doi:10.1515/jci-2021-0059},
	url          = {https://doi.org/10.1515/jci-2021-0059},
	lastchecked  = {2025-01-27}
}
@article{Conservative,
	title        = {Conservative inference for counterfactuals},
	author       = {Balakrishnan, Sivaraman and Kennedy, Edward and Wasserman, Larry},
	year         = 2023,
	journal      = {arXiv preprint arXiv:2310.12757}
}
@article{consistencyPearl,
	title        = {On the Consistency Rule in Causal Inference: Axiom, Definition, Assumption, or Theorem?},
	author       = {Pearl, Judea},
	year         = 2010,
	journal      = {Epidemiology},
	volume       = 21,
	number       = 6,
	url          = {https://journals.lww.com/epidem/fulltext/2010/11000/on\%5Fthe\%5Fconsistency\%5Frule\%5Fin\%5Fcausal\%5Finference\%5F.19.aspx},
	date-added   = {2025-01-15 14:59:31 +0100},
	date-modified = {2025-01-15 14:59:31 +0100},
	id           = {00001648-201011000-00019},
	n2           = {Abstract:  In 2 recent communications, Cole and Frangakis (Epidemiology. 2009;20:3--5) and VanderWeele (Epidemiology. 2009;20:880--883) conclude that the consistency rule used in causal inference is an assumption that precludes any side-effects of treatment/exposure on the outcomes of interest. They further develop auxiliary notation to make this assumption formal and explicit. I argue that the consistency rule is a theorem in the logic of counterfactuals and need not be altered. Instead, warnings of potential side-effects should be embodied in standard modeling practices that make causal assumptions explicit and transparent.},
	bdsk-url-1   = {https://journals.lww.com/epidem/fulltext/2010/11000/on_the_consistency_rule_in_causal_inference_.19.aspx}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% After thesis 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article{Correa_Bareinboim_2020,
	title        = {A Calculus for Stochastic Interventions: Causal Effect Identification and Surrogate Experiments},
	author       = {Correa, Juan and Bareinboim, Elias},
	year         = 2020,
	month        = 4,
	journal      = {Proceedings of the AAAI Conference on Artificial Intelligence},
	volume       = 34,
	number       = {06},
	pages        = {10093--10100},
	doi          = {10.1609/aaai.v34i06.6567},
	url          = {https://ojs.aaai.org/index.php/AAAI/article/view/6567},
	abstractnote = {\&lt;p\&gt;Some of the most prominent results in causal inference have been developed in the context of atomic interventions, following the semantics of the \&lt;em\&gt;do\&lt;/em\&gt;-operator and the inferential power of the \&lt;em\&gt;do\&lt;/em\&gt;-calculus. In practice, many real-world settings require more complex types of interventions that cannot be represented by a simple atomic intervention. In this paper, we investigate a general class of interventions that covers some non-trivial types of policies (conditional and stochastic), which goes beyond the atomic class. Our goal is to develop general understanding and formal machinery to be able to reason about the effects of those policies, similar to the robust treatment developed to handle the atomic case. Specifically, in this paper, we introduce a new set of inference rules (akin to \&lt;em\&gt;do\&lt;/em\&gt;-calculus) that can be used to derive claims about general interventions, which we call \ensuremath{\sigma}-calculus. We develop a systematic and efficient procedure for finding estimands of the effect of general policies as a function of the available observational and experimental distributions. We then prove that our algorithm and \ensuremath{\sigma}-calculus are both sound for the tasks of identification (Pearl, 1995) and z-identification (Bareinboim and Pearl, 2012) under this class of interventions.\&lt;/p\&gt;}
}
@article{Correa_Tian_Bareinboim_2018,
	title        = {Generalized Adjustment Under Confounding and Selection Biases},
	author       = {Correa, Juan and Tian, Jin and Bareinboim, Elias},
	year         = 2018,
	month        = 4,
	journal      = {Proceedings of the AAAI Conference on Artificial Intelligence},
	volume       = 32,
	number       = 1,
	doi          = {10.1609/aaai.v32i1.12125},
	url          = {https://ojs.aaai.org/index.php/AAAI/article/view/12125},
	abstractnote = {Selection and confounding biases are the two most common impediments to the applicability of causal inference methods in large-scale settings. We generalize the notion of backdoor adjustment to account for both biases and leverage external data that may be available without selection bias (e.g., data from census). We introduce the notion of adjustment pair and present complete graphical conditions for identifying causal effects by adjustment. We further design an algorithm for listing all admissible adjustment pairs in polynomial delay, which is useful for researchers interested in evaluating certain properties of some admissible pairs but not all (common properties include cost, variance, and feasibility to measure). Finally, we describe a statistical estimation procedure that can be performed once a set is known to be admissible, which entails different challenges in terms of finite samples.},
	bdsk-url-1   = {https://ojs.aaai.org/index.php/AAAI/article/view/12125},
	bdsk-url-2   = {https://doi.org/10.1609/aaai.v32i1.12125}
}
@article{Correa_Tian_Bareinboim_2019,
	title        = {Identification of Causal Effects in the Presence of Selection Bias},
	author       = {Correa, Juan and Tian, Jin and Bareinboim, Elias},
	year         = 2019,
	month        = {Jul.},
	journal      = {Proceedings of the AAAI Conference on Artificial Intelligence},
	volume       = 33,
	number       = {01},
	pages        = {2744--2751},
	doi          = {10.1609/aaai.v33i01.33012744},
	url          = {https://ojs.aaai.org/index.php/AAAI/article/view/4125},
	abstractnote = {Cause-and-effect relations are one of the most valuable types of knowledge sought after throughout the data-driven sciences since they translate into stable and generalizable explanations as well as efficient and robust decision-making capabilities. Inferring these relations from data, however, is a challenging task. Two of the most common barriers to this goal are known as confounding and selection biases. The former stems from the systematic bias introduced during the treatment assignment, while the latter comes from the systematic bias during the collection of units into the sample. In this paper, we consider the problem of identifiability of causal effects when both confounding and selection biases are simultaneously present. We first investigate the problem of identifiability when all the available data is biased. We prove that the algorithm proposed by [Bareinboim and Tian, 2015] is, in fact, complete, namely, whenever the algorithm returns a failure condition, no identifiability claim about the causal relation can be made by any other method. We then generalize this setting to when, in addition to the biased data, another piece of external data is available, without bias. It may be the case that a subset of the covariates could be measured without bias (e.g., from census). We examine the problem of identifiability when a combination of biased and unbiased data is available. We propose a new algorithm that subsumes the current state-of-the-art method based on the back-door criterion.},
	bdsk-url-1   = {https://ojs.aaai.org/index.php/AAAI/article/view/4125},
	bdsk-url-2   = {https://doi.org/10.1609/aaai.v33i01.33012744}
}
@inproceedings{Correa2017,
	title        = {Causal Effect Identification by Adjustment under Confounding and Selection Biases},
	author       = {Correa, Juan D. and Bareinboim, Elias},
	year         = 2017,
	booktitle    = {Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence},
	location     = {San Francisco, California, USA},
	publisher    = {AAAI Press},
	series       = {Aaai'17},
	pages        = {3740--3746},
	abstract     = {Controlling for selection and confounding biases are two of the most challenging problems in the empirical sciences as well as in artificial intelligence tasks. Covariate adjustment (or, Backdoor Adjustment) is the most pervasive technique used for controlling confounding bias, but the same is oblivious to issues of sampling selection. In this paper, we introduce a generalized version of covariate adjustment that simultaneously controls for both confounding and selection biases. We first derive a sufficient and necessary condition for recovering causal effects using covariate adjustment from an observational distribution collected under preferential selection. We then relax this setting to consider cases when additional, unbiased measurements over a set of covariates are available for use (e.g., the age and gender distribution obtained from census data). Finally, we present a complete algorithm with polynomial delay to find all sets of admissible covariates for adjustment when confounding and selection biases are simultaneously present and unbiased data is available.},
	numpages     = 7
}
@inproceedings{Correa2019,
	title        = {Adjustment Criteria for Generalizing Experimental Findings},
	author       = {Correa, Juan and Tian, Jin and Bareinboim, Elias},
	year         = 2019,
	month        = {09--15 Jun},
	booktitle    = {Proceedings of the 36th International Conference on Machine Learning},
	publisher    = {Pmlr},
	series       = {Proceedings of Machine Learning Research},
	volume       = 97,
	pages        = {1361--1369},
	url          = {https://proceedings.mlr.press/v97/correa19a.html},
	abstract     = {Generalizing causal effects from a controlled experiment to settings beyond the particular study population is arguably one of the central tasks found in empirical circles. While a proper design and careful execution of the experiment would support, under mild conditions, the validity of inferences about the population in which the experiment was conducted, two challenges make the extrapolation step to different populations somewhat involved, namely, transportability and sampling selection bias. The former is concerned with disparities in the distributions and causal mechanisms between the domain (i.e., settings, population, environment) where the experiment is conducted and where the inferences are intended; the latter with distortions in the sample's proportions due to preferential selection of units into the study. In this paper, we investigate the assumptions and machinery necessary for using <em>covariate adjustment</em> to correct for the biases generated by both of these problems, and generalize experimental data to infer causal effects in a new domain. We derive complete graphical conditions to determine if a set of covariates is admissible for adjustment in this new setting. Building on the graphical characterization, we develop an efficient algorithm that enumerates all possible admissible sets with poly-time delay guarantee; this can be useful for when some variables are preferred over the others due to different costs or amenability to measurement.},
	editor       = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
	pdf          = {http://proceedings.mlr.press/v97/correa19a/correa19a.pdf},
	bdsk-url-1   = {https://proceedings.mlr.press/v97/correa19a.html}
}
@inproceedings{CorreaIjcai,
	title        = {From Statistical Transportability to Estimating the Effect of Stochastic Interventions},
	author       = {Correa, Juan and Bareinboim, Elias},
	year         = 2019,
	month        = 7,
	booktitle    = {Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence, {IJCAI-19}},
	publisher    = {International Joint Conferences on Artificial Intelligence Organization},
	pages        = {1661--1667},
	doi          = {10.24963/ijcai.2019/230},
	url          = {https://doi.org/10.24963/ijcai.2019/230}
}
@inproceedings{cortes2008sample,
	title        = {Sample selection bias correction theory},
	author       = {Cortes, Corinna and Mohri, Mehryar and Riley, Michael and Rostamizadeh, Afshin},
	year         = 2008,
	booktitle    = {International conference on algorithmic learning theory},
	pages        = {38--53},
	organization = {Springer}
}
@article{Cortese2018-qd,
	title        = {Comparative efficacy and tolerability of medications for attention-deficit hyperactivity disorder in children, adolescents, and adults: a systematic review and network meta-analysis},
	author       = {Cortese, Samuele and Adamo, Nicoletta and {Del Giovane}, Cinzia and Mohr-Jensen, Christina and Hayes, Adrian  and Carucci, Sara and Atkinson, Lauren and Tessari, Luca and Banaschewski, Tobias and Coghill, David and Hollis, Chris and Simonoff, Emily and Zuddas, Alessandro and Barbui, Corrado and Purgato, Marianna and Steinhausen, Hans-Christoph and Shokraneh, Farhad and Xia, Jun and Cipriani, Andrea},
	year         = 2018,
	month        = sep,
	journal      = {The lancet. Psychiatry},
	volume       = 5,
	number       = 9,
	pages        = {727--738},
	doi          = {10.1016/s2215-0366(18)30269-4},
	issn         = {2215-0374, 2215-0366},
	url          = {http://dx.doi.org/10.1016/S2215-0366(18)30269-4},
	language     = {en},
	pmc          = {Pmc6109107},
	pmid         = 30097390,
	bdsk-url-1   = {http://dx.doi.org/10.1016/S2215-0366(18)30269-4}
}
@article{Cortese2018qd,
	title        = {Comparative efficacy and tolerability of medications for attention-deficit hyperactivity disorder in children, adolescents, and adults: a systematic review and network meta-analysis},
	author       = {Cortese, Samuele and Adamo, Nicoletta and Del Giovane, Cinzia and Mohr-Jensen, Christina and Hayes, Adrian and Carucci, Sara and Atkinson, Lauren and Tessari, Luca and Banaschewski, Tobias and Coghill, David and Hollis, Chris and Simonoff, Emily and Zuddas, Alessandro and Barbui, Corrado and Purgato, Marianna and Steinhausen, Hans-Christoph and Shokraneh, Farhad and Xia, Jun and Cipriani, Andrea},
	year         = 2018,
	month        = sep,
	journal      = {The lancet. Psychiatry},
	volume       = 5,
	number       = 9,
	pages        = {727--738},
	doi          = {10.1016/s2215-0366(18)30269-4},
	issn         = {2215-0374, 2215-0366},
	url          = {http://dx.doi.org/10.1016/S2215-0366(18)30269-4},
	language     = {en},
	pmc          = {Pmc6109107},
	pmid         = 30097390,
	bdsk-url-1   = {http://dx.doi.org/10.1016/S2215-0366(18)30269-4}
}
@article{cortese2023incidence,
	title        = {Incidence, prevalence, and global burden of {ADHD} from 1990 to 2019 across 204 countries: data, with critical re-analysis, from the Global Burden of Disease study},
	author       = {Cortese, Samuele and Song, Minjin and Farhat, Luis and Yon, Dong and Lee, Seung and Kim, Min and Park, Seoyeon and Oh, Jae and Lee, San and Cheon, Keun-Ah},
	year         = 2023,
	journal      = {Molecular Psychiatry},
	publisher    = {Nature Publishing Group UK London},
	pages        = {1--8}
}
@article{Cui_2021,
	title        = {Individualized Decision Making Under Partial Identification: Three Perspectives, Two Optimality Results, and One Paradox},
	author       = {Cui, Yifan},
	year         = 2021,
	journal      = {Harvard Data Science Review},
	publisher    = {MIT Press - Journals},
	doi          = {10.1162/99608f92.d07b8d16},
	url          = {http://dx.doi.org/10.1162/99608f92.d07b8d16},
	bdsk-url-1   = {http://dx.doi.org/10.1162/99608f92.d07b8d16}
}
@article{dAdamo,
	title        = {Orthogonal policy learning under ambiguity},
	author       = {d'Adamo, Riccardo},
	year         = 2023,
	journal      = {arXiv preprint arXiv:2111.10904}
}
@article{Dashti2021,
	title        = {Handling missing data for causal effect estimation in cohort studies using Targeted Maximum Likelihood Estimation},
	author       = {Dashti, Ghazaleh and Lee, Katherine and Simpson, Julie and White, Ian  and Carlin, John and Moreno-Betancur, Margarita},
	year         = 2021,
	month        = {09},
	journal      = {International Journal of Epidemiology},
	volume       = 50,
	doi          = {10.1093/ije/dyab168.150},
	issn         = {0300-5771},
	url          = {https://doi.org/10.1093/ije/dyab168.150},
	abstract     = {Causal inference from cohort studies is central to epidemiological research. Targeted Maximum Likelihood Estimation (TMLE) is an appealing doubly robust method for causal effect estimation, but it is unclear how missing data should be handled when it is used in conjunction with machine learning approaches for the exposure and outcome models. This is problematic because missing data are ubiquitous and can result in biased estimates and loss of precision if handled inappropriately.Based on a motivating example from the Victorian Adolescent Health Cohort Study, we conducted a simulation study to evaluate the performance of available approaches for handling missing data when using TMLE with machine learning. These included complete-case analysis; an extended TMLE approach incorporating an outcome missingness probability model; the missing indicator approach for missing covariate data (MCMI); and multiple imputation (MI) using standard parametric approaches or machine learning algorithms. We considered 11 missingness mechanisms typical in cohort studies, and a simple and a complex setting, in which exposure and outcome generation models included two-way and higher-order interactions.MI using regression with no interactions and MI with random forest yielded estimates with the highest bias. MI with regression including two-way interactions was the best performing method overall. Of the non-MI approaches, MCMI performed the worstWhen using TMLE with machine learning to estimate the average causal effect, avoiding standard MI with no interactions and MCMI is recommended.We provide novel guidance for handling missing data for causal effect estimation using TMLE.},
	eprint       = {https://academic.oup.com/ije/article-pdf/50/Supplement_1/dyab168.150/40211905/dyab168.150.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/ije/dyab168.150}
}
@article{dawid2012imagine,
	title        = {"Imagine a Can Opener"--The Magic of Principal Stratum Analysis},
	author       = {Dawid, Philip and Didelez, Vanessa},
	year         = 2012,
	journal      = {The international journal of biostatistics},
	publisher    = {De Gruyter},
	volume       = 8,
	number       = 1
}
@article{deepmed,
	title        = {DeepMed: Semiparametric causal mediation analysis with debiased deep learning},
	author       = {Xu, Siqi and Liu, Lin and Liu, Zhonghua},
	year         = 2022,
	journal      = {Advances in Neural Information Processing Systems},
	volume       = 35,
	pages        = {28238--28251}
}
@article{DEMP1977,
	title        = {Maximum likelihood from incomplete data via the {EM} algorithm},
	author       = {Dempster, A. and Laird, N. and Rubin, D.},
	year         = 1977,
	journal      = {Journal of the Royal Statistical Society: Series B},
	volume       = 39,
	pages        = {1--38},
	url          = {http://web.mit.edu/6.435/www/Dempster77.pdf},
	added-at     = {2013-07-02t15:06:42.000+0200},
	biburl       = {https://www.bibsonomy.org/bibtex/220a2bf528cbc6504f573625ecb78362e/mjobst},
	interhash    = {6a3c3e7e36b05f7855a57eab65f93593},
	intrahash    = {20a2bf528cbc6504f573625ecb78362e},
	owner        = {plankensteiner},
	timestamp    = {2013-07-02t15:06:42.000+0200},
	bdsk-url-1   = {http://web.mit.edu/6.435/www/Dempster77.pdf}
}
@book{dePierris2015,
	title        = {Ideas, Evidence, and Method: Hume's Skepticism and Naturalism Concerning Knowledge and Causation},
	author       = {Graciela {de Pierris}},
	year         = 2015,
	publisher    = {Oxford University Press},
	address      = {Oxford, UK}
}
@inbook{diazChapter,
	title        = {Sensitivity Analysis},
	author       = {D{\'\i}az, Iv{\'a}n and Luedtke, Alexander and {van der Laan}, Mark},
	year         = 2018,
	publisher    = {Springer International Publishing},
	address      = {Cham},
	pages        = {511--522},
	doi          = {10.1007/978-3-319-65304-4_27},
	isbn         = {978-3-319-65303-7},
	url          = {https://doi.org/10.1007/978-3-319-65304-4\%5F27},
	bdsk-url-1   = {https://doi.org/10.1007/978-3-319-65304-4_27}
}
@article{DiazvanderLaan,
	title        = {Assessing the Causal Effect of Policies: An Example Using Stochastic Interventions},
	author       = {Iv\'{a}n D\'{\i}az and Mark {van der Laan}},
	year         = 2013,
	journal      = {The International Journal of Biostatistics},
	volume       = 9,
	number       = 2,
	pages        = {161--174},
	doi          = {doi:10.1515/ijb-2013-0014},
	url          = {https://doi.org/10.1515/ijb-2013-0014},
	lastchecked  = {2025-01-11}
}
@article{didelez2010graphical,
	title        = {Graphical models for inference under outcome-dependent sampling},
	author       = {Didelez, V. and Kreiner, S. and Keiding, N.},
	year         = 2010,
	journal      = {Statistical Science},
	volume       = 25,
	number       = 3,
	pages        = {368--387}
}
@article{ding2016sensitivity,
	title        = {Sensitivity analysis without assumptions},
	author       = {Ding, Peng and VanderWeele, Tyler},
	year         = 2016,
	journal      = {Epidemiology},
	publisher    = {Lww},
	volume       = 27,
	number       = 3,
	pages        = {368--377}
}
@article{diw,
	title        = {Double Inverse-Weighted Estimation of Cumulative Treatment Effects Under Nonproportional Hazards and Dependent Censoring},
	author       = {Schaubel, Douglas E. and Wei, Guanghui},
	year         = 2011,
	journal      = {Biometrics},
	volume       = 67,
	number       = 1,
	pages        = {29--38},
	doi          = {https://doi.org/10.1111/j.1541-0420.2010.01449.x},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1541-0420.2010.01449.x},
	abstract     = {Summary In medical studies of time-to-event data, nonproportional hazards and dependent censoring are very common issues when estimating the treatment effect. A traditional method for dealing with time-dependent treatment effects is to model the time-dependence parametrically. Limitations of this approach include the difficulty to verify the correctness of the specified functional form and the fact that, in the presence of a treatment effect that varies over time, investigators are usually interested in the cumulative as opposed to instantaneous treatment effect. In many applications, censoring time is not independent of event time. Therefore, we propose methods for estimating the cumulative treatment effect in the presence of nonproportional hazards and dependent censoring. Three measures are proposed, including the ratio of cumulative hazards, relative risk, and difference in restricted mean lifetime. For each measure, we propose a double inverse-weighted estimator, constructed by first using inverse probability of treatment weighting (IPTW) to balance the treatment-specific covariate distributions, then using inverse probability of censoring weighting (IPCW) to overcome the dependent censoring. The proposed estimators are shown to be consistent and asymptotically normal. We study their finite-sample properties through simulation. The proposed methods are used to compare kidney wait-list mortality by race.},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1541-0420.2010.01449.x},
	keywords     = {Cumulative hazard, Dependent censoring, Inverse weighting, Relative risk, Restricted mean lifetime, Survival analysis, Treatment effect},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1541-0420.2010.01449.x},
	bdsk-url-2   = {https://doi.org/10.1111/j.1541-0420.2010.01449.x}
}
@article{DML,
	title        = {{Double/debiased machine learning for treatment and structural parameters}},
	author       = {Chernozhukov, Victor and Chetverikov, Denis and Demirer, Mert and Duflo, Esther and Hansen, Christian and Newey, Whitney and Robins, James},
	year         = 2018,
	month        = {01},
	journal      = {The Econometrics Journal},
	volume       = 21,
	number       = 1,
	pages        = {C1-c68},
	doi          = {10.1111/ectj.12097},
	issn         = {1368-4221},
	url          = {https://doi.org/10.1111/ectj.12097},
	abstract     = {{We revisit the classic semi-parametric problem of inference on a low-dimensional parameter \texttheta{}0 in the presence of high-dimensional nuisance parameters \ensuremath{\eta}0. We depart from the classical setting by allowing for \ensuremath{\eta}0 to be so high-dimensional that the traditional assumptions (e.g. Donsker properties) that limit complexity of the parameter space for this object break down. To estimate \ensuremath{\eta}0, we consider the use of statistical or machine learning (ML) methods, which are particularly well suited to estimation in modern, very high-dimensional cases. ML methods perform well by employing regularization to reduce variance and trading off regularization bias with overfitting in practice. However, both regularization bias and overfitting in estimating \ensuremath{\eta}0 cause a heavy bias in estimators of \texttheta{}0 that are obtained by naively plugging ML estimators of \ensuremath{\eta}0 into estimating equations for \texttheta{}0. This bias results in the naive estimator failing to be N-1/2 consistent, where N is the sample size. We show that the impact of regularization bias and overfitting on estimation of the parameter of interest \texttheta{}0 can be removed by using two simple, yet critical, ingredients: (1) using Neyman-orthogonal moments/scores that have reduced sensitivity with respect to nuisance parameters to estimate \texttheta{}0; (2) making use of cross-fitting, which provides an efficient form of data-splitting. We call the resulting set of methods double or debiased ML (DML). We verify that DML delivers point estimators that concentrate in an N-1/2-neighbourhood of the true parameter values and are approximately unbiased and normally distributed, which allows construction of valid confidence statements. The generic statistical theory of DML is elementary and simultaneously relies on only weak theoretical requirements, which will admit the use of a broad array of modern ML methods for estimating the nuisance parameters, such as random forests, lasso, ridge, deep neural nets, boosted trees, and various hybrids and ensembles of these methods. We illustrate the general theory by applying it to provide theoretical properties of the following: DML applied to learn the main regression parameter in a partially linear regression model; DML applied to learn the coefficient on an endogenous variable in a partially linear instrumental variables model; DML applied to learn the average treatment effect and the average treatment effect on the treated under unconfoundedness; DML applied to learn the local average treatment effect in an instrumental variables setting. In addition to these theoretical applications, we also illustrate the use of DML in three empirical examples.}},
	eprint       = {https://academic.oup.com/ectj/article-pdf/21/1/C1/27684918/ectj00c1.pdf},
	bdsk-url-1   = {https://doi.org/10.1111/ectj.12097}
}
@inbook{DRbookVariance,
	title        = {Double Robustness},
	author       = {Daniel, Rhian},
	year         = 2018,
	booktitle    = {Wiley StatsRef: Statistics Reference Online},
	publisher    = {John Wiley and Sons, Ltd},
	pages        = {1--14},
	doi          = {https://doi.org/10.1002/9781118445112.stat08068},
	isbn         = 9781118445112,
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118445112.stat08068},
	abstract     = {Abstract Double robustness is a prevalent topic in current statistical thinking, especially in causal inference and missing data methods. The most popular class of doubly robust (DR) estimators -- known as locally efficient augmented inverse probability weighted (AIPW) estimators -- possess additional properties, linked to but distinct from double robustness, which lead to tractable statistical inferences and other attractive features. In this article, we start by briefly introducing the concepts of nuisance models and multiple (double) robustness, before turning to a particular setting for a more formal introduction, namely that of estimating a population mean from incomplete data. For this setting, we describe the DR AIPW estimator and discuss the other properties alluded to above as well as double robustness itself. We then show how this setting is more general than it might seem at first sight, before going on to discuss many extensions, both to more complex settings and to recently developed improved DR estimation strategies.},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781118445112.stat08068},
	keywords     = {causal inference, convergence, data-adaptive estimation, inverse probability weighting, local efficiency, missing data, nuisance functionals, outcome regression},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.1002/9781118445112.stat08068},
	bdsk-url-2   = {https://doi.org/10.1002/9781118445112.stat08068}
}
@article{DREE,
	title        = {Doubly robust augmented-estimating-equations estimation with nonignorable nonresponse data},
	author       = {Liu, Tianqing and Yuan, Xiaohui},
	year         = 2020,
	journal      = {Statistical Papers},
	volume       = 61,
	number       = 6,
	pages        = {2241--2270},
	doi          = {10.1007/s00362-018-1046-5},
	isbn         = {1613-9798},
	url          = {https://doi.org/10.1007/s00362-018-1046-5},
	abstract     = {The problem of nonignorable nonresponse data is ubiquitous in medical and social science studies. Analyses focused only on the missing-at-random assumption may lead to biased results. Various debias methods have been extensively studied in the literature, particularly the doubly robust (DR) estimators. We propose DR augmented-estimating-equations (AEE) estimators of the mean response which enjoy the double-robustness property under correct specification of the log odds ratio model. An advantage of DR AEE estimators is that they can efficiently use the completely observed covariates to improve estimation efficiency of existing DR estimators with nonignorable nonresponse data. We propose a model selection criterion that can consistently select the correct parametric model of the log odds ratio model from a group of candidate models. Moreover, the correctness of the required working models can be evaluated via straightforward goodness-of-fit tests. Simulation results indicate that doubly robust augmented-estimating-equations estimators are very robust to a misspecification of the baseline outcome density model or the baseline response model and dominate other competitors in the sense of having smaller mean-square errors. The analysis of a real dataset illustrates the flexibility and usefulness of the proposed methods.},
	date         = {2020/12/01},
	date-added   = {2024-01-23 10:56:44 +0100},
	date-modified = {2024-01-23 10:56:44 +0100},
	id           = {Liu2020},
	bdsk-url-1   = {https://doi.org/10.1007/s00362-018-1046-5}
}
@article{DRlearner,
	title        = {Towards optimal doubly robust estimation of heterogeneous causal effects},
	author       = {Edward Kennedy},
	year         = 2023,
	journal      = {Electronic Journal of Statistics},
	publisher    = {Institute of Mathematical Statistics and Bernoulli Society},
	volume       = 17,
	number       = 2,
	pages        = {3008 -- 3049},
	doi          = {10.1214/23-ejs2157},
	url          = {https://doi.org/10.1214/23-EJS2157},
	keywords     = {Conditional effects, influence function, Minimax rate, Nonparametric regression},
	bdsk-url-1   = {https://doi.org/10.1214/23-EJS2157}
}
@article{dumbgen1993,
	title        = {On nondifferentiable functions and the bootstrap},
	author       = {D{\"u}mbgen, Lutz},
	year         = 1993,
	journal      = {Probability Theory and Related Fields},
	publisher    = {Springer},
	volume       = 95,
	pages        = {125--140}
}
@article{dw,
	title        = {Doubly weighted {M}-estimation for nonrandom assignment and missing outcomes},
	author       = {Akanksha Negi},
	year         = 2024,
	journal      = {Journal of Causal Inference},
	volume       = 12,
	number       = 1,
	pages        = 20230016,
	doi          = {doi:10.1515/jci-2023-0016},
	url          = {https://doi.org/10.1515/jci-2023-0016},
	lastchecked  = {2024-08-22},
	bdsk-url-1   = {https://doi.org/10.1515/jci-2023-0016}
}
@misc{educationact1998,
	title        = {Act relating to Primary and Secondary Education and Training (the Education Act). [Last consolidated 2019]},
	author       = {Kunnskapsdepartementet},
	year         = 1998,
	url          = {https://lovdata.no/dokument/NLE/lov/1998-07-17-61},
	bdsk-url-1   = {https://lovdata.no/dokument/NLE/lov/1998-07-17-61}
}
@inproceedings{EhsanCSI,
	title        = {Causal Effect Identification with Context-specific Independence Relations of Control Variables},
	author       = {Mokhtarian, Ehsan and Jamshidi, Fateme and Etesami, Jalal and Kiyavash, Negar},
	year         = 2022,
	month        = 3,
	booktitle    = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
	publisher    = {Pmlr},
	series       = {Proceedings of Machine Learning Research},
	volume       = 151,
	pages        = {11237--11246},
	url          = {https://proceedings.mlr.press/v151/mokhtarian22a.html},
	editor       = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel},
	pdf          = {https://proceedings.mlr.press/v151/mokhtarian22a/mokhtarian22a.pdf},
	abstract     = {We study the problem of causal effect identification from observational distribution given the causal graph and some context-specific independence (CSI) relations. It was recently shown that this problem is NP-hard, and while a sound algorithm to learn the causal effects is proposed in Tikka et al. (2019), no complete algorithm for the task exists. In this work, we propose a sound and complete algorithm for the setting when the CSI relations are limited to observed nodes with no parents in the causal graph. One limitation of the state of the art in terms of its applicability is that the CSI relations among all variables, even unobserved ones, must be given (as opposed to learned). Instead, We introduce a set of graphical constraints under which the CSI relations can be learned from mere observational distribution. This expands the set of identifiable causal effects beyond the state of the art.}
}
@article{EMMI,
	title        = {Principled missing data methods for researchers},
	author       = {Dong, Yiran and Peng, Chao-Ying Joanne},
	year         = 2013,
	journal      = {SpringerPlus},
	publisher    = {Springer},
	volume       = 2,
	pages        = {1--17}
}
@article{enders2001primer,
	title        = {A primer on maximum likelihood algorithms available for use with missing data},
	author       = {Enders, Craig K},
	year         = 2001,
	journal      = {Structural Equation Modeling},
	publisher    = {Taylor and Francis},
	volume       = 8,
	number       = 1,
	pages        = {128--141}
}
@misc{entangled,
	title        = {Graphical Models of Entangled Missingness},
	author       = {Ranjani Srinivasan and Rohit Bhattacharya and Razieh Nabi and Elizabeth Ogburn and Ilya Shpitser},
	year         = 2023,
	url          = {https://arxiv.org/abs/2304.01953},
	eprint       = {2304.01953},
	archiveprefix = {arXiv},
	primaryclass = {stat.ME}
}
@article{Espen,
	title        = {How interactions between {ADHD} and schools affect educational achievement: a family-based genetically sensitive study},
	author       = {Cheesman, Rosa and Eilertsen, Espen and Ayorech, Ziada and Borgen, Nicolai and Andreassen, Ole and Larsson, Henrik and Zachrisson, Henrik and Torvik, Fartein and Ystrom, Eivind},
	year         = 2022,
	journal      = {Journal of Child Psychology and Psychiatry},
	volume       = 63,
	number       = 10,
	pages        = {1174--1185},
	doi          = {https://doi.org/10.1111/jcpp.13656},
	url          = {https://acamh.onlinelibrary.wiley.com/doi/abs/10.1111/jcpp.13656},
	keywords     = {ADHD, gene–environment interaction, school performance, school, genetics},
	eprint       = {https://acamh.onlinelibrary.wiley.com/doi/pdf/10.1111/jcpp.13656},
	abstract     = {Background Children with ADHD tend to achieve less than their peers in school. It is unknown whether schools moderate this association. Nonrandom selection of children into schools related to variations in their ADHD risk poses a methodological problem. Methods We linked data on ADHD symptoms of inattention and hyperactivity and parent–child ADHD polygenic scores (PGS) from the Norwegian Mother, Father, and Child Cohort Study (MoBa) to achievement in standardised tests and school identifiers. We estimated interactions of schools with individual differences between students in inattention, hyperactivity, and ADHD-PGS using multilevel models with random slopes for ADHD effects on achievement over schools. In our PGS analyses, we adjust for parental selection of schools by adjusting for parental ADHD-PGS (a within-family PGS design). We then tested whether five school sociodemographic measures explained any interactions. Results Analysis of up to 23,598 students attending 2,579 schools revealed interactions between school and ADHD effects on achievement. The variability between schools in the effects of inattention, hyperactivity and within-family ADHD-PGS on achievement was 0.08, 0.07 and 0.05 SDs, respectively. For example, the average effect of inattention on achievement was \ensuremath{\beta}=-0.23 (SE=0.009), but in 2.5\% of schools with the weakest effects, the value was -0.07 or less. ADHD has a weaker effect on achievement in higher-performing schools. Schools make more of a difference to the achievements of students with higher levels of ADHD, explaining over four times as much variance in achievement for those with high versus average inattention symptoms. School sociodemographic measures could not explain the ADHD-by-school interactions. Conclusions Although ADHD symptoms and genetic risk tend to hinder achievement, schools where their effects are weaker do exist. Differences between schools in support for children with ADHD should be evened out.}
}
@article{EuroADHD,
	title        = {Challenges in {ADHD} care for ethnic minority children: A review of the current literature},
	author       = {Ortal Slobodin and Rafik Masalha},
	year         = 2020,
	journal      = {Transcultural Psychiatry},
	volume       = 57,
	number       = 3,
	pages        = {468--483},
	doi          = {10.1177/1363461520902885},
	url          = {https://doi.org/10.1177/1363461520902885},
	note         = {Pmid: 32233772},
	eprint       = {https://doi.org/10.1177/1363461520902885},
	abstract     = {While attention deficit hyperactivity disorder (ADHD) has been extensively studied in the past decades, the role of social and cultural practices in its assessment, diagnosis, and treatment has been often overlooked. This selective review provides an overview of research that explores social and cultural influences on help-seeking behavior in ethnic minority children with {ADHD}. Studies were selected that address cultural diversity in three areas of {ADHD} help-seeking: problem recognition, access to mental health services, and treatment. Special attention was given to studies of treatment selection and adherence in minority groups. Findings suggested that cultural disparities in {ADHD} care among ethnic minority children occur in the early stages of problem recognition, through service selection, and in the quality of treatment. Ethnic minority children were less likely than their nonminority counterparts to be diagnosed with {ADHD} and its comorbid conditions and less likely to be prescribed and adhere to stimulant drug treatment. These differences reflect cultural diversity in norms and attitudes towards mental health issues (e.g., fear of social stigma) as well as limited access to qualified health care. Paradoxically, cultural, racial, and language bias may also lead to the overidentification of ethnic minority children as disabled and to higher ratings of {ADHD} symptoms. This review highlights the importance of sociocultural factors in understanding developmental psychopathology and help-seeking behavior. In addition, it further supports calls for increasing cultural competence in communications during clinical assessment, diagnosis, and treatment in minority communities. Clinical, theoretical, and methodological considerations for future research are discussed.}
}
@article{evolutionSelection,
	title        = {{The Evolution of Selection Bias in the Recent Epidemiologic Literature---A Selective Overview}},
	author       = {Lu, Haidong and Howe, Chanelle and Zivich, Paul and Gonsalves, Gregg and Westreich, Daniel},
	year         = 2024,
	month        = {08},
	journal      = {American Journal of Epidemiology},
	pages        = {kwae282},
	doi          = {10.1093/aje/kwae282},
	issn         = {0002-9262},
	url          = {https://doi.org/10.1093/aje/kwae282},
	abstract     = {{Selection bias has long been central in methodological discussions across epidemiology and other fields. In epidemiology, the concept of selection bias has been continually evolving over time. In this issue of the Journal, Mathur and Shpitser (Am J Epidemiol. XXXX;XXX(XX):XXXX--XXXX) present simple graphical rules for using a Single World Intervention Graph (SWIG) to assess the presence of selection bias when estimating treatment effects in both the general population and a selected sample. Notably, the authors examine the setting in which the treatment affects selection, an issue not well-addressed in the existing literature on selection bias. To place the work by Mathur and Shpitser in context, we review the evolution of the concept of selection bias in epidemiology, with a primary focus on the developments in the last 20-30 years since the introduction of causal directed acyclic graphs (DAGs) to epidemiologic research.}},
	eprint       = {https://academic.oup.com/aje/advance-article-pdf/doi/10.1093/aje/kwae282/58800340/kwae282.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/aje/kwae282}
}
@article{Fairness,
	title        = {Causal Fairness Analysis: A Causal Toolkit for Fair Machine Learning},
	author       = {Drago Ple{\v c}ko and Elias Bareinboim},
	year         = 2024,
	journal      = {Foundations and Trends{\textregistered} in Machine Learning},
	volume       = 17,
	number       = 3,
	pages        = {304--589},
	doi          = {10.1561/2200000106},
	issn         = {1935-8237},
	url          = {http://dx.doi.org/10.1561/2200000106},
	bdsk-url-1   = {http://dx.doi.org/10.1561/2200000106}
}
@article{fang2019inference,
	title        = {Inference on Directionally Differentiable Functions},
	author       = {Fang, Zheng and Santos, Andres},
	year         = 2019,
	journal      = {The Review of Economic Studies},
	publisher    = {Jstor},
	volume       = 86,
	number       = {1 (306)},
	pages        = {377--412}
}
@article{faraone2021world,
	title        = {The world federation of {ADHD} international consensus statement: 208 evidence-based conclusions about the disorder},
	author       = {Faraone, Stephen and Banaschewski, Tobias and Coghill, David and Zheng, Yi and Biederman, Joseph and Bellgrove, Mark and Newcorn, Jeffrey and Gignac, Martin and Al Saud, Nouf and Manor, Iris and others},
	year         = 2021,
	journal      = {Neuroscience \& Biobehavioral Reviews},
	publisher    = {Elsevier},
	volume       = 128,
	pages        = {789--818}
}
@article{FaraoneStephenV.2024,
	title        = {Attention-deficit/hyperactivity disorder},
	author       = {Faraone, Stephen and Bellgrove, Mark and Brikell, Isabell and Cortese, Samuele and Hartman, Catharina and Hollis, Chris and Newcorn, Jeffrey and Philipsen, Alexandra and Polanczyk, Guilherme and Rubia, Katya and Sibley, Margaret and Buitelaar, Jan},
	year         = 2024,
	journal      = {Nature reviews. Disease primers},
	publisher    = {Nature Publishing Group UK},
	address      = {London},
	volume       = 10,
	number       = 1,
	pages        = {11--11},
	issn         = {2056-676x},
	copyright    = {Springer Nature Limited 2024. corrected publication 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.},
	abstract     = {Attention-deficit/hyperactivity disorder (ADHD;also known as hyperkinetic disorder) is a common neurodevelopmental condition that affects children and adults worldwide. {ADHD} has a predominantly genetic aetiology that involves common and rare genetic variants. Some environmental correlates of the disorder have been discovered but causation has been difficult to establish. The heterogeneity of the condition is evident in the diverse presentation of symptoms and levels of impairment, the numerous co-occurring mental and physical conditions, the various domains of neurocognitive impairment, and extensive minor structural and functional brain differences. The diagnosis of {ADHD} is reliable and valid when evaluated with standard diagnostic criteria. Curative treatments for {ADHD} do not exist but evidence-based treatments substantially reduce symptoms and/or functional impairment. Medications are effective for core symptoms and are usually well tolerated. Some non-pharmacological treatments are valuable, especially for improving adaptive functioning. Clinical and neurobiological research is ongoing and could lead to the creation of personalized diagnostic and therapeutic approaches for this disorder. Attention-deficit/hyperactivity disorder (ADHD) is a neurodevelopmental disorder that typically starts in childhood. This Primer summarizes the epidemiology, mechanisms, diagnosis and treatment of {ADHD}.},
	language     = {eng},
	keywords     = {631/208/1516 ; 631/378/2649 ; Adult ; Attention Deficit Disorder with Hyperactivity - complications ; Attention Deficit Disorder with Hyperactivity - diagnosis ; Attention Deficit Disorder with Hyperactivity - epidemiology ; Attention deficit hyperactivity disorder ; Brain ; Cancer Research ; Child ; Epidemiology ; Humans ; Hyperactivity ; Internal Medicine ; Medical Microbiology ; Medicin och h\"{a}lsovetenskap ; Medicine ; Medicine \& Public Health ; Primer ; Quality of Life Research}
}
@article{Fink,
	title        = {Estimation for the multiple factor model when data are missing},
	author       = {Finkbeiner, Carl},
	year         = 1979,
	journal      = {Psychometrika},
	volume       = 44,
	number       = 4,
	pages        = {409--420},
	doi          = {10.1007/bf02296204},
	isbn         = {1860-0980},
	url          = {https://doi.org/10.1007/BF02296204},
	abstract     = {A maximum likelihood method of estimating the parameters of the multiple factor model when data are missing from the sample is presented. A Monte Carlo study compares the method with 5 heuristic methods of dealing with the problem. The present method shows some advantage in accuracy of estimation over the heuristic methods but is considerably more costly computationally.},
	date         = {1979/12/01},
	date-added   = {2023-08-16 23:15:32 +0200},
	date-modified = {2023-08-16 23:15:32 +0200},
	id           = {Finkbeiner1979},
	bdsk-url-1   = {https://doi.org/10.1007/BF02296204}
}
@techreport{Firpo,
	title        = {Bounds on functionals of the distribution treatment effects},
	author       = {Firpo, Sergio and Ridder, Geert},
	year         = 2010,
	month        = 6,
	number       = 201,
	url          = {https://ideas.repec.org/p/fgv/eesptd/201.html},
	abstract     = {Bounds on the distribution function of the sum of two random variables with known marginal distributions obtained by Makarov (1981) can be used to bound the cumulative distribution function (c.d.f.) of individual treatment effects. Identification of the distribution of individual treatment effects is important for policy purposes if we are interested in functionals of that distribution, such as the proportion of individuals who gain from the treatment and the expected gain from the treatment for these individuals. Makarov bounds on the c.d.f. of the individual treatment effect distribution are pointwise sharp, i.e. they cannot be improved in any single point of the distribution. We show that the Makarov bounds are not uniformly sharp. Specifically, we show that the Makarov bounds on the region that contains the c.d.f. of the treatment effect distribution in two (or more) points can be improved, and we derive the smallest set for the c.d.f. of the treatment effect distribution in two (or more) points. An implication is that the Makarov bounds on a functional of the c.d.f. of the individual treatment effect distribution are not best possible.},
	institution  = {FGV EESP - Escola de Economia de S{\~a}o Paulo, Funda{\c c}{\~a}o Getulio Vargas (Brazil)},
	type         = {Textos para discuss{\~a}o},
	bdsk-url-1   = {https://ideas.repec.org/p/fgv/eesptd/201.html}
}
@article{flanders2019,
	title        = {Limits for the Magnitude of {M}-bias and Certain Other Types of Structural Selection Bias},
	author       = {Flanders, W. and Ye, Dongni},
	year         = 2019,
	journal      = {Epidemiology},
	publisher    = {Lippincott Williams and Wilkins},
	volume       = 30,
	number       = 4,
	pages        = {501--508},
	doi          = {10.1097/ede.0000000000001031},
	bdsk-url-1   = {https://doi.org/10.1097/EDE.0000000000001031}
}
@article{frechet1951,
	title        = {Sur les tableaux de corr{\'e}lation dont les marges sont donn{\'e}es},
	author       = {Maurice Fr{\'e}chet},
	year         = 1951,
	journal      = {Annales de l'Universit{\'e} de Lyon. S{\'e}rie A: Sciences math{\'e}matiques et astronomie},
	volume       = 14,
	pages        = {53--77}
}
@article{fredriksen2014childhood,
	title        = {Childhood and persistent {ADHD} symptoms associated with educational failure and long-term occupational disability in adult {ADHD}},
	author       = {Fredriksen, Mats and Dahl, Alv and Martinsen, Egil and Klungsoyr, Ole and Faraone, Stephen and Peleikis, Dawn},
	year         = 2014,
	journal      = {{ADHD} Attention Deficit and Hyperactivity Disorders},
	publisher    = {Springer},
	volume       = 6,
	number       = 2,
	pages        = {87--99}
}
@article{gelu,
	title        = {Mathematical Analysis and Performance Evaluation of the {GELU} Activation Function in Deep Learning},
	author       = {Lee, Minhyeok},
	year         = 2023,
	journal      = {Journal of Mathematics},
	volume       = 2023,
	number       = 1,
	pages        = 4229924,
	doi          = {https://doi.org/10.1155/2023/4229924},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1155/2023/4229924},
	abstract     = {Selecting the most suitable activation function is a critical factor in the effectiveness of deep learning models, as it influences their learning capacity, stability, and computational efficiency. In recent years, the Gaussian error linear unit (GELU) activation function has emerged as a dominant method, surpassing traditional functions such as the rectified linear unit (ReLU) in various applications. This study presents a rigorous mathematical investigation of the GELU activation function, exploring its differentiability, boundedness, stationarity, and smoothness properties in detail. In addition, we conduct an extensive experimental comparison of the GELU function against a broad range of alternative activation functions, utilizing a residual convolutional network trained on the CIFAR-10, CIFAR-100, and STL-10 datasets as the empirical testbed. Our results demonstrate the superior performance of GELU compared to other activation functions, establishing its suitability for a wide range of deep learning applications. This comprehensive study contributes to a more profound understanding of the underlying mathematical properties of GELU and provides valuable insights for practitioners aiming to select activation functions that optimally align with their specific objectives and constraints in deep learning.},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1155/2023/4229924},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.1155/2023/4229924},
	bdsk-url-2   = {https://doi.org/10.1155/2023/4229924}
}
@article{gelu0,
	title        = {Gaussian Error Linear Units (GELUs)},
	author       = {Hendrycks, Dan and Gimpel, Kevin},
	year         = 2016,
	journal      = {arXiv preprint arXiv:1606.08415}
}
@article{gene2019,
	title        = {Genetics of attention deficit hyperactivity disorder},
	author       = {Faraone, Stephen and Larsson, Henrik},
	year         = 2019,
	journal      = {Molecular Psychiatry},
	volume       = 24,
	number       = 4,
	pages        = {562--575},
	doi          = {10.1038/s41380-018-0070-0},
	url          = {https://doi.org/10.1038/s41380-018-0070-0},
	abstract     = {Decades of research show that genes play an vital role in the etiology of attention deficit hyperactivity disorder (ADHD) and its comorbidity with other disorders. Family, twin, and adoption studies show that ADHD runs in families. ADHD's high heritability of 74{\%} motivated the search for ADHD susceptibility genes. Genetic linkage studies show that the effects of DNA risk variants on ADHD must, individually, be very small. Genome-wide association studies (GWAS) have implicated several genetic loci at the genome-wide level of statistical significance. These studies also show that about a third of ADHD's heritability is due to a polygenic component comprising many common variants each having small effects. From studies of copy number variants we have also learned that the rare insertions or deletions account for part of ADHD's heritability. These findings have implicated new biological pathways that may eventually have implications for treatment development.},
	date         = {2019-04-01},
	date-added   = {2025-01-17},
	date-modified = {2025-01-17},
	id           = {Faraone2019},
	bdsk-url-1   = {https://doi.org/10.1038/s41380-018-0070-0}
}
@article{geneADHD,
	title        = {Genome-wide analyses of {ADHD} identify 27 risk loci, refine the genetic architecture and implicate several cognitive domains},
	author       = {Demontis, Ditte and Walters, Bragi and Athanasiadis, Georgios and Walters, Raymond and Therrien, Karen and Nielsen, Trine and Farajzadeh, Leila and Voloudakis, Georgios and Bendl, Jaroslav and Zeng, Biau and Zhang, Wen and Grove, Jakob and Als, Thomas and Duan, Jinjie and Satterstrom, Kyle and Bybjerg-Grauholm, Jonas and B{\ae}kved-Hansen, Marie and Gudmundsson, Olafur and Magnusson, Sigurdur and Baldursson, Gisli and Davidsdottir, Katrin and Haraldsdottir, Gyda and Agerbo, Esben and Hoffman, Gabriel and Dalsgaard, S{\o}ren and Martin, Joanna and Ribas{\'e}s, Marta and Boomsma, Dorret and Soler, Maria and Roth, Nina and Howrigan, Daniel and Medland, Sarah and Zayats, Tetyana and Rajagopal, Veera and Havdahl, Alexandra and Doyle, Alysa and Reif, Andreas and Thapar, Anita and Cormand, Bru and Liao, Calwing and Burton, Christie and Bau, Claiton and Rovaris, Diego and Sonuga-Barke, Edmund and Corfield, Elizabeth and Grevet, Eugenio and Larsson, Henrik and Gizer, Ian and Waldman, Irwin and Brikell, Isabell and Haavik, Jan and Crosbie, Jennifer and McGough, James and Kuntsi, Jonna and Glessner, Joseph and Langley, Kate and Lesch, Klaus-Peter and Rohde, Luis and Hutz, Mara and Klein, Marieke and Bellgrove, Mark and Tesli, Martin and O'Donovan, Michael and Andreassen, Ole and Leung, Patrick  and Pan, Pedro and Joober, Ridha and Schachar, Russel and Loo, Sandra and Witt, Stephanie and Reichborn-Kjennerud, Ted and Banaschewski, Tobias and Hawi, Ziarih and Daly, Mark and Mors, Ole and Nordentoft, Merete and Hougaard, David and Mortensen, Preben and Daly, Mark and Faraone, Stephen and Stefansson, Hreinn and Roussos, Panos and Franke, Barbara and Werge, Thomas and Neale, Benjamin and Stefansson, Kari and B{\o}rglum, Anders and {ADHD} Working Group of the Psychiatric Genomics Consortium and {iPSYCH-Broad} Consortium},
	year         = 2023,
	journal      = {Nature Genetics},
	volume       = 55,
	number       = 2,
	pages        = {198--208},
	doi          = {10.1038/s41588-022-01285-8},
	url          = {https://doi.org/10.1038/s41588-022-01285-8},
	abstract     = {Attention-deficit hyperactivity disorder (ADHD) is a prevalent neurodevelopmental disorder with a major genetic component. Here, we present a genome-wide association study meta-analysis of ADHD comprising 38,691 individuals with ADHD and 186,843 controls. We identified 27 genome-wide significant loci, highlighting 76 potential risk genes enriched among genes expressed particularly in early brain development. Overall, ADHD genetic risk was associated with several brain-specific neuronal subtypes and midbrain dopaminergic neurons. In exome-sequencing data from 17,896 individuals, we identified an increased load of rare protein-truncating variants in ADHD for a set of risk genes enriched with probable causal common variants, potentially implicating SORCS3 in ADHD by both common and rare variants. Bivariate Gaussian mixture modeling estimated that 84--98{\%} of ADHD-influencing variants are shared with other psychiatric disorders. In addition, common-variant ADHD risk was associated with impaired complex cognition such as verbal reasoning and a range of executive functions, including attention.},
	date         = {2023-02-01},
	date-added   = {2024-12-31},
	date-modified = {2024-12-31},
	id           = {Demontis2023},
	bdsk-url-1   = {https://doi.org/10.1038/s41588-022-01285-8}
}
@article{geneletti2009adjusting,
	title        = {Adjusting for selection bias in retrospective, case-control studies},
	author       = {Geneletti, Sara and Richardson, Sylvia and Best, Nicky},
	year         = 2009,
	journal      = {Biostatistics},
	volume       = 10,
	number       = 1,
	pages        = {17--31}
}
@inproceedings{gID2020,
	title        = {General Identifiability with Arbitrary Surrogate Experiments},
	author       = {Lee, Sanghack and Correa, Juan and Bareinboim, Elias},
	year         = 2020,
	month        = 7,
	booktitle    = {Proceedings of The 35th Uncertainty in Artificial Intelligence Conference},
	publisher    = {Pmlr},
	series       = {Proceedings of Machine Learning Research},
	volume       = 115,
	pages        = {389--398},
	url          = {https://proceedings.mlr.press/v115/lee20b.html},
	abstract     = {We study the problem of causal identification from an arbitrary collection of observational and experimental distributions, and substantive knowledge about the phenomenon under investigation, which usually comes in the form of a causal graph. We call this problem  \textit{g-identifiability}, or gID for short. The gID setting encompasses two  well-known problems in causal inference, namely, identifiability [Pearl, 1995] and z-identifiability [Bareinboim and Pearl, 2012] -- the former assumes that an observational distribution is necessarily available, and no experiments can be performed, conditions that are both relaxed in the gID setting; the latter assumes that \textit{all} combinations of experiments are available, i.e., the power set of the experimental set $\mathbf{Z}$, which gID does not require a priori. In this paper, we introduce a general strategy to prove non-gID based on \textit{hedgelets} and \textit{thickets}, which leads to a necessary and sufficient graphical condition for the corresponding decision problem. We further develop a procedure for systematically computing the target effect, and prove that it is sound and complete for gID instances. In other words, failure of the algorithm in returning an expression implies that the target effect is not computable from the available distributions. Finally, as a corollary of these results, we show that do-calculus is complete for the task of g-identifiability.},
	editor       = {Adams, Ryan P. and Gogate, Vibhav},
	pdf          = {http://proceedings.mlr.press/v115/lee20b/lee20b.pdf},
	bdsk-url-1   = {https://proceedings.mlr.press/v115/lee20b.html}
}
@article{goksoyr2008burden,
	title        = {The burden of untreated {ADHD} among adults: the role of stimulant medication},
	author       = {Goks{\o}yr, Per Kristian and N{\o}ttestad, Jim Aage},
	year         = 2008,
	journal      = {Addictive Behaviors},
	publisher    = {Elsevier},
	volume       = 33,
	number       = 2,
	pages        = {342--346}
}
@article{graham2008adverse,
	title        = {Adverse effects of pharmacotherapies for attention-deficit hyperactivity disorder: epidemiology, prevention and management},
	author       = {Graham, Johnny and Coghill, David},
	year         = 2008,
	journal      = {CNS drugs},
	publisher    = {Springer},
	volume       = 22,
	pages        = {213--237}
}
@article{greenland1995critical,
	title        = {A Critical Look at Methods for Handling Missing Covariates in Epidemiologic Regression Analyses},
	author       = {Greenland, Sander and Finkle, William},
	year         = 1995,
	journal      = {American Journal of Epidemiology},
	publisher    = {Oxford University Press},
	volume       = 142,
	number       = 12,
	pages        = {1255--1264}
}
@article{greenland2003,
	title        = {Quantifying biases in causal models: classical confounding vs collider-stratification bias},
	author       = {Greenland, Sander},
	year         = 2003,
	journal      = {Epidemiology},
	publisher    = {Lippincott Williams and Wilkins},
	volume       = 14,
	number       = 3,
	pages        = {300--306}
}
@article{gruber2009targeted,
	title        = {Targeted Maximum Likelihood Estimation: A Gentle Introduction},
	author       = {Gruber, Susan and {van der Laan}, Mark},
	year         = 2009,
	journal      = {The American Statistician},
	publisher    = {Taylor and Francis},
	volume       = 63,
	number       = 4,
	pages        = {1--38}
}
@article{Gustafson2010,
	title        = {Bayesian Inference for Partially Identified Models},
	author       = {Paul Gustafson},
	year         = 2010,
	journal      = {The International Journal of Biostatistics},
	volume       = 6,
	number       = 2,
	doi          = {doi:10.2202/1557-4679.1206},
	url          = {https://doi.org/10.2202/1557-4679.1206},
	lastchecked  = {2024-05-21},
	bdsk-url-1   = {https://doi.org/10.2202/1557-4679.1206}
}
@article{hampel1974influence,
	title        = {The influence curve and its role in robust estimation},
	author       = {Hampel, Frank},
	year         = 1974,
	journal      = {Journal of the american statistical association},
	publisher    = {Taylor \& Francis},
	volume       = 69,
	number       = 346,
	pages        = {383--393}
}
@article{han2016combining,
	title        = {Combining Inverse Probability Weighting and Multiple Imputation to Improve Robustness of Estimation},
	author       = {Han, P.},
	year         = 2016,
	journal      = {Scandinavian Journal of Statistics},
	volume       = 43,
	pages        = {246--260},
	doi          = {10.1111/sjos.12177},
	bdsk-url-1   = {https://doi.org/10.1111/sjos.12177}
}
@article{Harel2018,
	title        = {Multiple Imputation for Incomplete Data in Epidemiologic Studies},
	author       = {Harel, Ofer and others},
	year         = 2018,
	journal      = {American Journal of Epidemiology},
	volume       = 187,
	number       = 3,
	pages        = {576--584},
	doi          = {10.1093/aje/kwx349},
	url          = {https://doi.org/10.1093/aje/kwx349},
	bdsk-url-1   = {https://doi.org/10.1093/aje/kwx349}
}
@article{hartley1971,
	title        = {The analysis of incomplete data},
	author       = {Hartley, HO and Hocking, RR},
	year         = 1971,
	journal      = {Biometrics},
	publisher    = {Jstor},
	pages        = {783--823}
}
@article{Haug03072014,
	title        = {The practices of dealing with children with special needs in school: a Norwegian perspective},
	author       = {Peder Haug},
	year         = 2014,
	journal      = {Emotional and Behavioural Difficulties},
	publisher    = {Routledge},
	volume       = 19,
	number       = 3,
	pages        = {296--310},
	doi          = {10.1080/13632752.2014.883788},
	url          = {https://doi.org/10.1080/13632752.2014.883788},
	eprint       = {https://doi.org/10.1080/13632752.2014.883788}
}
@article{hernan2004structural,
	title        = {A structural approach to selection bias},
	author       = {Hern{\'a}n, Miguel  and Hern{\'a}ndez-D{\'\i}az, Sonia and Robins, James},
	year         = 2004,
	journal      = {Epidemiology (Cambridge, Mass.)},
	publisher    = {Lippincott Williams and Wilkins},
	volume       = 15,
	number       = 5,
	pages        = {615--625},
	doi          = {10.1097/01.ede.0000135174.63482.43},
	bdsk-url-1   = {https://doi.org/10.1097/01.ede.0000135174.63482.43}
}
@article{hernan2013,
	title        = {Selection bias due to conditioning on a collider},
	author       = {Hern{\'a}n, Migue and Monge, Susana},
	year         = 2023,
	journal      = {Bmj},
	publisher    = {BMJ Publishing Group Ltd},
	volume       = 381,
	doi          = {10.1136/bmj.p1135},
	url          = {https://www.bmj.com/content/381/bmj.p1135},
	elocation-id = {p1135},
	eprint       = {https://www.bmj.com/content/381/bmj.p1135.full.pdf},
	bdsk-url-1   = {https://www.bmj.com/content/381/bmj.p1135},
	bdsk-url-2   = {https://doi.org/10.1136/bmj.p1135}
}
@article{Hernan2017,
	title        = {{Invited Commentary: Selection Bias Without Colliders}},
	author       = {Hern{\'a}n, Miguel},
	year         = 2017,
	month        = {05},
	journal      = {American Journal of Epidemiology},
	volume       = 185,
	number       = 11,
	pages        = {1048--1050},
	doi          = {10.1093/aje/kwx077},
	issn         = {0002-9262},
	url          = {https://doi.org/10.1093/aje/kwx077},
	abstract     = {{In causal analyses, conditioning on a collider generally results in selection bias. Conditioning on a prognostic factor that is independent of the exposure---and therefore is not a collider---can also result in selection bias when 1) the exposure has a non-null effect on the outcome and 2) the association between the noncollider and the outcome is heterogenous across levels of the exposure. This result was empirically demonstrated by Greenland in 1977 (Am J Epidemiol. 1977;106(3):184--187).}},
	eprint       = {https://academic.oup.com/aje/article-pdf/185/11/1048/29016569/kwx077.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/aje/kwx077}
}
@book{hernan2020causal,
	title        = {Causal Inference: What If},
	author       = {Hern{\'a}n, Miguel  and Robins, James},
	year         = 2020,
	publisher    = {Boca Raton: Chapman and Hall/CRC}
}
@article{highMed,
	title        = {A machine learning based approach towards high-dimensional mediation analysis},
	author       = {Tanmay Nath and Brian Caffo and Tor Wager and Martin A. Lindquist},
	year         = 2023,
	journal      = {NeuroImage},
	volume       = 268,
	pages        = 119843,
	doi          = {https://doi.org/10.1016/j.neuroimage.2022.119843},
	issn         = {1053-8119},
	url          = {https://www.sciencedirect.com/science/article/pii/S1053811922009648},
	abstract     = {Mediation analysis is used to investigate the role of intermediate variables (mediators) that lie in the path between an exposure and an outcome variable. While significant research has focused on developing methods for assessing the influence of mediators on the exposure-outcome relationship, current approaches do not easily extend to settings where the mediator is high-dimensional. These situations are becoming increasingly common with the rapid increase of new applications measuring massive numbers of variables, including brain imaging, genomics, and metabolomics. In this work, we introduce a novel machine learning based method for identifying high dimensional mediators. The proposed algorithm iterates between using a machine learning model to map the high-dimensional mediators onto a lower-dimensional space, and using the predicted values as input in a standard three-variable mediation model. Hence, the machine learning model is trained to maximize the likelihood of the mediation model. Importantly, the proposed algorithm is agnostic to the machine learning model that is used, providing significant flexibility in the types of situations where it can be used. We illustrate the proposed methodology using data from two functional Magnetic Resonance Imaging (fMRI) studies. First, using data from a task-based fMRI study of thermal pain, we combine the proposed algorithm with a deep learning model to detect distributed, network-level brain patterns mediating the relationship between stimulus intensity (temperature) and reported pain at the single trial level. Second, using resting-state fMRI data from the Human Connectome Project, we combine the proposed algorithm with a connectome-based predictive modeling approach to determine brain functional connectivity measures that mediate the relationship between fluid intelligence and working memory accuracy. In both cases, our multivariate mediation model links exposure variables (thermal pain or fluid intelligence), high dimensional brain measures (single-trial brain activation maps or resting-state brain connectivity) and behavioral outcomes (pain report or working memory accuracy) into a single unified model. Using the proposed approach, we are able to identify brain-based measures that simultaneously encode the exposure variable and correlate with the behavioral outcome.},
	keywords     = {Machine learning, Deep learning, Mediation analysis, fMRI, Resting-state functional connectivity, Pain},
	bdsk-url-1   = {https://www.sciencedirect.com/science/article/pii/S1053811922009648},
	bdsk-url-2   = {https://doi.org/10.1016/j.neuroimage.2022.119843}
}
@article{hines2022demystifying,
	title        = {Demystifying statistical learning based on efficient influence functions},
	author       = {Hines, Oliver and Dukes, Oliver and D{\'\i}az-Ordaz, Karla and Vansteelandt, Stijn},
	year         = 2022,
	journal      = {The American Statistician},
	publisher    = {Taylor \& Francis},
	volume       = 76,
	number       = 3,
	pages        = {292--304}
}
@article{hirano2009,
	title        = {Asymptotics for Statistical Treatment Rules},
	author       = {Hirano, Keisuke and Porter, Jack},
	year         = 2009,
	journal      = {Econometrica},
	publisher    = {Jstor},
	volume       = 77,
	number       = 5,
	pages        = {1683--1701},
	url          = {http://www.jstor.org/stable/25621374},
	bdsk-url-1   = {http://www.jstor.org/stable/25621374}
}
@book{hoeffding1940,
	title        = {Masstabinvariante Korrelationstheorie},
	author       = {Wassily Hoeffding},
	year         = 1940,
	publisher    = {Universit{\"a}t Berlin},
	address      = {Berlin, Germany},
	series       = {Schriften des Mathematischen Instituts und des Institutes f{\"u}r Angewandte Mathematik der Universit{\"a}t Berlin},
	volume       = 5
}
@article{holland,
	title        = {Statistics and Causal Inference},
	author       = {Paul W. Holland},
	year         = 1986,
	journal      = {Journal of the American Statistical Association},
	publisher    = {[American Statistical Association, Taylor \& Francis, Ltd.]},
	volume       = 81,
	number       = 396,
	pages        = {945--960},
	issn         = {01621459, 1537274x},
	url          = {http://www.jstor.org/stable/2289064},
	urldate      = {2024-07-08},
	abstract     = {Problems involving causal inference have dogged at the heels of statistics since its earliest days. Correlation does not imply causation, and yet causal conclusions drawn from a carefully designed experiment are often valid. What can a statistical model say about causation? This question is addressed by using a particular model for causal inference (Holland and Rubin 1983; Rubin 1974) to critique the discussions of other writers on causation and causal inference. These include selected philosophers, medical researchers, statisticians, econometricians, and proponents of causal modeling.},
	bdsk-url-1   = {http://www.jstor.org/stable/2289064}
}
@inproceedings{HuangComplete,
	title        = {Pearl's Calculus of Intervention is Complete},
	author       = {Huang, Yimin and Valtorta, Marco},
	year         = 2006,
	booktitle    = {Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence},
	location     = {Cambridge, MA, USA},
	publisher    = {AUAI Press},
	address      = {Arlington, Virginia, USA},
	series       = {Uai'06},
	pages        = {217--224},
	isbn         = {0974903922},
	abstract     = {This paper is concerned with graphical criteria that can be used to solve the problem of identifying casual effects from nonexperimental data in a causal Bayesian network structure, i.e., a directed acyclic graph that represents causal relationships. We first review Pearl's work on this topic [Pearl, 1995], in which several useful graphical criteria are presented. Then we present a complete algorithm [Huang and Valtorta, 2006b] for the identifiability problem. By exploiting the completeness of this algorithm, we prove that the three basic do-calculus rules that Pearl presents are complete, in the sense that, if a causal effect is identifiable, there exists a sequence of applications of the rules of the do-calculus that transforms the causal effect formula into a formula that only includes observational quantities.},
	numpages     = 8
}
@article{Huber,
	title        = {Double Machine Learning for Sample Selection Models},
	author       = {Bia, Michela and Huber, Martin and Laff{\'e}rs, Luk{\'a}{\v s}},
	year         = 2024,
	journal      = {Journal of Business and Economic Statistics},
	publisher    = {ASA Website},
	volume       = 42,
	number       = 3,
	pages        = {958--969},
	doi          = {10.1080/07350015.2023.2271071},
	url          = {https://doi.org/10.1080/07350015.2023.2271071},
	eprint       = {https://doi.org/10.1080/07350015.2023.2271071},
	bdsk-url-1   = {https://doi.org/10.1080/07350015.2023.2271071}
}
@article{HuberDW,
	title        = {Identification of Average Treatment Effects in Social Experiments Under Alternative Forms of Attrition},
	author       = {Martin Huber},
	year         = 2012,
	journal      = {Journal of Educational and Behavioral Statistics},
	volume       = 37,
	number       = 3,
	pages        = {443--474},
	doi          = {10.3102/1076998611411917},
	url          = {https://doi.org/10.3102/1076998611411917},
	abstract     = {As any empirical method used for causal analysis, social experiments are prone to attrition which may flaw the validity of the results. This article considers the problem of partially missing outcomes in experiments. First, it systematically reveals under which forms of attrition---in terms of its relation to observable and/or unobservable factors---experiments do (not) yield causal parameters. Second, it shows how the various forms of attrition can be controlled for by different methods of inverse probability weighting (IPW) that are tailored to the specific missing data problem at hand. In particular, it discusses IPW methods that incorporate instrumental variables (IVs) when attrition is related to unobservables, which has been widely ignored in the experimental literature before.},
	eprint       = {https://doi.org/10.3102/1076998611411917},
	bdsk-url-1   = {https://doi.org/10.3102/1076998611411917}
}
@article{HuberDW2,
	title        = {Treatment Evaluation in the Presence of Sample Selection},
	author       = {Martin Huber},
	year         = 2014,
	journal      = {Econometric Reviews},
	publisher    = {Taylor and Francis},
	volume       = 33,
	number       = 8,
	pages        = {869--905},
	doi          = {10.1080/07474938.2013.806197},
	url          = {https://doi.org/10.1080/07474938.2013.806197},
	eprint       = {https://doi.org/10.1080/07474938.2013.806197},
	bdsk-url-1   = {https://doi.org/10.1080/07474938.2013.806197}
}
@article{HuberIV,
	title        = {Endogeneity and non-response bias in treatment evaluation -- nonparametric identification of causal effects by instruments},
	author       = {Fricke, Hans and Fr{\"o}lich, Markus and Huber, Martin and Lechner, Michael},
	year         = 2020,
	journal      = {Journal of Applied Econometrics},
	volume       = 35,
	number       = 5,
	pages        = {481--504},
	doi          = {https://doi.org/10.1002/jae.2764},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jae.2764},
	abstract     = {Summary This paper proposes a nonparametric method for evaluating treatment effects in the presence of both treatment endogeneity and attrition/non-response bias, based on two instrumental variables. Using a discrete instrument for the treatment and an instrument with rich (in general continuous) support for non-response/attrition, we identify the average treatment effect on compliers as well as the total population under the assumption of additive separability of observed and unobserved variables affecting the outcome. We suggest non- and semiparametric estimators and apply the latter to assess the treatment effect of gym training, which is instrumented by a randomized cash incentive paid out conditional on visiting the gym, on self-assessed health among students at a Swiss university. The measurement of health is prone to non-response, which is instrumented by a cash lottery for participating in the follow-up survey.},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/jae.2764},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jae.2764},
	bdsk-url-2   = {https://doi.org/10.1002/jae.2764}
}
@article{hunermund2023double,
	title        = {Double machine learning and automated confounder selection: A cautionary tale},
	author       = {H{\"u}nermund, Paul and Louw, Beyers and Caspi, Itamar},
	year         = 2023,
	journal      = {Journal of Causal Inference},
	publisher    = {De Gruyter},
	volume       = 11,
	number       = 1,
	pages        = 20220078
}
@article{Hurwitz,
	title        = {Special Education and Individualized Academic Growth: A Longitudinal Assessment of Outcomes for Students With Disabilities},
	author       = {Sarah Hurwitz and Brea Perry and Emma Cohen and Russell Skiba},
	year         = 2020,
	journal      = {American Educational Research Journal},
	volume       = 57,
	number       = 2,
	pages        = {576--611},
	doi          = {10.3102/0002831219857054},
	url          = {https://doi.org/10.3102/0002831219857054},
	abstract     = {This study examined the effectiveness of participating in special education on the academic outcomes of students with disabilities. A sample of 575 students from a large, urban school district were followed longitudinally as they transitioned between general and special education to evaluate whether receiving special education services was associated with improvements in academic trajectories. Using student fixed effects models of within-person change over time, individuals' performance on standardized tests were compared before, during, and/or after special education placement. Results indicate that test scores of students with disabilities improved after being enrolled in special education. Additionally, students exiting special education exhibited a sustained trajectory of academic growth, suggesting that participation in special education in this district was associated with enduring improvements over time.},
	eprint       = {https://doi.org/10.3102/0002831219857054},
	bdsk-url-1   = {https://doi.org/10.3102/0002831219857054}
}
@inproceedings{ibeling2023comparing,
	title        = {Comparing causal frameworks: potential outcomes, structural models, graphs, and abstractions},
	author       = {Ibeling, Duligur and Icard, Thomas},
	year         = 2023,
	booktitle    = {Proceedings of the 37th International Conference on Neural Information Processing Systems},
	pages        = {80130--80141}
}
@misc{icd11,
	title        = {{International Classification of Diseases 11th Revision}},
	author       = {{World Health Organization}},
	year         = 2022,
	url          = {https://icd.who.int/en},
	shortauthor  = {{Who}},
	bdsk-url-1   = {https://icd.who.int/en}
}
@article{ichimura,
	title        = {The influence function of semiparametric estimators},
	author       = {Ichimura, Hidehiko and Newey, Whitney},
	year         = 2022,
	journal      = {Quantitative Economics},
	volume       = 13,
	number       = 1,
	pages        = {29--61},
	doi          = {https://doi.org/10.3982/QE826},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.3982/QE826},
	abstract     = {There are many economic parameters that depend on nonparametric first steps. Examples include games, dynamic discrete choice, average exact consumer surplus, and treatment effects. Often estimators of these parameters are asymptotically equivalent to a sample average of an object referred to as the influence function. The influence function is useful in local policy analysis, in evaluating local sensitivity of estimators, and constructing debiased machine learning estimators. We show that the influence function is a Gateaux derivative with respect to a smooth deviation evaluated at a point mass. This result generalizes the classic Von Mises (1947) and Hampel (1974) calculation to estimators that depend on smooth nonparametric first steps. We give explicit influence functions for first steps that satisfy exogenous or endogenous orthogonality conditions. We use these results to generalize the omitted variable bias formula for regression to policy analysis for and sensitivity to structural changes. We apply this analysis and find no sensitivity to endogeneity of average equivalent variation estimates in a gasoline demand application.},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.3982/QE826},
	keywords     = {Influence function, semiparametric estimation, NPIV, C13, C14, C20, C26, C36},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.3982/QE826},
	bdsk-url-2   = {https://doi.org/10.3982/QE826}
}
@article{IFVariance,
	title        = {How estimating nuisance parameters can reduce the variance (with consistent variance estimation)},
	author       = {Lok, Judith},
	year         = 2024,
	journal      = {Statistics in Medicine},
	volume       = 43,
	number       = 23,
	pages        = {4456--4480},
	doi          = {https://doi.org/10.1002/sim.10164},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.10164},
	abstract     = {We often estimate a parameter of interest \ensuremath{\psi}\$\$ \psi \$\$ when the identifying conditions involve a finite-dimensional nuisance parameter \texttheta{}\in{}\mathbb{R}d\$\$ \theta \in {\mathbb{R}}^d \$\$. Examples from causal inference are inverse probability weighting, marginal structural models and structural nested models, which all lead to unbiased estimating equations. This article presents a consistent sandwich estimator for the variance of estimators \ensuremath{\psi}^\$\$ \hat{\psi} \$\$ that solve unbiased estimating equations including \texttheta{}\$\$ \theta \$\$ which is also estimated by solving unbiased estimating equations. This article presents four additional results for settings where \texttheta{}^\$\$ \hat{\theta} \$\$ solves (partial) score equations and \ensuremath{\psi}\$\$ \psi \$\$ does not depend on \texttheta{}\$\$ \theta \$\$. This includes many causal inference settings where \texttheta{}\$\$ \theta \$\$ describes the treatment probabilities, missing data settings where \texttheta{}\$\$ \theta \$\$ describes the missingness probabilities, and measurement error settings where \texttheta{}\$\$ \theta \$\$ describes the error distribution. These four additional results are: (1) Counter-intuitively, the asymptotic variance of \ensuremath{\psi}^\$\$ \hat{\psi} \$\$ is typically smaller when \texttheta{}\$\$ \theta \$\$ is estimated. (2) If estimating \texttheta{}\$\$ \theta \$\$ is ignored, the sandwich estimator for the variance of \ensuremath{\psi}^\$\$ \hat{\psi} \$\$ is conservative. (3) A consistent sandwich estimator for the variance of \ensuremath{\psi}^\$\$ \hat{\psi} \$\$. (4) If \ensuremath{\psi}^\$\$ \hat{\psi} \$\$ with the true \texttheta{}\$\$ \theta \$\$ plugged in is efficient, the asymptotic variance of \ensuremath{\psi}^\$\$ \hat{\psi} \$\$ does not depend on whether \texttheta{}\$\$ \theta \$\$ is estimated. To illustrate we use observational data to calculate confidence intervals for (1) the effect of cazavi versus colistin on bacterial infections and (2) how the effect of antiretroviral treatment depends on its initiation time in HIV-infected patients.},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.10164},
	keywords     = {confidence intervals, estimating equations, nuisance parameters, variance estimation},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.10164},
	bdsk-url-2   = {https://doi.org/10.1002/sim.10164}
}
@article{impossibility,
	title        = {Impossibility results for nondifferentiable functionals},
	author       = {Keisuke Hirano and Jack Porter},
	year         = 2012,
	journal      = {Econometrica},
	publisher    = {[Wiley, Econometric Society]},
	volume       = 80,
	number       = 4,
	pages        = {1769--1790},
	issn         = {00129682, 14680262},
	url          = {http://www.jstor.org/stable/23271416},
	urldate      = {2024-04-01},
	abstract     = {We examine challenges to estimation and inference when the objects of interest are nondifferentiable functionals of the underlying data distribution. This situation arises in a number of applications of bounds analysis and moment inequality models, and in recent work on estimating optimal dynamic treatment regimes. Drawing on earlier work relating differentiability to the existence of unbiased and regular estimators, we show that if the target object is not differentiable in the parameters of the data distribution, there exist no estimator sequences that are locally asymptotically unbiased or \ensuremath{\alpha}-quantile unbiased. This places strong limits on estimators, bias correction methods, and inference procedures, and provides motivation for considering other criteria for evaluating estimators and inference procedures, such as local asymptotic minimaxity and one-sided quantile unbiasedness.},
	bdsk-url-1   = {http://www.jstor.org/stable/23271416}
}
@inproceedings{inducing,
	title        = {Equivalence and synthesis of causal models},
	author       = {Verma, Thomas and Pearl, Judea},
	year         = 1990,
	booktitle    = {Proceedings of the Sixth Annual Conference on Uncertainty in Artificial Intelligence},
	publisher    = {Elsevier Science Inc.},
	address      = {Usa},
	series       = {Uai '90},
	pages        = {255--270},
	isbn         = {0444892648},
	numpages     = 16
}
@article{instability,
	title        = {Comment: Performance of Double-Robust Estimators When ``Inverse Probability'' Weights Are Highly Variable},
	author       = {James Robins and Mariela Sued and Quanhong Lei-Gomez and Andrea Rotnitzky},
	year         = 2007,
	journal      = {Statistical Science},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 22,
	number       = 4,
	pages        = {544 -- 559},
	doi          = {10.1214/07-sts227d},
	url          = {https://doi.org/10.1214/07-STS227D},
	bdsk-url-1   = {https://doi.org/10.1214/07-STS227D}
}
@article{intbounds,
	title        = {Intersection bounds: estimation and inference},
	author       = {Victor Chernozhukov and Sokbae Lee and Adam Rosen},
	year         = 2013,
	journal      = {Econometrica},
	publisher    = {Wiley, Econometric Society},
	volume       = 81,
	number       = 2,
	pages        = {667--737},
	issn         = {00129682, 14680262},
	url          = {http://www.jstor.org/stable/23524295},
	urldate      = {2024-02-06},
	abstract     = {We develop a practical and novel method for inference on intersection bounds, namely bounds defined by either the infimum or supremum of a parametric or nonparametric function, or, equivalently, the value of a linear programming problem with a potentially infinite constraint set. We show that many bounds characterizations in econometrics, for instance bounds on parameters under conditional moment inequalities, can be formulated as intersection bounds. Our approach is especially convenient for models comprised of a continuum of inequalities that are separable in parameters, and also applies to models with inequalities that are nonseparable in parameters. Since analog estimators for intersection bounds can be severely biased in finite samples, routinely underestimating the size of the identified set, we also offer a medianbias-corrected estimator of such bounds as a by-product of our inferential procedures. We develop theory for large sample inference based on the strong approximation of a sequence of series or kernel-based empirical processes by a sequence of "penultimate" Gaussian processes. These penultimate processes are generally not weakly convergent, and thus are non-Donsker. Our theoretical results establish that we can nonetheless perform asymptotically valid inference based on these processes. Our construction also provides new adaptive inequality/moment selection methods. We provide conditions for the use of nonparametric kernel and series estimators, including a novel result that establishes strong approximation for any general series estimator admitting linearization, which may be of independent interest.},
	bdsk-url-1   = {http://www.jstor.org/stable/23524295}
}
@article{JANGMO2019423,
	title        = {Attention-Deficit/Hyperactivity Disorder, School Performance, and Effect of Medication},
	author       = {Andreas Jangmo and Amanda St{\aa}lhandske and Zheng Chang and Qi Chen and Catarina Almqvist and Inna Feldman and Cynthia M. Bulik and Paul Lichtenstein and Brian D'Onofrio and Ralf Kuja-Halkola and Henrik Larsson},
	year         = 2019,
	journal      = {Journal of the American Academy of Child and Adolescent Psychiatry},
	volume       = 58,
	number       = 4,
	pages        = {423--432},
	doi          = {https://doi.org/10.1016/j.jaac.2018.11.014},
	issn         = {0890-8567},
	url          = {https://www.sciencedirect.com/science/article/pii/S0890856719300590},
	keywords     = {ADHD, school performance, medication, treatment},
	bdsk-url-1   = {https://www.sciencedirect.com/science/article/pii/S0890856719300590},
	bdsk-url-2   = {https://doi.org/10.1016/j.jaac.2018.11.014}
}
@article{jeong2022finding,
	title        = {Finding and listing front-door adjustment sets},
	author       = {Jeong, Hyunchai and Tian, Jin and Bareinboim, Elias},
	year         = 2022,
	journal      = {Advances in Neural Information Processing Systems},
	volume       = 35,
	pages        = {33173--33185}
}
@misc{ji2023,
	title        = {Model-Agnostic Covariate-Assisted Inference on Partially Identified Causal Effects},
	author       = {Wenlong Ji and Lihua Lei and Asher Spector},
	year         = 2023,
	url          = {https://arxiv.org/abs/2310.08115},
	archiveprefix = {arXiv},
	eprint       = {2310.08115},
	primaryclass = {econ.EM},
	bdsk-url-1   = {https://arxiv.org/abs/2310.08115}
}
@article{jones1996indicator,
	title        = {Indicator and stratification methods for missing explanatory variables in multiple linear regression},
	author       = {Jones, Michael},
	year         = 1996,
	journal      = {Journal of the American Statistical Association},
	publisher    = {Taylor \& Francis},
	volume       = 91,
	number       = 433,
	pages        = {222--230}
}
@article{Jung_Tian_Bareinboim_20,
	title        = {Estimating Causal Effects Using Weighting-Based Estimators},
	author       = {Jung, Yonghan and Tian, Jin and Bareinboim, Elias},
	year         = 2020,
	month        = {Apr.},
	journal      = {Proceedings of the AAAI Conference on Artificial Intelligence},
	volume       = 34,
	number       = {06},
	pages        = {10186--10193},
	doi          = {10.1609/aaai.v34i06.6579},
	url          = {https://ojs.aaai.org/index.php/AAAI/article/view/6579},
	abstractnote = {Causal effect identification is one of the most prominent and well-understood problems in causal inference. Despite the generality and power of the results developed so far, there are still challenges in their applicability to practical settings, arguably due to the finitude of the samples. Simply put, there is a gap between causal effect identification and estimation. One popular setting in which sample-efficient estimators from finite samples exist is when the celebrated back-door condition holds. In this paper, we extend weighting-based methods developed for the back-door case to more general settings, and develop novel machinery for estimating causal effects using the weighting-based method as a building block. We derive graphical criteria under which causal effects can be estimated using this new machinery and demonstrate the effectiveness of the proposed method through simulation studies.},
	bdsk-url-1   = {https://ojs.aaai.org/index.php/AAAI/article/view/6579},
	bdsk-url-2   = {https://doi.org/10.1609/aaai.v34i06.6579}
}
@article{kang2007demystifying,
	title        = {Demystifying double robustness},
	author       = {Kang, Joseph and Schafer, Joseph},
	year         = 2007,
	journal      = {Statistical Science},
	volume       = 22,
	number       = 4,
	pages        = {523--539}
}
@conference{Karimietal23,
	title        = {On the Relationship Between Explanation and Prediction: A Causal View},
	author       = {Karimi, A.-H. and Muandet, K. and Kornblith, S. and Sch{\"o}lkopf, B. and Kim, B.},
	year         = 2023,
	month        = jul,
	booktitle    = {40th International Conference on Machine Learning (ICML)},
	month_numeric = 7
}
@inproceedings{kawakami2024,
	title        = {Probabilities of Causation for Continuous and Vector Variables},
	author       = {Yuta Kawakami and Manabu Kuroki and Jin Tian},
	year         = 2024,
	booktitle    = {The 40th Conference on Uncertainty in Artificial Intelligence},
	url          = {https://openreview.net/forum?id=em3fzm95So},
	bdsk-url-1   = {https://openreview.net/forum?id=em3fzm95So}
}
@article{kessler2014effects,
	title        = {The effects of temporally secondary co-morbid mental disorders on the associations of {DSM-IV} {ADHD} with adverse outcomes in the {US} National Comorbidity Survey Replication Adolescent Supplement ({NCS-A})},
	author       = {Kessler, Ronald and Adler, Lenard and Barkley, Russell and Biederman, Joseph and Conners, Keith and Demler, Olga and Faraone, Stephen and Greenhill, Laurence and Howes, Michael  and Secnik, Kristina and Spencer, Thomas and Ustun, Bedirhan and Walters, Ellen and Zaslavsky, Alan},
	year         = 2014,
	journal      = {Psychological Medicine},
	publisher    = {Cambridge University Press},
	volume       = 44,
	number       = 8,
	pages        = {1779--1792},
	doi          = {10.1017/s0033291713002419},
	url          = {https://doi.org/10.1017/S0033291713002419}
}
@article{kim2020environmental,
	title        = {Environmental risk factors, protective factors, and peripheral biomarkers for ADHD: an umbrella review},
	author       = {Kim, Jin and Cho, Gun-Ho and Shin, Young-Woo and Cho, Sang-Hyuk and Yoo, Han-Byul and Cheong, Jae-Hyun and Sohn, Seok-Ju},
	year         = 2020,
	journal      = {The Lancet Psychiatry},
	publisher    = {Elsevier},
	volume       = 7,
	number       = 12,
	pages        = {955--970}
}
@article{Kitagawa,
	title        = {Posterior distribution of nondifferentiable functions},
	author       = {Toru Kitagawa and Jos{\'e} {Montiel-Olea} and Jonathan Payne and Amilcar Velez},
	year         = 2020,
	journal      = {Journal of Econometrics},
	volume       = 217,
	number       = 1,
	pages        = {161--175},
	doi          = {https://doi.org/10.1016/j.jeconom.2019.10.009},
	issn         = {0304-4076},
	url          = {https://www.sciencedirect.com/science/article/pii/S0304407620300014},
	abstract     = {This paper examines the asymptotic behavior of the posterior distribution of a possibly nondifferentiable function g(\texttheta{}), where \texttheta{} is a finite-dimensional parameter of either a parametric or semiparametric model. The main assumption is that the distribution of a suitable estimator \texttheta{}\^n, its bootstrap approximation, and the Bayesian posterior for \texttheta{} all agree asymptotically. It is shown that whenever g is locally Lipschitz, though not necessarily differentiable, the posterior distribution of g(\texttheta{}) and the bootstrap distribution of g(\texttheta{}\^n) coincide asymptotically. One implication is that Bayesians can interpret bootstrap inference for g(\texttheta{}) as approximately valid posterior inference in a large sample. Another implication---built on known results about bootstrap inconsistency---is that credible intervals for a nondifferentiable parameter g(\texttheta{}) cannot be presumed to be approximately valid confidence intervals (even when this relation holds true for \texttheta{}).},
	keywords     = {Bootstrap, Bernstein--von Mises theorem, Directional differentiability, Posterior inference},
	bdsk-url-1   = {https://www.sciencedirect.com/science/article/pii/S0304407620300014},
	bdsk-url-2   = {https://doi.org/10.1016/j.jeconom.2019.10.009}
}
@book{koller2009,
	title        = {Probabilistic Graphical Models: Principles and Techniques},
	author       = {Koller, Daphne and Friedman, Nir},
	year         = 2009,
	publisher    = {MIT Press},
	address      = {Cambridge, MA},
	isbn         = {978-0-262-01319-2}
}
@article{Koshevnik,
	title        = {On a Non-Parametric Analogue of the Information Matrix},
	author       = {Koshevnik, Yu. and Levit, B.},
	year         = 1977,
	journal      = {Theory of Probability \& Its Applications},
	volume       = 21,
	number       = 4,
	pages        = {738--753},
	doi          = {10.1137/1121087},
	url          = {https://doi.org/10.1137/1121087},
	eprint       = {https://doi.org/10.1137/1121087}
}
@article{kunzel2019metalearners,
	title        = {Metalearners for estimating heterogeneous treatment effects using machine learning},
	author       = {K{\"u}nzel, S{\"o}ren and Sekhon, Jasjeet and Bickel, Peter and Yu, Bin},
	year         = 2019,
	journal      = {Proceedings of the national academy of sciences},
	publisher    = {National Acad Sciences},
	volume       = 116,
	number       = 10,
	pages        = {4156--4165}
}
@inproceedings{kuzmanovic2023,
	title        = {Estimating conditional average treatment effects with missing treatment information},
	author       = {Kuzmanovic, Milan and Hatt, Tobias and Feuerriegel, Stefan},
	year         = 2023,
	booktitle    = {International Conference on Artificial Intelligence and Statistics},
	pages        = {746--766},
	url          = {https://proceedings.mlr.press/v206/kuzmanovic23a/kuzmanovic23a.pdf},
	organization = {Pmlr}
}
@inproceedings{kyono2021miracle,
	title        = {{MIRACLE}: Causally-Aware Imputation via Learning Missing Data Mechanisms},
	author       = {Trent Kyono and Yao Zhang and Alexis Bellot and Mihaela van {der Schaar}},
	year         = 2021,
	booktitle    = {Advances in Neural Information Processing Systems},
	volume       = 34,
	pages        = {23806--23817},
	url          = {https://openreview.net/forum?id=GzeqcAUFGl0},
	editor       = {A. Beygelzimer and Y. Dauphin and P. Liang and J. Wortman Vaughan}
}
@book{Laan2003unified,
	title        = {Unified Methods for Censored Longitudinal Data and Causality},
	author       = {{van der Laan}, Mark  and Robins, J.},
	year         = 2003,
	publisher    = {Springer-Verlag, New York}
}
@article{laha2024finding,
	title        = {Finding the optimal dynamic treatment regimes using smooth Fisher consistent surrogate loss},
	author       = {Laha, Nilanjana and Sonabend-W, Aaron and Mukherjee, Rajarshi and Cai, Tianxi},
	year         = 2024,
	journal      = {The Annals of Statistics},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 52,
	number       = 2,
	pages        = {679--707}
}
@article{langberg2012does,
	title        = {Does long-term medication use improve the academic outcomes of youth with attention-deficit/hyperactivity disorder?},
	author       = {Langberg, Joshua and Becker, Stephen},
	year         = 2012,
	journal      = {Clinical child and family psychology review},
	publisher    = {Springer},
	volume       = 15,
	pages        = {215--233}
}
@book{lash2021modern,
	title        = {Modern Epidemiology},
	author       = {Lash, Timothy and VanderWeele, Tyler and Haneuse, Sebastien and Rothman, Kenneth},
	year         = 2021,
	publisher    = {Wolters Kluwer},
	address      = {Philadelphia},
	isbn         = 9781451193282,
	edition      = {Fourth},
	lccn         = 2020054540
}
@article{Lee202179,
	title        = {Framework for the treatment and reporting of missing data in observational studies: The Treatment And Reporting of Missing data in Observational Studies framework},
	author       = {Katherine J. Lee and Kate M. Tilling and Rosie P. Cornish and Roderick J.A. Little and Melanie L. Bell and Els Goetghebeur and Joseph W. Hogan and James R. Carpenter},
	year         = 2021,
	journal      = {Journal of Clinical Epidemiology},
	volume       = 134,
	pages        = {79--88},
	doi          = {https://doi.org/10.1016/j.jclinepi.2021.01.008},
	issn         = {0895-4356},
	url          = {https://www.sciencedirect.com/science/article/pii/S089543562100010X},
	abstract     = {Missing data are ubiquitous in medical research. Although there is increasing guidance on how to handle missing data, practice is changing slowly and misapprehensions abound, particularly in observational research. Importantly, the lack of transparency around methodological decisions is threatening the validity and reproducibility of modern research. We present a practical framework for handling and reporting the analysis of incomplete data in observational studies, which we illustrate using a case study from the Avon Longitudinal Study of Parents and Children. The framework consists of three steps: 1) Develop an analysis plan specifying the analysis model and how missing data are going to be addressed. An important consideration is whether a complete records' analysis is likely to be valid, whether multiple imputation or an alternative approach is likely to offer benefits and whether a sensitivity analysis regarding the missingness mechanism is required; 2) Examine the data, checking the methods outlined in the analysis plan are appropriate, and conduct the preplanned analysis; and 3) Report the results, including a description of the missing data, details on how the missing data were addressed, and the results from all analyses, interpreted in light of the missing data and the clinical relevance. This framework seeks to support researchers in thinking systematically about missing data and transparently reporting the potential effect on the study results, therefore increasing the confidence in and reproducibility of research findings.},
	keywords     = {Missing data, Multiple imputation, Observational studies, Reporting, ALSPAC, STRATOS initiative},
	bdsk-url-1   = {https://www.sciencedirect.com/science/article/pii/S089543562100010X},
	bdsk-url-2   = {https://doi.org/10.1016/j.jclinepi.2021.01.008}
}
@article{lee2023burden,
	title        = {The Burden of Attention-Deficit/Hyperactivity Disorder in Adults: A Real-World Linked Data Study},
	author       = {Lee, Lulu and Arunajadai, Srikesh and Mikl, Jaromir and Erensen, Jennifer G and Goodman, David W},
	year         = 2023,
	journal      = {The Primary Care Companion for CNS Disorders},
	publisher    = {Physicians Postgraduate Press, Inc.},
	volume       = 25,
	number       = 2,
	pages        = 46150
}
@article{levis2024stochastic,
	title        = {Stochastic interventions, sensitivity analysis, and optimal transport},
	author       = {Levis, Alexander and Kennedy, Edward and McClean, Alec and Balakrishnan, Sivaraman and Wasserman, Larry},
	year         = 2024,
	journal      = {arXiv preprint arXiv:2411.14285}
}
@article{lewin2018attrition,
	title        = {Attrition Bias Related to Missing Outcome Data: A Longitudinal Simulation Study},
	author       = {Lewin, A. and Brondeel, R. and Benmarhnia, T. and Thomas, F. and Chaix, B.},
	year         = 2018,
	journal      = {Epidemiology},
	volume       = 29,
	number       = 1,
	pages        = {87--95},
	doi          = {10.1097/ede.0000000000000755},
	bdsk-url-1   = {https://doi.org/10.1097/EDE.0000000000000755}
}
@article{Lewis2024,
	title        = {Robust causal inference for point exposures with missing confounders},
	author       = {Levis, Alexander and Mukherjee, Rajarshi and Wang, Rui and Haneuse, Sebastien},
	year         = 2024,
	journal      = {Canadian Journal of Statistics},
	volume       = {n/a},
	number       = {n/a},
	pages        = {e11832},
	doi          = {https://doi.org/10.1002/cjs.11832},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1002/cjs.11832},
	keywords     = {Causal inference, missing data, multiply robust, semiparametric theory},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/cjs.11832},
	abstract     = {Abstract Large observational databases are often subject to missing data. As such, methods for causal inference must simultaneously handle confounding and missingness; surprisingly little work has been done at this intersection. Motivated by this, we propose an efficient and robust estimator of the causal average treatment effect from cohort studies when confounders are missing at random. The approach is based on a novel factorization of the likelihood that, unlike alternative methods, facilitates flexible modelling of nuisance functions (e.g., with state-of-the-art machine learning methods) while maintaining nominal convergence rates of the final estimators. Simulated data, derived from an electronic health record-based study of the long-term effects of bariatric surgery on weight outcomes, verify the robustness properties of the proposed estimators in finite samples. Our approach may serve as a theoretical benchmark against which ad hoc methods may be assessed.}
}
@article{Li-IPW,
	title        = {Instability of inverse probability weighting methods and a remedy for nonignorable missing data},
	author       = {Li, Pengfei and Qin, Jing and Liu, Yukun},
	year         = 2023,
	journal      = {Biometrics},
	volume       = {n/a},
	number       = {n/a},
	doi          = {https://doi.org/10.1111/biom.13881},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1111/biom.13881},
	abstract     = {Abstract Inverse probability weighting (IPW) methods are commonly used to analyze nonignorable missing data (NIMD) under the assumption of a logistic model for the missingness probability. However, solving IPW equations numerically may involve nonconvergence problems when the sample size is moderate and the missingness probability is high. Moreover, those equations often have multiple roots, and identifying the best root is challenging. Therefore, IPW methods may have low efficiency or even produce biased results. We identify the pitfall in these methods pathologically: they involve the estimation of a moment-generating function (MGF), and such functions are notoriously unstable in general. As a remedy, we model the outcome distribution given the covariates of the completely observed individuals semiparametrically. After forming an induced logistic regression (LR) model for the missingness status of the outcome and covariate, we develop a maximum conditional likelihood method to estimate the underlying parameters. The proposed method circumvents the estimation of an MGF and hence overcomes the instability of IPW methods. Our theoretical and simulation results show that the proposed method outperforms existing competitors greatly. Two real data examples are analyzed to illustrate the advantages of our method. We conclude that if only a parametric LR is assumed but the outcome regression model is left arbitrary, then one has to be cautious in using any of the existing statistical methods in problems involving NIMD.},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/biom.13881},
	keywords     = {density ratio model, inverse probability weighting, location-scale model, logistic regression, nonignorable missing data},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.1111/biom.13881},
	bdsk-url-2   = {https://doi.org/10.1111/biom.13881}
}
@inproceedings{li2022unit,
	title        = {Unit selection with causal diagram},
	author       = {Li, Ang and Pearl, Judea},
	year         = 2022,
	booktitle    = {Proceedings of the AAAI conference on artificial intelligence},
	volume       = 36,
	pages        = {5765--5772}
}
@inproceedings{Li2024,
	title        = {Probabilities of causation with nonbinary treatment and effect},
	author       = {Li, Ang and Pearl, Judea},
	year         = 2024,
	booktitle    = {Proceedings of the AAAI Conference on Artificial Intelligence},
	volume       = 38,
	pages        = {20465--20472}
}
@inproceedings{li2024unit,
	title        = {Unit selection with nonbinary treatment and effect},
	author       = {Li, Ang and Pearl, Judea},
	year         = 2024,
	booktitle    = {Proceedings of the AAAI Conference on Artificial Intelligence},
	volume       = 38,
	pages        = {20473--20480}
}
@article{Luedtke2018,
	title        = {Parametric-Rate Inference for One-Sided Differentiable Parameters},
	author       = {Alexander Luedtke and Mark {van der Laan}},
	year         = 2018,
	journal      = {Journal of the American Statistical Association},
	publisher    = {Taylor \& Francis},
	volume       = 113,
	number       = 522,
	pages        = {780--788},
	doi          = {10.1080/01621459.2017.1285777},
	url          = {https://doi.org/10.1080/01621459.2017.1285777},
	note         = {Pmid: 30078921},
	eprint       = {https://doi.org/10.1080/01621459.2017.1285777},
	bdsk-url-1   = {https://doi.org/10.1080/01621459.2017.1285777}
}
@inproceedings{Malinsky,
	title        = {Causal inference with outcome-dependent missingness and self-censoring},
	author       = {Chen, Jacob and Malinsky, Daniel and Bhattacharya, Rohit},
	year         = 2023,
	month        = {31 Jul--04 Aug},
	booktitle    = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence},
	publisher    = {Pmlr},
	series       = {Proceedings of Machine Learning Research},
	volume       = 216,
	pages        = {358--368},
	url          = {https://proceedings.mlr.press/v216/chen23f.html},
	abstract     = {We consider missingness in the context of causal inference when the outcome of interest may be missing. If the outcome directly affects its own missingness status, i.e., it is ``self-censoring'', this may lead to severely biased causal effect estimates. Miao et al. (2015) proposed the shadow variable method to correct for bias due to self-censoring; however, verifying the required model assumptions can be difficult. Here, we propose a test based on a randomized incentive variable offered to encourage reporting of the outcome that can be used to verify identification assumptions that are sufficient to correct for both self-censoring and confounding bias. Concretely, the test confirms whether a given set of pre-treatment covariates is sufficient to block all backdoor paths between the treatment and outcome as well as all paths between the treatment and missingness indicator after conditioning on the outcome. We show that under these conditions, the causal effect is identified by using the treatment as a shadow variable, and it leads to an intuitive inverse probability weighting estimator that uses a product of the treatment and response weights. We evaluate the efficacy of our test and downstream estimator via simulations.},
	editor       = {Evans, Robin J. and Shpitser, Ilya},
	pdf          = {https://proceedings.mlr.press/v216/chen23f/chen23f.pdf},
	bdsk-url-1   = {https://proceedings.mlr.press/v216/chen23f.html}
}
@phdthesis{masterUiO,
	title        = {The older the better? Relative age and grade effects on Norwegian national test performance},
	author       = {J\o{}rstad, Oscarl},
	year         = 2020,
	series       = {Centre for Educational Measurement (Master Thesis)},
	url          = {http://hdl.handle.net/10852/78671},
	abstract     = {Previous studies has found that the youngest students perform more poorly, on average, than older peers in school. This phenomenon is known as the relative age effect (RAE). In Norway, the age difference within a grade year can be up to 12 months. All Norwegian students participates annually in national reading, numeracy and English tests in 5th, 8th and 9th grade, which tests students' basic curriculum skills. We apply population data on national tests to study RAE. Specifically, we aim to investigate: The linear effect of RAE on national tests, the ratio of RAE to the grade effect in grade 8/9 in numeracy and reading and lastly how RAE changes from grade 5 to 9 in numeracy. This study applies ordinary least square regression to estimate the linear effect of RAE, sharp regression discontinuity design to estimate RAE and grade effect on grade 8/9 in reading and numeracy. We incorporate vertical linking of the numeracy tests to investigate how RAE changes over grade years. In accordance with previous findings, we confirm that RAE is strongest in grade 5 and declines over grade years. We found that RAE has a larger impact than the grade effect on national reading and numeracy tests in grade 8/9. These results suggests that RAE has a stronger impact on national test proficiency than the amount of years spent in school at this point of the educational track.},
	language     = {eng},
	keywords     = {Relative age effect},
	school       = {University of Oslo}
}
@techreport{mathur2023,
	title        = {A common-cause principle for eliminating selection bias in causal estimands through covariate adjustment},
	author       = {Mathur, Maya and Shpitser, Ilya and VanderWeele, Tyler},
	year         = 2023,
	month        = Jan,
	number       = {ths4e},
	doi          = {10.31219/osf.io/ths4e},
	url          = {https://ideas.repec.org/p/osf/osfxxx/ths4e.html},
	abstract     = {Average treatment effects (ATEs) may be subject to selection bias when they are estimated among only a non-representative subset of the target population. Selection bias can sometimes be eliminated by conditioning on a ``sufficient adjustment set'' of covariates, even for some forms of missingness not at random (MNAR). Without requiring full specification of the causal structure, we consider sufficient adjustment sets to allow nonparametric identification of conditional ATEs in the target population. Covariates in the sufficient set may be collected among only the selected sample. We establish that if a sufficient set exists, then the set consisting of common causes of the outcome and selection, excluding the exposure and its descendants, also suffices. We establish simple graphical criteria for when a sufficient set will not exist, which could help indicate whether this is plausible for a given study. Simulations considering selection due to missing data indicated that sufficiently-adjusted complete-case analysis (CCA) can considerably outperform multiple imputation under MNAR and, if the sample size is not large, sometimes even under missingness at random. Analogous to the common-cause principle for confounding, these sufficiency results clarify when and how selection bias can be eliminated through covariate adjustment.},
	institution  = {Center for Open Science},
	type         = {OSF Preprints},
	bdsk-url-1   = {https://ideas.repec.org/p/osf/osfxxx/ths4e.html},
	bdsk-url-2   = {https://doi.org/10.31219/osf.io/ths4e}
}
@article{mathur2023m,
	title        = {The M-value: A simple sensitivity analysis for bias due to missing data in treatment effect estimates},
	author       = {Mathur, Maya B},
	year         = 2023,
	journal      = {American Journal of Epidemiology},
	publisher    = {Oxford University Press},
	volume       = 192,
	number       = 4,
	pages        = {612--620}
}
@article{mbias1,
	title        = {{Implications of M Bias in Epidemiologic Studies: A Simulation Study}},
	author       = {Liu, Wei and Brookhart, M. Alan and Schneeweiss, Sebastian and Mi, Xiaojuan and Setoguchi, Soko},
	year         = 2012,
	month        = 10,
	journal      = {American Journal of Epidemiology},
	volume       = 176,
	number       = 10,
	pages        = {938--948},
	doi          = {10.1093/aje/kws165},
	issn         = {0002-9262},
	url          = {https://doi.org/10.1093/aje/kws165},
	abstract     = {{Collider-stratification bias arises from conditioning on a variable (collider) which opens a path from exposure to outcome. M bias occurs when the collider-stratification bias is transmitted through ancestors of exposure and outcome. Previous theoretical work, but not empirical data, has demonstrated that M bias is smaller than confounding bias. The authors simulated data for large cohort studies with binary exposure, an outcome, a collider, and 2 predictors of the collider. They created 178 scenarios by changing the frequencies of variables and/or the magnitudes of associations among the variables. They calculated the effect estimate, percentage bias, and mean squared error. M bias in these realistic scenarios ranged from -2\\\% to -5\\\%. When the authors increased one or both relative risks for the relation between the collider and unmeasured factors to \geq{}8, the negative bias was more substantial (\andgt;15\\\%). The result was substantially biased (e.g., \andgt;20\\\%) if an unmeasured confounder that was also a collider was not adjusted to avoid M bias. In scenarios resembling those the authors examined, M bias had a small impact unless associations between the collider and unmeasured confounders were very large (relative risk \andgt; 8). When a collider is itself an important confounder, controlling for confounding would take precedence over avoiding M bias.}},
	eprint       = {https://academic.oup.com/aje/article-pdf/176/10/938/37829439/aje_176_10_938_s0.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/aje/kws165}
}
@article{mbias2,
	title        = {To Adjust or Not to Adjust? Sensitivity Analysis of M-Bias and Butterfly-Bias},
	author       = {Peng Ding and Luke Miratrix},
	year         = 2015,
	journal      = {Journal of Causal Inference},
	volume       = 3,
	number       = 1,
	pages        = {41--57},
	doi          = {doi:10.1515/jci-2013-0021},
	url          = {https://doi.org/10.1515/jci-2013-0021},
	lastchecked  = {2024-01-15},
	bdsk-url-1   = {https://doi.org/10.1515/jci-2013-0021}
}
@article{mcisaac2017,
	title        = {Statistical methods for incomplete data: Some results on model misspecification},
	author       = {McIsaac, Michelle and Cook, Richard},
	year         = 2017,
	journal      = {Statistical Methods in Medical Research},
	volume       = 26,
	number       = 1,
	pages        = {248--267},
	doi          = {10.1177/0962280214544251},
	url          = {https://pubmed.ncbi.nlm.nih.gov/25063681/},
	pmid         = 25063681,
	bdsk-url-1   = {https://pubmed.ncbi.nlm.nih.gov/25063681/},
	bdsk-url-2   = {https://doi.org/10.1177/0962280214544251}
}
@article{mcmurry2004,
	title        = {Nonparametric regression with infinite order flat-top kernels},
	author       = {McMurry, Timothy L and Politis, Dimitris N},
	year         = 2004,
	journal      = {Journal of Nonparametric Statistics},
	publisher    = {Taylor \& Francis},
	volume       = 16,
	number       = {3-4},
	pages        = {549--562}
}
@article{medicationNorway,
	title        = {{ADHD} treatment and diagnosis in relation to children's birth month: Nationwide cohort study from Norway},
	author       = {\O{}ystein Karlstad and Kari Furu and Camilla Stoltenberg and Siri H\aa{}berg and Inger Bakken},
	year         = 2017,
	journal      = {Scandinavian Journal of Public Health},
	volume       = 45,
	number       = 4,
	pages        = {343--349},
	doi          = {10.1177/1403494817708080},
	url          = {https://doi.org/10.1177/1403494817708080},
	note         = {Pmid: 28482754},
	eprint       = {https://doi.org/10.1177/1403494817708080},
	abstract     = {Background: Studies from several countries have reported that children youngest in grade are at higher risk of attention-deficit/hyperactivity disorder (ADHD) diagnosis and treatment. Norwegian children start school the year they turn six, making children born in December youngest in their grade. We used data on medication, specialist healthcare diagnoses, and primary healthcare diagnoses from national registers to investigate associations between birth month and ADHD. Methods: All children born in Norway between 1998 and 2006 (N=509,827) were followed from age six until 31 December 2014. We estimated hazard ratios for ADHD medication and diagnoses by birth month in Cox proportional-hazards models. We compared risk among siblings to control for potentially confounding socioeconomic factors, and assessed risk of receiving ADHD medication by birth month while attending different grades in cross-sectional time-series analyses. Results: At end of follow-up, 5.3\% of boys born in October–December had received ADHD medication, compared with 3.7\% of boys born in January–March. Corresponding numbers for girls were 2.2\% and 1.3\%, respectively. The adjusted hazard ratio for ADHD medication for children born in October–December (reference: January–March) was 1.4 (95\% confidence interval: 1.4–1.5) for boys and 1.8 (1.7–2.0) for girls. Analyses with diagnoses as outcome showed consistent results, and analyses restricted to siblings within the study population also supported the findings. Analysis by grade revealed an increased risk for children born late in the year from grade 3 onwards, with most marked differences in higher grades. Conclusions: Children youngest in grade had the highest risk of receiving ADHD treatment. Differences were most marked among older children.}
}
@article{mgraphs,
	title        = {Graphical Models for Processing Missing Data},
	author       = {Karthika Mohan and Judea Pearl},
	year         = 2021,
	journal      = {Journal of the American Statistical Association},
	publisher    = {Taylor and Francis},
	volume       = 116,
	number       = 534,
	pages        = {1023--1037},
	doi          = {10.1080/01621459.2021.1874961},
	url          = {https://doi.org/10.1080/01621459.2021.1874961},
	eprint       = {https://doi.org/10.1080/01621459.2021.1874961},
	bdsk-url-1   = {https://doi.org/10.1080/01621459.2021.1874961}
}
@article{miao2015,
	title        = {Identification, doubly robust estimation, and semiparametric efficiency theory of nonignorable missing data with a shadow variable},
	author       = {Miao, Wang and Liu, Lan and Tchetgen Tchetgen, Eric and Geng, Zhi},
	year         = 2015,
	journal      = {arXiv preprint arXiv:1509.02556}
}
@article{MIPW,
	title        = {{Principled Approaches to Missing Data in Epidemiologic Studies}},
	author       = {Perkins, Neil and Cole, Stephen and Harel, Ofer and Tchetgen Tchetgen, Eric and Sun, BaoLuo and Mitchell, Emily and Schisterman, Enrique F},
	year         = 2017,
	month        = 11,
	journal      = {American Journal of Epidemiology},
	volume       = 187,
	number       = 3,
	pages        = {568--575},
	doi          = {10.1093/aje/kwx348},
	issn         = {0002-9262},
	url          = {https://doi.org/10.1093/aje/kwx348},
	abstract     = {{Principled methods with which to appropriately analyze missing data have long existed; however, broad implementation of these methods remains challenging. In this and 2 companion papers (Am J Epidemiol. 2018;187(3):576--584 and Am J Epidemiol. 2018;187(3):585--591), we discuss issues pertaining to missing data in the epidemiologic literature. We provide details regarding missing-data mechanisms and nomenclature and encourage the conduct of principled analyses through a detailed comparison of multiple imputation and inverse probability weighting. Data from the Collaborative Perinatal Project, a multisite US study conducted from 1959 to 1974, are used to create a masked data-analytical challenge with missing data induced by known mechanisms. We illustrate the deleterious effects of missing data with naive methods and show how principled methods can sometimes mitigate such effects. For example, when data were missing at random, naive methods showed a spurious protective effect of smoking on the risk of spontaneous abortion (odds ratio (OR) = 0.43, 95\\\% confidence interval (CI): 0.19, 0.93), while implementation of principled methods multiple imputation (OR = 1.30, 95\\\% CI: 0.95, 1.77) or augmented inverse probability weighting (OR = 1.40, 95\\\% CI: 1.00, 1.97) provided estimates closer to the ``true'' full-data effect (OR = 1.31, 95\\\% CI: 1.05, 1.64). We call for greater acknowledgement of and attention to missing data and for the broad use of principled missing-data methods in epidemiologic research.}},
	eprint       = {https://academic.oup.com/aje/article-pdf/187/3/568/24134556/kwx348.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/aje/kwx348}
}
@article{mises1947asymptotic,
	title        = {On the asymptotic distribution of differentiable statistical functions},
	author       = {{von Mises}, R},
	year         = 1947,
	journal      = {The annals of mathematical statistics},
	publisher    = {Jstor},
	volume       = 18,
	number       = 3,
	pages        = {309--348}
}
@article{missConfounder,
	title        = {Causal inference with confounders missing not at random},
	author       = {Yang, S and Wang, L and Ding, P},
	year         = 2019,
	month        = 9,
	journal      = {Biometrika},
	volume       = 106,
	number       = 4,
	pages        = {875--888},
	doi          = {10.1093/biomet/asz048},
	issn         = {0006-3444},
	url          = {https://doi.org/10.1093/biomet/asz048},
	abstract     = {It is important to draw causal inference from observational studies, but this becomes challenging if the confounders have missing values. Generally, causal effects are not identifiable if the confounders are missing not at random. In this article we propose a novel framework for nonparametric identification of causal effects with confounders subject to an outcome-independent missingness, which means that the missing data mechanism is independent of the outcome, given the treatment and possibly missing confounders. We then propose a nonparametric two-stage least squares estimator and a parametric estimator for causal effects.},
	eprint       = {https://academic.oup.com/biomet/article-pdf/106/4/875/30646757/asz048.pdf}
}
@article{missingCov,
	title        = {Covariate adjustment in randomized clinical trials with missing covariate and outcome data},
	author       = {Chang, Chia-Rui and Song, Yue and Li, Fan and Wang, Rui},
	year         = 2023,
	journal      = {Statistics in Medicine},
	volume       = 42,
	number       = 22,
	pages        = {3919--3935},
	doi          = {https://doi.org/10.1002/sim.9840},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.9840},
	abstract     = {When analyzing data from randomized clinical trials, covariate adjustment can be used to account for chance imbalance in baseline covariates and to increase precision of the treatment effect estimate. A practical barrier to covariate adjustment is the presence of missing data. In this article, in the light of recent theoretical advancement, we first review several covariate adjustment methods with incomplete covariate data. We investigate the implications of the missing data mechanism on estimating the average treatment effect in randomized clinical trials with continuous or binary outcomes. In parallel, we consider settings where the outcome data are fully observed or are missing at random; in the latter setting, we propose a full weighting approach that combines inverse probability weighting for adjusting missing outcomes and overlap weighting for covariate adjustment. We highlight the importance of including the interaction terms between the missingness indicators and covariates as predictors in the models. We conduct comprehensive simulation studies to examine the finite-sample performance of the proposed methods and compare with a range of common alternatives. We find that conducting the proposed adjustment methods generally improves the precision of treatment effect estimates regardless of the imputation methods when the adjusted covariate is associated with the outcome. We apply the methods to the Childhood Adenotonsillectomy Trial to assess the effect of adenotonsillectomy on neurocognitive functioning scores.},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.9840},
	keywords     = {covariate balance, imputation, missingness indicator, outcome regression, overlap weighting, propensity score},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.9840},
	bdsk-url-2   = {https://doi.org/10.1002/sim.9840}
}
@article{missingcovariates,
	title        = {Generalizing treatment effects with incomplete covariates: Identifying assumptions and multiple imputation algorithms},
	author       = {Mayer, Imke and Josse, Julie and Traumabase Group},
	year         = 2023,
	journal      = {Biometrical Journal},
	volume       = 65,
	number       = 5,
	pages        = {210--294},
	doi          = {https://doi.org/10.1002/bimj.202100294},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1002/bimj.202100294},
	keywords     = {causal effect transportability, data integration, external validity, missing values, missing incorporated in attributes, multiple imputation, random forest},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/bimj.202100294},
	abstract     = {Abstract We focus on the problem of generalizing a causal effect estimated on a randomized controlled trial (RCT) to a target population described by a set of covariates from observational data. Available methods such as inverse propensity sampling weighting are not designed to handle missing values, which are however common in both data sources. In addition to coupling the assumptions for causal effect identifiability and for the missing values mechanism and to defining appropriate estimation strategies, one difficulty is to consider the specific structure of the data with two sources and treatment and outcome only available in the RCT. We propose three multiple imputation strategies to handle missing values when generalizing treatment effects, each handling the multisource structure of the problem differently (separate imputation, joint imputation with fixed effect, joint imputation ignoring source information). As an alternative to multiple imputation, we also propose a direct estimation approach that treats incomplete covariates as semidiscrete variables. The multiple imputation strategies and the latter alternative rely on different sets of assumptions concerning the impact of missing values on identifiability. We discuss these assumptions and assess the methods through an extensive simulation study. This work is motivated by the analysis of a large registry of over 20,000 major trauma patients and an RCT studying the effect of tranexamic acid administration on mortality in major trauma patients admitted to intensive care units. The analysis illustrates how the missing values handling can impact the conclusion about the effect generalized from the RCT to the target~population.}
}
@article{MLDR,
	title        = {{Machine learning in the estimation of causal effects: targeted minimum loss-based estimation and double/debiased machine learning}},
	author       = {D{\'\i}az, Iv{\'a}n},
	year         = 2019,
	month        = 11,
	journal      = {Biostatistics},
	volume       = 21,
	number       = 2,
	pages        = {353--358},
	doi          = {10.1093/biostatistics/kxz042},
	issn         = {1465-4644},
	url          = {https://doi.org/10.1093/biostatistics/kxz042},
	abstract     = {{In recent decades, the fields of statistical and machine learning have seen a revolution in the development of data-adaptive regression methods that have optimal performance under flexible, sometimes minimal, assumptions on the true regression functions. These developments have impacted all areas of applied and theoretical statistics and have allowed data analysts to avoid the biases incurred under the pervasive practice of parametric model misspecification. In this commentary, I discuss issues around the use of data-adaptive regression in estimation of causal inference parameters. To ground ideas, I focus on two estimation approaches with roots in semi-parametric estimation theory: targeted minimum loss-based estimation (TMLE; van der Laan and Rubin, 2006) and double/debiased machine learning (DML; Chernozhukov and others, 2018). This commentary is not comprehensive, the literature on these topics is rich, and there are many subtleties and developments which I do not address. These two frameworks represent only a small fraction of an increasingly large number of methods for causal inference using machine learning. To my knowledge, they are the only methods grounded in statistical semi-parametric theory that also allow unrestricted use of data-adaptive regression techniques.}},
	eprint       = {https://academic.oup.com/biostatistics/article-pdf/21/2/353/32914770/kxz042.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/biostatistics/kxz042}
}
@article{MLMI,
	title        = {{Maximum Likelihood Multiple Imputation: Faster Imputations and Consistent Standard Errors Without Posterior Draws}},
	author       = {Paul T. {von Hippel} and Jonathan W. Bartlett},
	year         = 2021,
	journal      = {Statistical Science},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 36,
	number       = 3,
	pages        = {400 -- 420},
	doi          = {10.1214/20-sts793},
	url          = {https://doi.org/10.1214/20-STS793},
	keywords     = {incomplete data, missing data},
	bdsk-url-1   = {https://doi.org/10.1214/20-STS793}
}
@inproceedings{Mohan2013,
	title        = {Graphical Models for Inference with Missing Data},
	author       = {Mohan, Karthika and Pearl, Judea and Tian, Jin},
	year         = 2013,
	booktitle    = {Advances in Neural Information Processing Systems},
	publisher    = {Curran Associates, Inc.},
	volume       = 26,
	url          = {https://proceedings.neurips.cc/paper_files/paper/2013/file/0ff8033cf9437c213ee13937b1c4c455-Paper.pdf},
	editor       = {C.J. Burges and L. Bottou and M. Welling and Z. Ghahramani and K.Q. Weinberger},
	bdsk-url-1   = {https://proceedings.neurips.cc/paper_files/paper/2013/file/0ff8033cf9437c213ee13937b1c4c455-Paper.pdf}
}
@inproceedings{Mohan2014,
	title        = {Graphical Models for Recovering Probabilistic and Causal Queries from Missing Data},
	author       = {Mohan, Karthika and Pearl, Judea},
	year         = 2014,
	booktitle    = {Advances in Neural Information Processing Systems},
	publisher    = {Curran Associates, Inc.},
	volume       = 27,
	url          = {https://papers.nips.cc/paper_files/paper/2014/hash/1835d9d1508eb178b500220a9ddf75a7-Abstract.html},
	editor       = {Z. Ghahramani and M. Welling and C. Cortes and N. Lawrence and K.Q. Weinberger},
	bdsk-url-1   = {https://papers.nips.cc/paper_files/paper/2014/hash/1835d9d1508eb178b500220a9ddf75a7-Abstract.html}
}
@article{montastruc2019pharmacoepidemiology,
	title        = {What is pharmacoepidemiology? Definition, methods, interest and clinical applications},
	author       = {Montastruc, Jean-Louis and Benevent, Justine and Montastruc, Fran{\c{c}}ois and Bagheri, Haleh and Despas, Fabien and Lapeyre-Mestre, Maryse and Sommet, Agn{\`e}s},
	year         = 2019,
	journal      = {Therapies},
	publisher    = {Elsevier},
	volume       = 74,
	number       = 2,
	pages        = {169--174}
}
@article{moore2019pharmacoepidemiology,
	title        = {Pharmacoepidemiology},
	author       = {Moore, Nicholas and Blin, Patrick and Droz, C{\'e}cile},
	year         = 2019,
	journal      = {Concepts and Principles of Pharmacology: 100 Years of the Handbook of Experimental Pharmacology},
	publisher    = {Springer},
	pages        = {433--451}
}
@article{MSM,
	title        = {Marginal Structural Models and Causal Inference in Epidemiology},
	author       = {Robins, James and Hern{\'a}n, Miguel and Brumback, Babette},
	year         = 2000,
	journal      = {Epidemiology},
	volume       = 11,
	number       = 5,
	url          = {https://journals.lww.com/epidem/fulltext/2000/09000/marginal\%5Fstructural\%5Fmodels\%5Fand\%5Fcausal\%5Finference\%5Fin.11.aspx},
	date-added   = {2023-09-15 16:47:28 +0200},
	date-modified = {2023-09-15 16:47:28 +0200},
	id           = {00001648-200009000-00011},
	keywords     = {causality; counterfactuals; epidemiologic methods; longitudinal data; structural models; confounding; intermediate variables},
	n2           = {In observational studies with exposures or treatments that vary over time, standard approaches for adjustment of confounding are biased when there exist time-dependent confounders that are also affected by previous treatment. This paper introduces marginal structural models, a new class of causal models that allow for improved adjustment of confounding in those situations. The parameters of a marginal structural model can be consistently estimated using a new class of estimators, the inverse-probability-of-treatment weighted estimators.},
	bdsk-url-1   = {https://journals.lww.com/epidem/fulltext/2000/09000/marginal_structural_models_and_causal_inference_in.11.aspx}
}
@techreport{mueller2023perspective,
	title        = {Perspective on harm in Personalized Medicine -- An Alternative Perspective},
	author       = {Mueller, Scott and Pearl, Judea},
	year         = 2023,
    institution = {Technical Report R-530, Department of Computer Science, University of California, Los Angeles, CA, 2023. Forthcoming, American Journal of Epidemiology, 2024}
}
@inproceedings{MuellerLiPearl,
	title        = {Causes of Effects: Learning Individual Responses from Population Data},
	author       = {Mueller, Scott and Li, Ang and Pearl, Judea},
	year         = 2022,
	month        = 7,
	booktitle    = {Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence, {IJCAI-22}},
	publisher    = {International Joint Conferences on Artificial Intelligence Organization},
	pages        = {2712--2718},
	doi          = {10.24963/ijcai.2022/376},
	url          = {https://doi.org/10.24963/ijcai.2022/376},
	note         = {Main Track},
	editor       = {Lud De Raedt},
	bdsk-url-1   = {https://doi.org/10.24963/ijcai.2022/376}
}
@techreport{muellerMonotonicity,
	title        = {Monotonicity: Detection, Refutation, and Ramification},
	author       = {Mueller, Scott and Pearl, Judea},
	year         = 2023,
	address      = {Ca},
	number       = {R-529},
	url          = {http://ftp.cs.ucla.edu/pub/stat\%5Fser/r529.pdf},
	institution  = {Department of Computer Science, University of California, Los Angeles},
	bdsk-url-1   = {http://ftp.cs.ucla.edu/pub/stat\%5C_ser/r529.pdf}
}
@article{MuellerPearl2023,
	title        = {Personalized decision making -- A conceptual introduction},
	author       = {Scott Mueller and Judea Pearl},
	year         = 2023,
	journal      = {Journal of Causal Inference},
	volume       = 11,
	number       = 1,
	pages        = 20220050,
	doi          = {doi:10.1515/jci-2022-0050},
	url          = {https://doi.org/10.1515/jci-2022-0050},
	lastchecked  = {2024-02-03},
	bdsk-url-1   = {https://doi.org/10.1515/jci-2022-0050}
}
@article{multiplyDR,
	title        = {Multiply robust estimation of the average treatment effect with missing outcomes},
	author       = {Kecheng Wei and Guoyou Qin and Jiajia Zhang and Xuemei Sui},
	year         = 2023,
	journal      = {Journal of Statistical Computation and Simulation},
	publisher    = {Taylor \& Francis},
	volume       = 93,
	number       = 10,
	pages        = {1479--1495},
	doi          = {10.1080/00949655.2022.2143501},
	url          = {https://doi.org/10.1080/00949655.2022.2143501},
	eprint       = {https://doi.org/10.1080/00949655.2022.2143501},
	bdsk-url-1   = {https://doi.org/10.1080/00949655.2022.2143501}
}
@article{murphyDTR,
	title        = {Optimal dynamic treatment regimes},
	author       = {Murphy, Susam},
	year         = 2003,
	journal      = {Journal of the Royal Statistical Society: Series B (Statistical Methodology)},
	volume       = 65,
	number       = 2,
	pages        = {331--355},
	doi          = {https://doi.org/10.1111/1467-9868.00389},
	url          = {https://rss.onlinelibrary.wiley.com/doi/abs/10.1111/1467-9868.00389},
	keywords     = {Adaptive strategies, Causal inference, Dynamic programming, Multistage decisions},
	abstract     = {Summary. A dynamic treatment regime is a list of decision rules, one per time interval, for how the level of treatment will be tailored through time to an individual's changing status. The goal of this paper is to use experimental or observational data to estimate decision regimes that result in a maximal mean response. To explicate our objective and to state the assumptions, we use the potential outcomes model. The method proposed makes smooth parametric assumptions only on quantities that are directly relevant to the goal of estimating the optimal rules. We illustrate the methodology proposed via a small simulation.}
}
@misc{nabi2022causal,
	title        = {Causal and Counterfactual Views of Missing Data Models},
	author       = {Razieh Nabi and Rohit Bhattacharya and Ilya Shpitser and James Robins},
	year         = 2024,
	url          = {https://arxiv.org/abs/2210.05558},
	eprint       = {2210.05558},
	archiveprefix = {arXiv},
	primaryclass = {stat.ME}
}
@inproceedings{NabiFull,
	title        = {Full law identification in graphical models of missing data: completeness results},
	author       = {Nabi, Razieh and Bhattacharya, Rohit and Shpitser, Ilya},
	year         = 2020,
	booktitle    = {Proceedings of the 37th International Conference on Machine Learning},
	publisher    = {JMLR.org},
	series       = {Icml'20},
	url          = {http://proceedings.mlr.press/v119/nabi20a/nabi20a.pdf},
	abstract     = {Missing data has the potential to affect analyses conducted in all fields of scientific study including healthcare, economics, and the social sciences. Several approaches to unbiased inference in the presence of non-ignorable missingness rely on the specification of the target distribution and its missingness process as a probability distribution that factorizes with respect to a directed acyclic graph. In this paper, we address the longstanding question of the characterization of models that are identifiable within this class of missing data distributions. We provide the first completeness result in this field of study - necessary and sufficient graphical conditions under which, the full data distribution can be recovered from the observed data distribution. We then simultaneously address issues that may arise due to the presence of both missing data and unmeasured confounding, by extending these graphical conditions and proofs of completeness, to settings where some variables are not just missing, but completely unobserved.},
	articleno    = 663,
	numpages     = 11,
	bdsk-url-1   = {http://proceedings.mlr.press/v119/nabi20a/nabi20a.pdf}
}
@inproceedings{NabiSemi,
	title        = {Sufficient identification conditions and semiparametric estimation under missing not at random mechanisms},
	author       = {Guo, Anna and Zhao, Jiwei and Nabi, Razieh},
	year         = 2023,
	booktitle    = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence},
	location     = {Pittsburgh, PA, USA},
	publisher    = {JMLR.org},
	series       = {Uai '23},
	url          = {https://proceedings.mlr.press/v216/guo23a/guo23a.pdf},
	abstract     = {Conducting valid statistical analyses is challenging in the presence of missing-not-at-random (MNAR) data, where the missingness mechanism is dependent on the missing values themselves even conditioned on the observed data. Here, we consider a MNAR model that generalizes several prior popular MNAR models in two ways: first, it is less restrictive in terms of statistical independence assumptions imposed on the underlying joint data distribution, and second, it allows for all variables in the observed sample to have missing values. This MNAR model corresponds to a so-called criss-cross structure considered in the literature on graphical models of missing data that prevents nonparametric identification of the entire missing data model. Nonetheless, part of the complete-data distribution remains nonparametrically identifiable. By exploiting this fact and considering a rich class of exponential family distributions, we establish sufficient conditions for identification of the complete-data distribution as well as the entire missingness mechanism. We then propose methods for testing the independence restrictions encoded in such models using odds ratio as our parameter of interest. We adopt two semiparametric approaches for estimating the odds ratio parameter and establish the corresponding asymptotic theories: one involves maximizing a conditional likelihood with order statistics and the other uses estimating equations. The utility of our methods is illustrated via simulation studies.},
	articleno    = 73,
	numpages     = 11,
	bdsk-url-1   = {https://proceedings.mlr.press/v216/guo23a/guo23a.pdf}
}
@inproceedings{NeuripsCorrea,
	title        = {General Transportability of Soft Interventions: Completeness Results},
	author       = {Correa, Juan and Bareinboim, Elias},
	year         = 2020,
	booktitle    = {Advances in Neural Information Processing Systems},
	publisher    = {Curran Associates, Inc.},
	volume       = 33,
	pages        = {10902--10912},
	url          = {https://papers.nips.cc/paper/2020/hash/7b497aa1b2a83ec63d1777a88676b0c2-Abstract.html},
	editor       = {H. Larochelle and M. Ranzato and R. Hadsell and M.F. Balcan and H. Lin}
}
@article{newey1994asymptotic,
	title        = {The asymptotic variance of semiparametric estimators},
	author       = {Newey, Whitney},
	year         = 1994,
	journal      = {Econometrica: Journal of the Econometric Society},
	publisher    = {Jstor},
	pages        = {1349--1382}
}
@article{Neyman1923,
	title        = {Sur les applications de la th{\'e}orie des probabilit{\'e}s aux exp{\'e}riences agricoles: Essai des principes},
	author       = {Neyman, Jerzy},
	year         = 1923,
	journal      = {Statistical Science},
	volume       = 5,
	pages        = {463--472},
	note         = {Master's Thesis. Excerpts reprinted in English in \textit{Statistical Science}, Vol. 5, pp. 463--472. Translated by D. M. Dabrowska and T. P. Speed},
	translator   = {Dabrowska, D. M. and Speed, T. P.}
}
@article{nonmed2013,
	title        = {Nonpharmacological Interventions for {ADHD}: Systematic Review and Meta-Analyses of Randomized Controlled Trials of Dietary and Psychological Treatments},
	author       = {Sonuga-Barke, Edmund and Brandeis, Daniel and Cortese, Samuele and Daley, David and Ferrin, Maite and Holtmann, Martin and Stevenson, Jim and Danckaerts, Marina and {van der Oord}, Saskia and D\"{o}pfner, Manfred and Dittmann, Ralf and Simonoff, Emily and Zuddas, Alessandro and Banaschewski, Tobias and Buitelaar, Jan and Coghill, David and Hollis, Chris and Konofal, Eric and Lecendreux, Michel and Wong, Ian and Sergeant, Joseph},
	year         = 2013,
	journal      = {American Journal of Psychiatry},
	volume       = 170,
	number       = 3,
	pages        = {275--289},
	doi          = {10.1176/appi.ajp.2012.12070991},
	url          = {https://doi.org/10.1176/appi.ajp.2012.12070991},
	note         = {Pmid: 23360949},
	eprint       = {https://doi.org/10.1176/appi.ajp.2012.12070991},
	abstract     = {A meta-analytic review of six types of nonpharmacological interventions, including dietary and psychological treatments, for children with ADHD found positive effects on ADHD symptoms for all types when raters were aware of treatment allocation (unblinded conditions). However, when raters were blinded, statistically significant effects on ADHD symptoms were found only for supplementation with omega-3/omega-6 free fatty acids or elimination of artificial food colorings, effects that were small or restricted to food-sensitive individuals.}
}
@article{nonmed2023,
	title        = {Non-pharmacological interventions for attention-deficit hyperactivity disorder in children and adolescents},
	author       = {Sibley, Margaret and Bruton, Alisha and Zhao, Xin and Johnstone, Jeanette and Mitchell, John and Hatsu, Irene and Arnold, Eugene and Basu, Hana and Levy, Laura and Vyas, Pooja and Macphee, Fiona and Gonzalez, Erin Schoenfelder and Kelley, Megan and Jusko, Morgan and Bolden, China and Zulauf-McCurdy, Courtney and Manzano, Maychelle and Torres, Gabriela},
	year         = 2023,
	journal      = {The Lancet Child \& Adolescent Health},
	publisher    = {Elsevier},
	volume       = 7,
	number       = 6,
	pages        = {415--428},
	doi          = {10.1016/s2352-4642(22)00381-9},
	url          = {https://doi.org/10.1016/S2352-4642(22)00381-9},
	annote       = {doi: 10.1016/S2352-4642(22)00381-9},
	date         = {2023-06-01},
	date-added   = {2025-01-02 11:22:14 +0100},
	date-modified = {2025-01-02 11:22:14 +0100},
	type         = {doi: 10.1016/S2352-4642(22)00381-9},
	year1        = 2023,
	bdsk-url-1   = {https://doi.org/10.1016/S2352-4642(22)00381-9}
}
@article{nonuniqueLuedtke,
	title        = {Statistical inference for the mean outcome under a possibly non-unique optimal treatment strategy},
	author       = {Luedtke, Alexander and {van der Laan}, Mark},
	year         = 2016,
	journal      = {Annals of statistics},
	publisher    = {NIH Public Access},
	volume       = 44,
	number       = 2,
	pages        = 713
}
@article{nuisanceModels,
	title        = {The Costs and Benefits of Uniformly Valid Causal Inference with High-Dimensional Nuisance Parameters},
	author       = {Niloofar Moosavi and Jenny H{\"a}ggstr{\"o}m and Xavier {de Luna}},
	year         = 2023,
	journal      = {Statistical Science},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 38,
	number       = 1,
	pages        = {1 -- 12},
	doi          = {10.1214/21-sts843},
	url          = {https://doi.org/10.1214/21-STS843},
	keywords     = {double robustness, machine learning, post-model selection inference, regularization, superefficiency},
	bdsk-url-1   = {https://doi.org/10.1214/21-STS843}
}
@inproceedings{Oberst2019,
	title        = {Counterfactual off-policy evaluation with gumbel-max structural causal models},
	author       = {Oberst, Michael and Sontag, David},
	year         = 2019,
	booktitle    = {International Conference on Machine Learning},
	pages        = {4881--4890},
	organization = {Pmlr}
}
@article{oracle,
	title        = {Asymptotics of cross-validated risk estimation in estimator selection and performance assessment},
	author       = {Sandrine Dudoit and Mark {van der Laan}},
	year         = 2005,
	journal      = {Statistical Methodology},
	volume       = 2,
	number       = 2,
	pages        = {131--154},
	doi          = {https://doi.org/10.1016/j.stamet.2005.02.003},
	issn         = {1572-3127},
	url          = {https://www.sciencedirect.com/science/article/pii/S1572312705000158},
	abstract     = {Risk estimation is an important statistical question for the purposes of selecting a good estimator (i.e., model selection) and assessing its performance (i.e., estimating generalization error). This article introduces a general framework for cross-validation and derives distributional properties of cross-validated risk estimators in the context of estimator selection and performance assessment. Arbitrary classes of estimators are considered, including density estimators and predictors for both continuous and polychotomous outcomes. Results are provided for general full data loss functions (e.g., absolute and squared error, indicator, negative log density). A broad definition of cross-validation is used in order to cover leave-one-out cross-validation, V-fold cross-validation, Monte Carlo cross-validation, and bootstrap procedures. For estimator selection, finite sample risk bounds are derived and applied to establish the asymptotic optimality of cross-validation, in the sense that a selector based on a cross-validated risk estimator performs asymptotically as well as an optimal oracle selector based on the risk under the true, unknown data generating distribution. The asymptotic results are derived under the assumption that the size of the validation sets converges to infinity and hence do not cover leave-one-out cross-validation. For performance assessment, cross-validated risk estimators are shown to be consistent and asymptotically linear for the risk under the true data generating distribution and confidence intervals are derived for this unknown risk. Unlike previously published results, the theorems derived in this and our related articles apply to general data generating distributions, loss functions (i.e., parameters), estimators, and cross-validation procedures.},
	keywords     = {Asymptotic linearity, Asymptotic optimality, Classification, Confidence interval, Cross-validation, Density estimation, Estimator selection, Generalization error, Indicator loss function, Loss function, loss function, Model selection, Multifold cross-validation, Performance assessment, Prediction, Quadratic loss function, Regression, Resubstitution estimator, Risk},
	bdsk-url-1   = {https://www.sciencedirect.com/science/article/pii/S1572312705000158},
	bdsk-url-2   = {https://doi.org/10.1016/j.stamet.2005.02.003}
}
@inproceedings{originalIDalgorithm,
	title        = {Identification of conditional interventional distributions},
	author       = {Shpitser, Ilya and Pearl, Judea},
	year         = 2006,
	booktitle    = {Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence},
	location     = {Cambridge, MA, USA},
	publisher    = {AUAI Press},
	address      = {Arlington, Virginia, USA},
	series       = {Uai'06},
	pages        = {437–444},
	isbn         = {0974903922},
	abstract     = {The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting distributions on post-action outcomes given a set of measurements. We provide a necessary and sufficient graphical condition for the cases where such distributions can be uniquely computed from the available information, as well as an algorithm which performs this computation whenever the condition holds. Furthermore, we use our results to prove completeness of do-calculus [Pearl, 1995] for the same identification problem, and show applications to sequential decision making.},
	numpages     = 8
}
@article{Oset,
	title        = {Complete Graphical Characterization and Construction of Adjustment Sets in {M}arkov Equivalence Classes of Ancestral Graphs},
	author       = {Perkovic, Emilija and Textor, Johannes and Kalisch, Markus and Maathuis, Marloes},
	year         = 2018,
	journal      = {Journal of Machine Learning Research},
	publisher    = {JMLR.org},
	volume       = 18,
	number       = 1,
	pages        = {8132--8193},
	issn         = {1532-4435},
	abstract     = {We present a graphical criterion for covariate adjustment that is sound and complete for four different classes of causal graphical models: directed acyclic graphs (DAGs), maximal ancestral graphs (MAGs), completed partially directed acyclic graphs (CPDAGs), and partial ancestral graphs (PAGs). Our criterion unifies covariate adjustment for a large set of graph classes. Moreover, we define an explicit set that satisfies our criterion, if there is any set that satisfies our criterion. We also give efficient algorithms for constructing all sets that fulfill our criterion, implemented in the R package dagitty. Finally, we discuss the relationship between our criterion and other criteria for adjustment, and we provide new soundness and completeness proofs for the adjustment criterion for DAGs.},
	keywords     = {latent variables, covariate adjustment, causal effects, graphical models, confounding},
	numpages     = 62
}
@article{Oset2,
	title        = {On Efficient Adjustment in Causal Graphs},
	author       = {Witte, Janine and Henckel, Leonard and Maathuis, Marloes and Didelez, Vanessa},
	year         = 2020,
	month        = 1,
	journal      = {J. Mach. Learn. Res.},
	publisher    = {JMLR.org},
	volume       = 21,
	number       = 1,
	issn         = {1532-4435},
	abstract     = {We consider estimation of a total causal effect from observational data via covariate adjustment. Ideally, adjustment sets are selected based on a given causal graph, reflecting knowledge of the underlying causal structure. Valid adjustment sets are, however, not unique. Recent research has introduced a graphical criterion for an 'optimal' valid adjustment set (O-set). For a given graph, adjustment by the O-set yields the smallest asymptotic variance compared to other adjustment sets in certain parametric and non-parametric models. In this paper, we provide three new results on the O-set. First, we give a novel, more intuitive graphical characterisation: We show that the O-set is the parent set of the outcome node(s) in a suitable latent projection graph, which we call the forbidden projection. An important property is that the forbidden projection preserves all information relevant to total causal effect estimation via covariate adjustment, making it a useful methodological tool in its own right. Second, we extend the existing IDA algorithm to use the O-set, and argue that the algorithm remains semi-local. This is implemented in the R-package pcalg. Third, we present assumptions under which the O-set can be viewed as the target set of popular non-graphical variable selection algorithms such as stepwise backward selection.},
	articleno    = 246,
	issue_date   = {January 2020},
	keywords     = {causal discovery, sufficient adjustment set, model selection, IDA algorithm, graphical models, efficiency, confounding, confounder selection, causal inference},
	numpages     = 45
}
@misc{oslo2010exemption,
	title        = {Bruk av fritaksbestemmelsene ved nasjonale pr\o ver - konsekvenser for styringsinformasjon om skolene i Oslo. Kommunerevisjonen. [{Use of the exemption provisions by National tests - implications for management information on schools in Oslo. Municipal audit.}]},
	author       = {{Oslo Kommune}},
	year         = 2010,
	url          = {https://www.nkrf.no/filarkiv/File/Alle\%5Frapporter\%5Fi\%5Fpdf/Oslo\%5Fkommunerevisjon/Nasjonale\%5Fproever\%5F-\%5Fbruk\%5Fav\%5Ffritaksbestemmelsene.pdf},
	bdsk-url-1   = {https://www.nkrf.no/filarkiv/File/Alle_rapporter_i_pdf/Oslo_kommunerevisjon/Nasjonale_proever_-_bruk_av_fritaksbestemmelsene.pdf}
}
@article{ours,
    url = {https://doi.org/10.1515/jci-2024-0009},
    title = {Recovery and inference of causal effects with sequential adjustment for confounding and attrition},
	author       = {Johan {de Aguas} and Johan Pensar and Tom{\'a}s {Varnet P{\'e}rez} and Guido Biele},
    pages = {20240009},
    volume = {13},
    number = {1},
    journal = {Journal of Causal Inference},
    doi = {doi:10.1515/jci-2024-0009},
    year = {2025},
    lastchecked = {2025-05-20}
}
@article{over1,
	title        = {Overadjustment Bias and Unnecessary Adjustment in Epidemiologic Studies},
	author       = {Enrique Schisterman and Stephen Cole and Robert Platt},
	year         = 2009,
	journal      = {Epidemiology},
	publisher    = {Lippincott Williams and Wilkins},
	volume       = 20,
	number       = 4,
	pages        = {488--495},
	issn         = 10443983,
	url          = {http://www.jstor.org/stable/25662692},
	urldate      = {2024-08-26},
	abstract     = {Overadjustment is defined inconsistently. This term is meant to describe control (eg, by regression adjustment, stratification, or restriction) for a variable that either increases net bias or decreases precision without affecting bias. We define overadjustment bias as control for an intermediate variable (or a descending proxy for an intermediate variable) on a causal path from exposure to outcome. We define unnecessary adjustment as control for a variable that does not affect bias of the causal relation between exposure and outcome but may affect its precision. We use causal diagrams and an empirical example (the effect of maternal smoking on neonatal mortality) to illustrate and clarify the definition of overadjustment bias, and to distinguish overadjustment bias from unnecessary adjustment. Using simulations, we quantify the amount of bias associated with overadjustment. Moreover, we show that this bias is based on a different causal structure from confounding or selection biases. Overadjustment bias is not a finite sample bias, while inefficiencies due to control for unnecessary variables are a function of sample size.},
	bdsk-url-1   = {http://www.jstor.org/stable/25662692}
}
@article{over2,
	title        = {Commentary: On the Relative Nature of Overadjustment and Unnecessary Adjustment},
	author       = {Tyler VanderWeele},
	year         = 2009,
	journal      = {Epidemiology},
	publisher    = {Lippincott Williams and Wilkins},
	volume       = 20,
	number       = 4,
	pages        = {496--499},
	issn         = 10443983,
	url          = {http://www.jstor.org/stable/25662693},
	urldate      = {2024-08-26},
	bdsk-url-1   = {http://www.jstor.org/stable/25662693}
}
@article{over3,
	title        = {To Adjust or Not to Adjust? When a ``Confounder''Is Only Measured After Exposure},
	author       = {Groenwold, Rolf and Palmer, Tom and Tilling, Kate},
	year         = 2021,
	journal      = {Epidemiology},
	volume       = 32,
	number       = 2,
	url          = {https://journals.lww.com/epidem/fulltext/2021/03000/to\%5Fadjust\%5For\%5Fnot\%5Fto\%5Fadjust\%5F\%5Fwhen\%5Fa\%5F\%5Fconfounder\%5F\%5Fis.6.aspx},
	date-added   = {2024-08-26 16:24:00 +0200},
	date-modified = {2024-08-26 16:24:00 +0200},
	id           = {00001648-202103000-00006},
	keywords     = {Bias; Confounding; Mediation; Observational study},
	n2           = {Advice regarding the analysis of observational studies of exposure effects usually is against adjustment for factors that occur after the exposure, as they may be caused by the exposure (or mediate the effect of exposure on outcome), so potentially leading to collider stratification bias. However, such factors could also be caused by unmeasured confounding factors, in which case adjusting for them will also remove some of the bias due to confounding. We derive expressions for collider stratification bias when conditioning and confounding bias when not conditioning on the mediator, in the presence of unmeasured confounding (assuming that all associations are linear and there are no interactions). Using simulations, we show that generally neither the conditioned nor the unconditioned estimate is unbiased, and the trade-off between them depends on the magnitude of the effect of the exposure that is mediated relative to the effect of the unmeasured confounders and their relations with the mediator. We illustrate the use of the bias expressions via three examples: neuroticism and mortality (adjusting for the mediator appears the least biased option), glycated hemoglobin levels and systolic blood pressure (adjusting gives smaller bias), and literacy in primary school pupils (not adjusting gives smaller bias). Our formulae and simulations can inform quantitative bias analysis as well as analysis strategies for observational studies in which there is a potential for unmeasured confounding.},
	bdsk-url-1   = {https://journals.lww.com/epidem/fulltext/2021/03000/to_adjust_or_not_to_adjust__when_a__confounder__is.6.aspx}
}
@article{partialBayesian,
	title        = {Bayesian inference in a class of partially identified models},
	author       = {Kline, Brendan and Tamer, Elie},
	year         = 2016,
	journal      = {Quantitative Economics},
	volume       = 7,
	number       = 2,
	pages        = {329--366},
	doi          = {https://doi.org/10.3982/QE399},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.3982/QE399},
	abstract     = {This paper develops a Bayesian approach to inference in a class of partially identified econometric models. Models in this class are characterized by a known mapping between a point identified reduced-form parameter \ensuremath{\mu} and the identified set for a partially identified parameter \texttheta{}. The approach maps posterior inference about \ensuremath{\mu} to various posterior inference statements concerning the identified set for \texttheta{}, without the specification of a prior for \texttheta{}. Many posterior inference statements are considered, including the posterior probability that a particular parameter value (or a set of parameter values) is in the identified set. The approach applies also to functions of \texttheta{}. The paper develops general results on large sample approximations, which illustrate how the posterior probabilities over the identified set are revised by the data, and establishes conditions under which the Bayesian credible sets also are valid frequentist confidence sets. The approach is computationally attractive even in high-dimensional models, in that the approach avoids an exhaustive search over the parameter space. The performance of the approach is illustrated via Monte Carlo experiments and an empirical application to a binary entry game involving airlines.},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.3982/QE399},
	keywords     = {Partial identification, identified set, criterion function, Bayesian inference, C10, C11},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.3982/QE399},
	bdsk-url-2   = {https://doi.org/10.3982/QE399}
}
@inproceedings{Pearl_NDE_2001,
	title        = {Direct and Indirect Effects},
	author       = {Pearl, Judea},
	year         = 2001,
	booktitle    = {Proceedings of the Seventeenth Conference on Uncertainty in Artificial Intelligence},
	location     = {Seattle, Washington},
	publisher    = {Morgan Kaufmann Publishers Inc.},
	address      = {San Francisco, CA, USA},
	series       = {Uai'01},
	pages        = {411--420},
	isbn         = 1558608001,
	abstract     = {The direct effect of one event on another can be defined and measured by holding constant all intermediate variables between the two. Indirect effects present conceptual and practical difficulties (in nonlinear models), because they cannot be isolated by holding certain variables constant. This paper presents a new way of defining the effect transmitted through a restricted set of paths, without controlling variables on the remaining paths. This permits the assessment of a more natural type of direct and indirect effects, one that is applicable in both linear and nonlinear models and that has broader policy-related interpretations. The paper establishes conditions under which such assessments can be estimated consistently from experimental and nonexperimental data, and thus extends path-analytic techniques to nonlinear and nonparametric models.},
	numpages     = 10
}
@article{Pearl_NDE_2014,
	title        = {Interpretation and Identification of Causal Mediation},
	author       = {Pearl, Judea},
	year         = 2014,
	month        = {06},
	journal      = {Psychological methods},
	volume       = 19,
	doi          = {10.1037/a0036434},
	bdsk-url-1   = {https://doi.org/10.1037/a0036434}
}
@inbook{Pearl_NDE_2022,
	title        = {Direct and Indirect Effects},
	author       = {Pearl, Judea},
	year         = 2022,
	booktitle    = {Probabilistic and Causal Inference: The Works of Judea Pearl},
	publisher    = {Association for Computing Machinery},
	address      = {New York, NY, USA},
	pages        = {373--392},
	isbn         = 9781450395861,
	url          = {https://doi.org/10.1145/3501714.3501736},
	edition      = 1,
	numpages     = 20,
	bdsk-url-1   = {https://doi.org/10.1145/3501714.3501736}
}
@book{pearl1988probabilistic,
	title        = {Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference},
	author       = {Pearl, Judea},
	year         = 1988,
	publisher    = {Morgan Kaufmann},
	address      = {San Mateo, CA}
}
@article{Pearl1995,
	title        = {Causal Diagrams for Empirical Research},
	author       = {Judea Pearl},
	year         = 1995,
	journal      = {Biometrika},
	publisher    = {[Oxford University Press, Biometrika Trust]},
	volume       = 82,
	number       = 4,
	pages        = {669--688},
	issn         = {00063444},
	url          = {http://www.jstor.org/stable/2337329},
	urldate      = {2023-06-02},
	abstract     = {The primary aim of this paper is to show how graphical models can be used as a mathematical language for integrating statistical and subject-matter information. In particular, the paper develops a principled, nonparametric framework for causal inference, in which diagrams are queried to determine if the assumptions available are sufficient for identifying causal effects from nonexperimental data. If so the diagrams can be queried to produce mathematical expressions for causal effects in terms of observed distributions; otherwise, the diagrams can be queried to suggest additional observations or auxiliary experiments from which the desired inferences can be obtained.},
	bdsk-url-1   = {http://www.jstor.org/stable/2337329}
}
@inproceedings{pearl2010class,
	title        = {On a class of bias-amplifying variables that endanger effect estimates},
	author       = {Pearl, Judea},
	year         = 2010,
	booktitle    = {Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence},
	pages        = {417--424}
}
@inproceedings{Pearl2013simple,
	title        = {A simple criterion for controlling selection bias},
	author       = {Chen, Eunice and Pearl, Judea},
	year         = 2013,
	month        = 4,
	booktitle    = {Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics},
	publisher    = {Pmlr},
	address      = {Scottsdale, Arizona, USA},
	series       = {Proceedings of Machine Learning Research},
	volume       = 31,
	pages        = {170--177},
	url          = {https://proceedings.mlr.press/v31/chen13b.html},
	abstract     = {Controlling selection bias, a statistical error caused by preferential sampling of data, is a fundamental problem in machine learning and statistical inference. This paper presents a simple criterion for controlling selection bias in the odds ratio, a widely used measure for association between variables, that connects the nature of selection bias with the graph modeling the selection mechanism. If the graph contains certain paths, we show that the odds ratio cannot be expressed using data with selection bias. Otherwise, we show that a d-separability test can determine whether the odds ratio can be recovered, and when the answer is affirmative, output an unbiased estimand of the odds ratio. The criterion can be test in linear time and enhances the power of the estimand.},
	editor       = {Carvalho, Carlos M. and Ravikumar, Pradeep},
	pdf          = {http://proceedings.mlr.press/v31/chen13b.pdf},
	bdsk-url-1   = {https://proceedings.mlr.press/v31/chen13b.html}
}
@book{pearl2018book,
	title        = {The Book of Why: The New Science of Cause and Effect},
	author       = {Pearl, Judea and Mackenzie, Dana},
	year         = 2018,
	publisher    = {Basic Books},
	address      = {New York},
	isbn         = {978-0465097609}
}
@article{Pearl7Tools,
	title        = {The Seven Tools of Causal Inference, with Reflections on Machine Learning},
	author       = {Pearl, Judea},
	year         = 2019,
	month        = {feb},
	journal      = {Commun. ACM},
	publisher    = {Association for Computing Machinery},
	address      = {New York, NY, USA},
	volume       = 62,
	number       = 3,
	pages        = {54--60},
	doi          = {10.1145/3241036},
	issn         = {0001-0782},
	url          = {https://doi.org/10.1145/3241036},
	abstract     = {The kind of causal inference seen in natural human thought can be "algorithmitized" to help produce human-level machine intelligence.},
	issue_date   = {March 2019},
	numpages     = 7,
	bdsk-url-1   = {https://doi.org/10.1145/3241036}
}
@book{PearlCausality,
	title        = {Causality},
	author       = {Pearl, Judea},
	year         = 2009,
	publisher    = {Cambridge University Press},
	address      = {Cambridge, UK},
	doi          = {10.1017/cbo9780511803161},
	isbn         = {978-0-521-89560-6},
	abstract     = {Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations. Cited in more than 2,100 scientific publications, it continues to liberate scientists from the traditional molds of statistical thinking. In this revised edition, Judea Pearl elucidates thorny issues, answers readers' questions, and offers a panoramic view of recent advances in this field of research.},
	added-at     = {2018-09-17t16:24:20.000+0200},
	biburl       = {https://www.bibsonomy.org/bibtex/2378bd006b231f81cddd091429ceb0f80/flint63},
	edition      = 2,
	file         = {2009/Pearl09.pdf},
	interhash    = {e7828b9bdefba2511eb63114c0c32b1b},
	intrahash    = {378bd006b231f81cddd091429ceb0f80},
	isbn10       = {052189560x},
	keywords     = {01901 103 ai algorithm book knowledge numerical processing theory},
	language     = {american},
	owner        = {flint},
	sortdate     = {2009-12-01},
	subtitle     = {Models, Reasoning, and Inference},
	timestamp    = {2018-09-17t16:24:20.000+0200},
	bdsk-url-1   = {https://doi.org/10.1017/CBO9780511803161}
}
@inproceedings{PearlDo,
	title        = {The Do-Calculus Revisited},
	author       = {Pearl, Judea},
	year         = 2012,
	booktitle    = {Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence},
	location     = {Catalina Island, CA},
	publisher    = {AUAI Press},
	address      = {Arlington, Virginia, USA},
	series       = {Uai'12},
	pages        = {3--11},
	isbn         = 9780974903989,
	abstract     = {The do-calculus was developed in 1995 to facilitate the identification of causal effects in non-parametric models. The completeness proofs of [Huang and Valtorta, 2006] and [Shpitser and Pearl, 2006] and the graphical criteria of [Tian and Shpitser, 2010] have laid this identification problem to rest. Recent explorations unveil the usefulness of the do-calculus in three additional areas: mediation analysis [Pearl, 2012], transportability [Pearl and Bareinboim, 2011] and meta-synthesis. Meta-synthesis (freshly coined) is the task of fusing empirical results from several diverse studies, conducted on heterogeneous populations and under different conditions, so as to synthesize an estimate of a causal relation in some target environment, potentially different from those under study. The talk surveys these results with emphasis on the challenges posed by meta-synthesis. For background material, see (http://bayes.cs.ucla.edu/csl_papers.html).},
	numpages     = 9
}
@inproceedings{pearlGeneralID,
	title        = {A General Identification Condition for Causal Effects},
	author       = {Tian, Jin and Pearl, Judea},
	year         = 2002,
	booktitle    = {Eighteenth National Conference on Artificial Intelligence},
	location     = {Edmonton, Alberta, Canada},
	publisher    = {American Association for Artificial Intelligence},
	address      = {Usa},
	pages        = {567--573},
	isbn         = {0262511290},
	abstract     = {This paper concerns the assessment of the effects of actions or policy interventions from a combination of: (i) nonexperimental data, and (ii) substantive assumptions. The assumptions are encoded in the form of a directed acyclic graph, also called "causal graph", in which some variables are presumed to be unobserved. The paper establishes a necessary and sufficient criterion for the identifiability of the causal effects of a singleton variable on all other variables in the model, and a powerful sufficient criterion for the effects of a singleton variable on any set of variables.},
	numpages     = 7
}
@book{PearlPrimer,
	title        = {Causal inference in statistics: a primer},
	author       = {Pearl, Judea},
	year         = 2016,
	booktitle    = {Causal inference in statistics: a primer},
	publisher    = {Wiley},
	address      = {Chichester, West Sussex},
	isbn         = 9781119186847,
	keywords     = {Causation},
	language     = {eng},
	lccn         = 2015033010
}
@article{PearlPT,
	title        = {Conditioning on Post-treatment Variables},
	author       = {Judea Pearl},
	year         = 2015,
	journal      = {Journal of Causal Inference},
	volume       = 3,
	number       = 1,
	pages        = {131--137},
	doi          = {doi:10.1515/jci-2015-0005},
	url          = {https://doi.org/10.1515/jci-2015-0005},
	lastchecked  = {2023-11-06},
	bdsk-url-1   = {https://doi.org/10.1515/jci-2015-0005}
}
@inproceedings{PearlRobins,
	title        = {Probabilistic Evaluation of Sequential Plans from Causal Models with Hidden Variables},
	author       = {Pearl, Judea and Robins, James},
	year         = 1995,
	booktitle    = {Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence},
	location     = {Montr\'{e}al, Qu\'{e}, Canada},
	publisher    = {Morgan Kaufmann Publishers Inc.},
	address      = {San Francisco, CA, USA},
	series       = {Uai'95},
	pages        = {444--453},
	isbn         = 1558603859,
	abstract     = {The paper concerns the probabilistic evaluation of plans in the presence of unmeasured variables, each plan consisting of several concurrent or sequential actions. We establish a graphical criterion for recognizing when the effects of a given plan can be predicted from passive observations on measured variables only. When the criterion is satisfied, a closed-form expression is provided for the probability that the plan will achieve a specified goal.},
	keywords     = {graphical models, sequential treatments, causal diagrams, causal effect, plan evaluation},
	numpages     = 10
}
@article{pelham2022effect,
	title        = {The effect of stimulant medication on the learning of academic curricula in children with {ADHD}: A randomized crossover study.},
	author       = {Pelham, William and Altszuler, Amy and Merrill, Brittany and Raiker, Joseph and Macphee, Fiona and Ramos, Marcela and Gnagy, Elizabeth and Greiner, Andrew and Coles, Erika and Connor, Carol and others},
	year         = 2022,
	journal      = {Journal of consulting and clinical psychology},
	publisher    = {American Psychological Association},
	volume       = 90,
	number       = 5,
	pages        = 367
}
@article{pena2023bounding,
	title        = {Bounding the probabilities of benefit and harm through sensitivity parameters and proxies},
	author       = {Pe{\~n}a, Jos{\'e}},
	year         = 2023,
	journal      = {Journal of Causal Inference},
	publisher    = {De Gruyter},
	volume       = 11,
	number       = 1,
	pages        = 20230012
}
@article{Pensar2015,
	title        = {Labeled directed acyclic graphs: a generalization of context-specific independence in directed graphical models},
	author       = {Pensar, Johan and Nyman, Henrik and Koski, Timo and Corander, Jukka},
	year         = 2015,
	journal      = {Data Mining and Knowledge Discovery},
	volume       = 29,
	number       = 2,
	pages        = {503--533},
	doi          = {10.1007/s10618-014-0355-0},
	url          = {https://doi.org/10.1007/s10618-014-0355-0},
	abstract     = {We introduce a novel class of labeled directed acyclic graph (LDAG) models for finite sets of discrete variables. LDAGs generalize earlier proposals for allowing local structures in the conditional probability distribution of a node, such that unrestricted label sets determine which edges can be deleted from the underlying directed acyclic graph (DAG) for a given context. Several properties of these models are derived, including a generalization of the concept of Markov equivalence classes. Efficient Bayesian learning of LDAGs is enabled by introducing an LDAG-based factorization of the Dirichlet prior for the model parameters, such that the marginal likelihood can be calculated analytically. In addition, we develop a novel prior distribution for the model structures that can appropriately penalize a model for its labeling complexity. A non-reversible Markov chain Monte Carlo algorithm combined with a greedy hill climbing approach is used for illustrating the useful properties of LDAG models for both real and synthetic data sets.},
	id           = {Pensar2015},
	bdsk-url-1   = {https://doi.org/10.1007/s10618-014-0355-0}
}
@phdthesis{phd,
	title        = {Various approaches to deal with missing data when estimating causal effects with targeted maximum likelihood estimation},
	author       = {Christoph Wiederkehr},
	year         = 2023,
	series       = {Department of Statistics: Technical Reports (Master Thesis)},
	url          = {https://epub.ub.uni-muenchen.de/107264/},
	school       = {Ludwig Maximilian University of Munich},
	bdsk-url-1   = {https://epub.ub.uni-muenchen.de/107264/}
}
@phdthesis{phd2,
	title        = {Selection into the Sample and into Treatment: Tools for Internally Valid Causal Inference},
	author       = {Adam Rohde},
	year         = 2023,
    school       = {University of California in Los Angeles},
	series       = {{UCLA} Electronic Theses and Dissertations},
	url          = {https://escholarship.org/uc/item/5z86z6jm},
	bdsk-url-1   = {https://escholarship.org/uc/item/5z86z6jm}
}
@article{policyAsym,
	title        = {Policy Learning with Asymmetric Counterfactual Utilities},
	author       = {Eli Ben-Michael, Kosuke Imai and Zhichao Jiang},
	year         = 2024,
	journal      = {Journal of the American Statistical Association},
	publisher    = {Taylor \& Francis},
	volume       = {0},
	number       = {0},
	pages        = {1--14},
	doi          = {10.1080/01621459.2023.2300507},
	url          = {https://doi.org/10.1080/01621459.2023.2300507},
	eprint       = {https://doi.org/10.1080/01621459.2023.2300507},
	bdsk-url-1   = {https://doi.org/10.1080/01621459.2023.2300507}
}
@phdthesis{Ponomarev,
	title        = {Essays in Econometrics},
	author       = {Ponomarev, Kirill},
	year         = 2022,
    school       = {University of California in Los Angeles},
	series       = {{UCLA} Electronic Theses and Dissertations},
	url          = {https://escholarship.org/uc/item/1kz2n299},
	bdsk-url-1   = {https://escholarship.org/uc/item/1kz2n299}
}
@article{possebom2022,
	title        = {Probability of Causation with Sample Selection: A Reanalysis of the Impacts of {J\'ovenes en Acci\'on} on Formality},
	author       = {Possebom, Vitor and Riva, Flavio},
	year         = 2022,
	journal      = {arXiv preprint arXiv:2210.01938}
}
@article{probcausation,
	title        = {Probabilities Of Causation: Three Counterfactual Interpretations And Their Identification},
	author       = {Pearl, Judea},
	year         = 1999,
	journal      = {Synthese},
	volume       = 121,
	number       = 1,
	pages        = {93--149},
	doi          = {10.1023/a:1005233831499},
	url          = {https://doi.org/10.1023/A:1005233831499},
	abstract     = {According to common judicial standard, judgment in favor ofplaintiff should be made if and only if it is ``more probable than not''thatthe defendant's action was the cause for the plaintiff's damage (or death). This paper provides formal semantics, based on structural models ofcounterfactuals, for the probability that event x was a necessary orsufficient cause (or both) of another event y. The paper then explicates conditions under which the probability of necessary (or sufficient)causation can be learned from statistical data, and shows how data fromboth experimental and nonexperimental studies can be combined to yieldinformation that neither study alone can provide. Finally, we show thatnecessity and sufficiency are two independent aspects of causation, andthat both should be invoked in the construction of causal explanations for specific scenarios.},
	date         = {1999-11-01},
	date-added   = {2024-02-03},
	date-modified = {2024-02-03},
	id           = {Pearl1999},
	bdsk-url-1   = {https://doi.org/10.1023/A:1005233831499}
}
@article{pryce2024causal,
	title        = {Causal machine learning for heterogeneous treatment effects in the presence of missing outcome data},
	author       = {Pryce, Matthew and D\'{\i}az-Ordaz, Karla and Keogh, Ruth and Vansteelandt, Stijn},
	year         = 2024,
	journal      = {arXiv preprint arXiv:2412.19711}
}
@book{Puterman2014,
	title        = {{M}arkov decision processes: discrete stochastic dynamic programming},
	author       = {Puterman, Martin L},
	year         = 2014,
	publisher    = {John Wiley and Sons},
	added-at     = {2017-04-07t12:13:11.000+0200},
	biburl       = {https://www.bibsonomy.org/bibtex/22e7ac99cd30c4892171e5a7cef1bc7a7/becker},
	interhash    = {6cec8f775a265d8741171d17e4a4e7d0},
	intrahash    = {2e7ac99cd30c4892171e5a7cef1bc7a7},
	keywords     = {inthesis diss {M}arkov chain decision process citedby:scholar:count:9594 citedby:scholar:timestamp:2017-4-7},
	timestamp    = {2017-04-07t12:13:11.000+0200}
}
@article{radicalEmp,
	title        = {Radical Empiricism and Machine Learning Research},
	author       = {Judea Pearl},
	year         = 2021,
	journal      = {Journal of Causal Inference},
	publisher    = {De Gruyter},
	volume       = 9,
	number       = 1,
	pages        = {78--82},
	doi          = {10.1515/jci-2021-0006}
}
@article{rcensoringTMLE,
	title        = {A Note on Targeted Maximum Likelihood and Right Censored Data},
	author       = {{van der Laan}, Mark  and Rubin, Daniel},
	year         = 2007,
	journal      = {Berkeley Division of Biostatistics Working Paper Series},
	volume       = {Working Paper 226},
	url          = {https://biostats.bepress.com/ucbbiostat/paper226},
	bdsk-url-1   = {https://biostats.bepress.com/ucbbiostat/paper226}
}
@misc{regulationseducationact2023,
	title        = {Forskrift til oppl{\ae}ringslova. Kapittel 2. Rapportering og evaluering av oppl{\ae}ringsverksemda [{Regulations for the Education Act. Chapter 2. Reporting and evaluation of educational activity}] [Revised 2023]},
	author       = {Kunnskapsdepartementet},
	year         = 2006,
	url          = {https://lovdata.no/dokument/SF/forskrift/2006-06-23-724/KAPITTEL\%5F4#%C2%A72-8},
	bdsk-url-1   = {https://lovdata.no/dokument/SF/forskrift/2006-06-23-724/KAPITTEL_4\#\%C2\%A72-8}
}
@article{retro,
	title        = {{Retrospective causal inference with multiple effect variables}},
	author       = {Wei Li and Zitong Lu and Jinzhu Jia and Min Xie and  Zhi Geng},
	year         = 2023,
	month        = {09},
	journal      = {Biometrika},
	volume       = 111,
	number       = 2,
	pages        = {573--589},
	doi          = {10.1093/biomet/asad056},
	issn         = {1464-3510},
	url          = {https://doi.org/10.1093/biomet/asad056},
	abstract     = {{As highlighted in Dawid (2000) and Pearl \\\&amp; Mackenzie (2018), deducing the causes of given effects is a more challenging problem than evaluating the effects of causes in causal inference. Lu et al. (2023) proposed an approach for deducing causes of a single effect variable based on posterior causal effects. In many applications, there are multiple effect variables, and they can be used simultaneously to more accurately deduce the causes. To retrospectively deduce causes from multiple effects, we propose multivariate posterior total, intervention and direct causal effects conditional on the observed evidence. We describe the assumptions of no confounding and monotonicity, under which we prove identifiability of the multivariate posterior causal effects and provide their identification equations. The proposed approach can be applied for causal attributions, medical diagnosis, blame and responsibility in various studies with multiple effect or outcome variables. Two examples are used to illustrate the proposed approach.}},
	eprint       = {https://academic.oup.com/biomet/article-pdf/111/2/573/57467431/asad056_supplementary_data.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/biomet/asad056}
}
@inproceedings{revisiting,
	title        = {Revisiting the general identifiability problem},
	author       = {Kivva, Yaroslav and Mokhtarian, Ehsan and Etesami, Jalal and Kiyavash, Negar},
	year         = 2022,
	month        = 8,
	booktitle    = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence},
	publisher    = {Pmlr},
	series       = {Proceedings of Machine Learning Research},
	volume       = 180,
	pages        = {1022--1030},
	url          = {https://proceedings.mlr.press/v180/kivva22a.html},
	abstract     = {We revisit the problem of general identifiability originally introduced in [Lee et al., 2019] for causal inference and note that it is necessary to add positivity assumption of observational distribution to the original definition of the problem. We show that without such an assumption the rules of do-calculus and consequently the proposed algorithm in [Lee et al., 2019] are not sound. Moreover, adding the assumption will cause the completeness proof in [Lee et al., 2019] to fail. Under positivity assumption, we present a new algorithm that is provably both sound and complete. A nice property of this new algorithm is that it establishes a connection between  general identifiability and classical identifiability by Pearl [1995] through decomposing the general identifiability problem into a series of classical identifiability  sub-problems.},
	editor       = {Cussens, James and Zhang, Kun},
	pdf          = {https://proceedings.mlr.press/v180/kivva22a/kivva22a.pdf},
	bdsk-url-1   = {https://proceedings.mlr.press/v180/kivva22a.html}
}
@article{Robins_1992,
	title        = {Identifiability and Exchangeability for Direct and Indirect Effects},
	author       = {James Robins and Sander Greenland},
	year         = 1992,
	journal      = {Epidemiology},
	publisher    = {Lippincott Williams and Wilkins},
	volume       = 3,
	number       = 2,
	pages        = {143--155},
	issn         = 10443983,
	url          = {http://www.jstor.org/stable/3702894},
	urldate      = {2023-03-24},
	abstract     = {We consider the problem of separating the direct effects of an exposure from effects relayed through an intermediate variable (indirect effects). We show that adjustment for the intermediate variable, which is the most common method of estimating direct effects, can be biased. We also show that, even in a randomized crossover trial of exposure, direct and indirect effects cannot be separated without special assumptions; in other words, direct and indirect effects are not separately identifiable when only exposure is randomized. If the exposure and intermediate never interact to cause disease and if intermediate effects can be controlled, that is, blocked by a suitable intervention, then a trial randomizing both exposure and the intervention can separate direct from indirect effects. Nonetheless, the estimation must be carried out using the G-computation algorithm. Conventional adjustment methods remain biased. When exposure and the intermediate interact to cause disease, direct and indirect effects will not be separable even in a trial in which both the exposure and the intervention blocking intermediate effects are randomly assigned. Nonetheless, in such a trial, one can still estimate the fraction of exposure-induced disease that could be prevented by control of the intermediate. Even in the absence of an intervention blocking the intermediate effect, the fraction of exposure-induced disease that could be prevented by control of the intermediate can be estimated with the G-computation algorithm if data are obtained on additional confounding variables.},
	bdsk-url-1   = {http://www.jstor.org/stable/3702894}
}
@article{robins1986gcomp,
	title        = {A new approach to causal inference in mortality studies with a sustained exposure period---application to control of the healthy worker survivor effect},
	author       = {Robins, James},
	year         = 1986,
	journal      = {Mathematical modelling},
	publisher    = {Elsevier},
	volume       = 7,
	number       = {9-12},
	pages        = {1393--1512}
}
@article{robins1992recovery,
	title        = {Recovery of information and adjustment for dependent censoring using surrogate markers, Aids Epidemiology, Methodological issues},
	author       = {Robins, James and Rotnitzky, Andrea},
	year         = 1992,
	journal      = {Proceedings of the American Statistical Association. Boston: Birkhauser},
	pages        = {24--33}
}
@article{Robins1994,
	title        = {Estimation of regression coefficients when some regressors are not always observed},
	author       = {Robins, James and Rotnitzky, Andrea and Zhao, Lue},
	year         = 1994,
	journal      = {Journal of the American Statistical Association},
	volume       = 89,
	number       = 427,
	pages        = {846--866}
}
@article{robins1995analysis,
	title        = {Analysis of semiparametric regression models for repeated outcomes in the presence of missing data},
	author       = {Robins, James and Rotnitzky, Andrea and Zhao, Lue},
	year         = 1995,
	journal      = {Journal of the American Statistical Association},
	publisher    = {Taylor \& Francis},
	volume       = 90,
	number       = 429,
	pages        = {106--121},
	doi          = {10.1080/01621459.1995.10476493}
}
@article{robins1997comment,
	title        = {Comment on the Bickel and Kwon article, `Inference for semiparametric models: Some questions and an answer'},
	author       = {Robins, James and Rotnitzky, Andrea},
	year         = 1997,
	journal      = {Statistica Sinica},
	publisher    = {Institute of Statistical Science, Academia Sinica},
	volume       = 7,
	number       = 1,
	pages        = {167--199}
}
@incollection{robins2004optimal,
	title        = {Optimal structural nested models for optimal sequential decisions},
	author       = {Robins, James},
	year         = 2004,
	booktitle    = {Proceedings of the Second Seattle Symposium in Biostatistics},
	publisher    = {Springer, New York},
	series       = {Lecture Notes in Statististics},
	pages        = {179--326},
	mr           = 2129402
}
@article{robins2007discussions,
	title        = {Discussions on" Principal Stratification Designs to Estimate Input Data Missing Due to Death"},
	author       = {Robins, James and Rotnitzky, Andrea and Vansteelandt, Stijn and Have, Tom and Xie, Yu and Murphy, Susan},
	year         = 2007,
	journal      = {Biometrics},
	publisher    = {Jstor},
	volume       = 63,
	number       = 3,
	pages        = {650--658}
}
@article{Robins89,
	title        = {The Probability of Causation under a Stochastic Model for Individual Risk},
	author       = {James Robins and Sander Greenland},
	year         = 1989,
	journal      = {Biometrics},
	publisher    = {[Wiley, International Biometric Society]},
	volume       = 45,
	number       = 4,
	pages        = {1125--1138},
	issn         = {0006341x, 15410420},
	url          = {http://www.jstor.org/stable/2531765},
	urldate      = {2024-02-03},
	abstract     = {In this paper we offer a mathematical definition for the probability of causation that formalizes the legal and ordinary-language meaning of the term. We show that, under this definition, even the average probability of causation among exposed cases is not identifiable from epidemiologic data. This is because the probability of causation depends both on the unknown mechanisms by which exposure affects disease risk and competing risks, and on the unknown degree of heterogeneity in the background disease risk of the exposed population. We derive the maximum and minimum values for the probability of causation consistent with the observable population quantities. We also derive the relationship of the "assigned share" (excess incidence rate as a proportion of total incidence rate) to the probability of causation.},
	bdsk-url-1   = {http://www.jstor.org/stable/2531765}
}
@article{robinsConsistency,
	title        = {The analysis of randomized and non-randomized AIDS treatment trials using a new approach to causal inference in longitudinal studies},
	author       = {James Robins},
	year         = 1989,
	journal      = {Health service research methodology: a focus on AIDS},
	publisher    = {US Public Health Service},
	pages        = {113--159}
}
@inbook{robinsDTR,
	title        = {Optimal Structural Nested Models for Optimal Sequential Decisions},
	author       = {Robins, James},
	year         = 2004,
	booktitle    = {Proceedings of the Second Seattle Symposium in Biostatistics: Analysis of Correlated Data},
	publisher    = {Springer New York},
	address      = {New York, NY},
	pages        = {189--326},
	doi          = {10.1007/978-1-4419-9076-1_11},
	isbn         = {978-1-4419-9076-1},
	url          = {https://doi.org/10.1007/978-1-4419-9076-1\%5F11},
	editor       = {Lin, D. Y. and Heagerty, P. J.},
	abstract     = {I describe two new methods for estimating the optimal treatment regime (equivalently, protocol, plan or strategy) from very high dimesional observational and experimental data: (i) g-estimation of an optimal double-regime structural nested mean model (drSNMM) and (ii) g-estimation of a standard single regime SNMM combined with sequential dynamic-programming (DP) regression. These methods are compared to certain regression methods found in the sequential decision and reinforcement learning literatures and to the regret modelling methods of Murphy (2003). I consider both Bayesian and frequentist inference. In particular, I propose a novel ``Bayes-frequentist compromise'' that combines honest subjective non- or semiparametric Bayesian inference with good frequentist behavior, even in cases where the model is so large and the likelihood function so complex that standard (uncompromised) Bayes procedures have poor frequentist performance.}
}
@book{rosenbaum2002observational,
	title        = {Observational Studies},
	author       = {Rosenbaum, P.},
	year         = 2002,
	publisher    = {Springer},
	address      = {New York}
}
@article{Rotnitzky,
	title        = {Efficient Adjustment Sets for Population Average Causal Treatment Effect Estimation in Graphical Models},
	author       = {Andrea Rotnitzky and Ezequiel Smucler},
	year         = 2020,
	journal      = {Journal of Machine Learning Research},
	volume       = 21,
	number       = 188,
	pages        = {1--86},
	url          = {http://jmlr.org/papers/v21/19-1026.html},
	bdsk-url-1   = {http://jmlr.org/papers/v21/19-1026.html}
}
@article{Rubin1976,
	title        = {Inference and missing data},
	author       = {Rubin, Donald},
	year         = 1976,
	journal      = {Biometrika},
	publisher    = {Oxford University Press},
	volume       = 63,
	number       = 3,
	pages        = {581--592}
}
@article{rubin74,
	title        = {Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies},
	author       = {Rubin, Donald},
	year         = 1974,
	journal      = {Journal of Educational Psychology},
	volume       = 66,
	number       = 5,
	pages        = {688--701},
	doi          = {10.1037/h0037350}
}
@book{RubinMIbook,
	title        = {Multiple Imputation for Nonresponse in Surveys},
	author       = {Rubin, Donald},
	year         = 1987,
	publisher    = {John Wiley and Sons}
}
@article{RubinMIpaper,
	title        = {Multiple imputations in sample surveys: a phenomenological {B}ayesian approach to nonresponse},
	author       = {Rubin, Donald},
	year         = 1978,
	journal      = {Journal of the American Statistical Association},
	publisher    = {Taylor and Francis},
	volume       = 73,
	number       = 362,
	pages        = {384--395}
}
@article{RubinObs,
	title        = {Should observational studies be designed to allow lack of balance in covariate distributions across treatment groups?},
	author       = {Rubin, Donald},
	year         = 2009,
	journal      = {Statistics in Medicine},
	volume       = 28,
	number       = 9,
	pages        = {1420--1423},
	doi          = {https://doi.org/10.1002/sim.3565},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1002/sim.3565},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/sim.3565}
}
@article{Rusell,
	title        = {Sharp Bounds on Functionals of the Joint Distribution in the Analysis of Treatment Effects},
	author       = {Thomas Russell},
	year         = 2021,
	journal      = {Journal of Business \& Economic Statistics},
	publisher    = {Taylor \& Francis},
	volume       = 39,
	number       = 2,
	pages        = {532--546},
	doi          = {10.1080/07350015.2019.1684300},
	url          = {https://doi.org/10.1080/07350015.2019.1684300},
	eprint       = {https://doi.org/10.1080/07350015.2019.1684300},
	bdsk-url-1   = {https://doi.org/10.1080/07350015.2019.1684300}
}
@inproceedings{saadati2019adjustment,
	title        = {Adjustment criteria for recovering causal effects from missing data},
	author       = {Saadati, Mojdeh and Tian, Jin},
	year         = 2019,
	booktitle    = {Joint European Conference on Machine Learning and Knowledge Discovery in Databases},
	pages        = {561--577},
	organization = {Springer}
}
@article{sant2023impact,
	title        = {Impact of adverse drug reactions on the outcomes of tuberculosis treatment},
	author       = {Sant'Anna, Fl{\`a}via and Ara{\'u}jo-Pereira, Mariana and Schmaltz, Carolina and Arriaga, Mar{\'\i}a and Andrade, Bruno and Rolla, Valeria},
	year         = 2023,
	journal      = {Plos one},
	publisher    = {Public Library of Science San Francisco, CA USA},
	volume       = 18,
	number       = 2,
	pages        = {e0269765}
}
@article{Sarvet2023,
	title        = {{Perspective on Harm in Personalized Medicine}},
	author       = {Sarvet, Aaron and Stensrud, Mats},
	year         = 2023,
	month        = {07},
	journal      = {American Journal of Epidemiology},
	pages        = {kwad162},
	doi          = {10.1093/aje/kwad162},
	issn         = {0002-9262},
	url          = {https://doi.org/10.1093/aje/kwad162},
	abstract     = {{Avoiding harm is an uncontroversial aim of personalized medicine and other epidemiologic initiatives. However, the precise mathematical translation of ``harm'' is disputable. Here we use a formal causal language to study common, but distinct, definitions of ``harm''. We clarify that commitment to a definition of harm has important practical and philosophical implications for decision making. We relate our practical and philosophical considerations to ideas from medical ethics and legal practice.}},
	eprint       = {https://academic.oup.com/aje/advance-article-pdf/doi/10.1093/aje/kwad162/50913986/kwad162.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/aje/kwad162}
}
@article{sarvet2024rejoinder,
	title        = {Rejoinder to" Perspectives on harm in personalized medicine--an alternative perspective"},
	author       = {Sarvet, Aaron and Stensrud, Mats},
	year         = 2024,
	journal      = {arXiv preprint arXiv:2403.14869}
}
@article{scalesNorway,
	title        = {Numeracy across grades -- vertically scaling the Norwegian national numeracy tests},
	author       = {Henrik R{\ae}der and Bj{\"o}rn Andersson and Rolf Olsen},
	year         = 2022,
	journal      = {Assessment in Education: Principles, Policy \& Practice},
	publisher    = {Routledge},
	volume       = 29,
	number       = 6,
	pages        = {653--673},
	doi          = {10.1080/0969594x.2022.2147483},
	url          = {https://doi.org/10.1080/0969594X.2022.2147483},
	eprint       = {https://doi.org/10.1080/0969594X.2022.2147483},
	bdsk-url-1   = {https://doi.org/10.1080/0969594X.2022.2147483}
}
@article{scallable,
	title        = {Scalable collaborative targeted learning for high-dimensional data},
	author       = {Cheng Ju and Susan Gruber and Samuel Lendle and Antoine Chambaz and Jessica Franklin and Richard Wyss and Sebastian Schneeweiss and Mark {van der Laan}},
	year         = 2019,
	journal      = {Statistical Methods in Medical Research},
	volume       = 28,
	number       = 2,
	pages        = {532--554},
	doi          = {10.1177/0962280217729845},
	url          = {https://doi.org/10.1177/0962280217729845},
	note         = {Pmid: 28936917},
	abstract     = {Robust inference of a low-dimensional parameter in a large semi-parametric model relies on external estimators of infinite-dimensional features of the distribution of the data. Typically, only one of the latter is optimized for the sake of constructing a well-behaved estimator of the low-dimensional parameter of interest. Optimizing more than one of them for the sake of achieving a better bias-variance trade-off in the estimation of the parameter of interest is the core idea driving the general template of the collaborative targeted minimum loss-based estimation procedure. The original instantiation of the collaborative targeted minimum loss-based estimation template can be presented as a greedy forward stepwise collaborative targeted minimum loss-based estimation algorithm. It does not scale well when the number p of covariates increases drastically. This motivates the introduction of a novel instantiation of the collaborative targeted minimum loss-based estimation template where the covariates are pre-ordered. Its time complexity is O(p) as opposed to the original O(p2), a remarkable gain. We propose two pre-ordering strategies and suggest a rule of thumb to develop other meaningful strategies. Because it is usually unclear a priori which pre-ordering strategy to choose, we also introduce another instantiation called SL-C-TMLE algorithm that enables the data-driven choice of the better pre-ordering strategy given the problem at hand. Its time complexity is O(p) as well. The computational burden and relative performance of these algorithms were compared in simulation studies involving fully synthetic data or partially synthetic data based on a real world large electronic health database; and in analyses of three real, large electronic health databases. In all analyses involving electronic health databases, the greedy collaborative targeted minimum loss-based estimation algorithm is unacceptably slow. Simulation studies seem to indicate that our scalable collaborative targeted minimum loss-based estimation and SL-C-TMLE algorithms work well. All C-TMLEs are publicly available in a Julia software package.},
	eprint       = {https://doi.org/10.1177/0962280217729845},
	bdsk-url-1   = {https://doi.org/10.1177/0962280217729845}
}
@article{schein2022economic,
	title        = {Economic burden of attention-deficit/hyperactivity disorder among children and adolescents in the United States: a societal perspective},
	author       = {Schein, Jeff and Adler, Lenard A and Childress, Ann and Cloutier, Martin and Gagnon-Sanschagrin, Patrick and Davidson, Mikha{\"\i}l and Kinkead, Fr{\'e}d{\'e}ric and Guerin, Annie and Lefebvre, Patrick},
	year         = 2022,
	journal      = {Journal of Medical Economics},
	publisher    = {Taylor and Francis},
	volume       = 25,
	number       = 1,
	pages        = {193--205}
}
@article{schmengler2022educational,
	title        = {Educational level, attention problems, and externalizing behaviour in adolescence and early adulthood: the role of social causation and health-related selection},
	author       = {Schmengler, H. and Peeters, M. and Stevens, G. and Kunst, A. and Hartman, C. and Oldehinkel, A. and \&Vollebergh, W.},
	year         = 2023,
	journal      = {European Child \& Adolescent Psychiatry},
	publisher    = {Springer},
	volume       = 32,
	number       = 5,
	pages        = {809–824},
	doi          = {https://doi.org/10.1007/s00787-021-01913-4}
}
@article{schnitzer2016variable,
	title        = {Variable selection for confounder control, flexible modeling and collaborative targeted minimum loss-based estimation in causal inference},
	author       = {Schnitzer, Mireille and Lok, Judith and Gruber, Susan},
	year         = 2016,
	journal      = {The international journal of biostatistics},
	publisher    = {De Gruyter},
	volume       = 12,
	number       = 1,
	pages        = {97--115}
}
@inproceedings{Scholkopf2012,
	title        = {On Causal and Anticausal Learning},
	author       = {Sch\"{o}lkopf, Bernhard and Janzing, Dominik and Peters, Jonas and Sgouritsa, Eleni and Zhang, Kun and Mooij, Joris},
	year         = 2012,
	booktitle    = {Proceedings of the 29th International Coference on International Conference on Machine Learning},
	location     = {Edinburgh, Scotland},
	publisher    = {Omnipress},
	address      = {Madison, WI, USA},
	series       = {Icml'12},
	pages        = {459--466},
	isbn         = 9781450312851,
	abstract     = {We consider the problem of function estimation in the case where an underlying causal model can be inferred. This has implications for popular scenarios such as covariate shift, concept drift, transfer learning and semi-supervised learning. We argue that causal knowledge may facilitate some approaches for a given problem, and rule out others. In particular, we formulate a hypothesis for when semi-supervised learning can help, and corroborate it with empirical results.},
	numpages     = 8
}
@article{Schwartz,
	title        = {The Effects of Special Education on the Academic Performance of Students with Learning Disabilities},
	author       = {Schwartz, Amy and Hopkins, Bryant and Stiefel, Leanna},
	year         = 2021,
	journal      = {Journal of Policy Analysis and Management},
	volume       = 40,
	number       = 2,
	pages        = {480--520},
	doi          = {https://doi.org/10.1002/pam.22282},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1002/pam.22282},
	abstract     = {Abstract In the 40-plus years since the Individuals with Disabilities Education Act, special education has grown in the number of students and amount spent on services. Despite this growth, academic performance of students with disabilities remains troublingly low compared to general education students. To some extent, these differences reflect persistent underlying disabilities, but they also may reflect ineffective services. Does special education improve academic outcomes for students with disabilities? There is surprisingly little evidence to guide policy and answer this question. This paper provides an answer for the largest disability group, students with specific learning disabilities (LDs), using rich New York City public school data. Because the majority of LDs are classified after school entry, we observe outcomes before and after classification, allowing us to estimate impacts using within-student pre/post comparisons (student fixed effects) and an intent-to-treat specification. We find that academic outcomes improve for LDs following classification into special education and impacts are largest for those entering special education in earlier grades. Attendance, however, shows little change after classification. Results are robust to alternative specifications and falsification tests bolster confidence in a causal interpretation. Differences in impacts by gender, race/ethnicity, grade of classification, and settings illuminate possible mechanisms.},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/pam.22282},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.1002/pam.22282},
	bdsk-url-2   = {https://doi.org/10.1002/pam.22282}
}
@article{seaman2012combining,
	title        = {Combining multiple imputation and inverse-probability weighting},
	author       = {Seaman, Shaun and White, Ian and Copas, Andrew and Li, Lingling},
	year         = 2012,
	journal      = {Biometrics},
	volume       = 68,
	number       = 1,
	pages        = {129--137},
	doi          = {10.1111/j.1541-0420.2011.01666.x},
	url          = {https://doi.org/10.1111/j.1541-0420.2011.01666.x},
	pmcid        = {Pmc3412287},
	pmid         = 22050039,
	bdsk-url-1   = {https://doi.org/10.1111/j.1541-0420.2011.01666.x}
}
@article{seaman2013review,
	title        = {Review of inverse probability weighting for dealing with missing data},
	author       = {Seaman, Shaun and White, Ian},
	year         = 2013,
	journal      = {Statistical Methods in Medical Research},
	volume       = 22,
	number       = 3,
	pages        = {278--295}
}
@incollection{SelandIdunn2017,
	title        = {National Tests in Norway: An Undeclared Standard in Education? Practical and Political Implications of Norm-Referenced Standards},
	author       = {Seland, Idunn and Hovdhaugen, Elisabeth and Bl\"{o}meke, Sigrid and Gustafsson, Jan-Eric},
	year         = 2017,
	booktitle    = {Standard Setting in Education},
	publisher    = {Springer International Publishing},
	address      = {Cham},
	series       = {Methodology of Educational Measurement and Assessment},
	pages        = {161--179},
	isbn         = 9783319508559,
	issn         = {2367-170x},
	copyright    = {Springer International Publishing AG 2017},
	abstract     = {Educational standards were not the official object of national tests, when they were introduced as a tool for quality assessment in Norwegian schools in 2004. As the national curriculum relies on teachers' professional judgement for setting criteria for student learning, there are no direct links between the standardised tests and the managerial and pedagogical employment of the norm- referenced test results. In this study, we investigate how municipalities and teachers conceptualise and utilise results from national tests. We find that whereas school owners simply set future results from national tests to be above the national mean, many teachers either disregard or do not seem to comprehend the relationship between the norm-referenced test results and the national curriculum. Consequently, teachers seem to under-exploit test results for student learning development, while school owners seem to over-exploit the same results, as the national norm-based mean demonstrates that there is little variance at a local level, nor does it provide explanatory power. Results and teaching have never been linked to through authors' explanation: teaching in Norway has of course been linked to curriculum aims. Our point is that results from national tests have not been ``fed back'' to teaching linked to these curricular aims. Results and teaching have never been linked through set curricular aims, which is partly a political process. Instead, national tests emerge as an undeclared standard in Norwegian education, causing ambiguous political demands and signs of professional frustration.},
	language     = {eng},
	keywords     = {Competence aims ; National tests ; Norm-referenced standards ; Quality assessment ; Standards in education}
}
@article{semiparMediationTchetgen,
	title        = {Semiparametric theory for causal mediation analysis: Efficiency bounds, multiple robustness and sensitivity analysis},
	author       = {Eric Tchetgen Tchetgen and Ilya Shpitser},
	year         = 2012,
	journal      = {The Annals of Statistics},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 40,
	number       = 3,
	pages        = {1816 -- 1845},
	doi          = {10.1214/12-aos990},
	url          = {https://doi.org/10.1214/12-AOS990},
	keywords     = {double robust, local efficiency, mediation analysis, Natural direct effects, natural indirect effects},
	bdsk-url-1   = {https://doi.org/10.1214/12-AOS990}
}
@article{semiRazieh,
	title        = {Semiparametric Inference For Causal Effects In Graphical Models With Hidden Variables},
	author       = {Rohit Bhattacharya and Razieh Nabi and Ilya Shpitser},
	year         = 2022,
	journal      = {Journal of Machine Learning Research},
	volume       = 23,
	number       = 295,
	pages        = {1--76},
	url          = {http://jmlr.org/papers/v23/20-296.html},
	bdsk-url-1   = {http://jmlr.org/papers/v23/20-296.html}
}
@inbook{seqSuper,
	title        = {Sequential Super Learning},
	author       = {Rose, Sherri and van der Laan, Mark},
	year         = 2018,
	booktitle    = {Targeted Learning in Data Science: Causal Inference for Complex Longitudinal Studies},
	publisher    = {Springer International Publishing},
	address      = {Cham},
	pages        = {27--34},
	doi          = {10.1007/978-3-319-65304-4_3},
	isbn         = {978-3-319-65304-4},
	url          = {https://doi.org/10.1007/978-3-319-65304-4\%5F3},
	abstract     = {Suppose a doctor is interested in predicting the individual outcomes for a group of patients under two particular drug regimens at two time points in the future. She is therefore asking, what would happen to each of these patient's future outcomes at these time points if I were to enforce drug regimen 1 or drug regimen 2? Which treatment will be better for the patients' efficacy outcomes? Which treatment will be better for the patients' safety outcomes? Prediction problems can be longitudinal in nature, generally, and we frequently wish to understand what the mean outcome of patients with certain characteristics would be months or years in the future. Often, this is under the setting where we would hypothetically assign a particular treatment ``rule'' to the patients.},
	bdsk-url-1   = {https://doi.org/10.1007/978-3-319-65304-4_3}
}
@article{shaw2012systematic,
	title        = {A systematic review and analysis of long-term outcomes in attention deficit hyperactivity disorder: effects of treatment and non-treatment},
	author       = {Shaw, Monica and Hodgkins, Paul and Caci, Herv{\'e} and Young, Susan and Kahle, Jennifer and Woods, Alisa G and Arnold, L Eugene},
	year         = 2012,
	journal      = {BMC medicine},
	publisher    = {Springer},
	volume       = 10,
	number       = 1,
	pages        = {1--15}
}
@misc{shi2024missingexposure,
	title        = {Causal Inference on Missing Exposure via Robust Estimation},
	author       = {Yuliang Shi and Yeying Zhu and Joel Dubin},
	year         = 2024,
	url          = {https://arxiv.org/abs/2406.08668},
	eprint       = {2406.08668},
	archiveprefix = {arXiv},
	primaryclass = {stat.ME}
}
@article{shook2024Variance,
	title        = {Double Robust Variance Estimation},
	author       = {Shook-Sa, Bonnie and Zivich, Paul and Lee, Chanhwa and Xue, Keyi and Ross, Rachael and Edwards, Jessie and Stringer, Jeffrey and Cole, Stephen},
	year         = 2024,
	journal      = {arXiv preprint arXiv:2404.16166}
}
@inproceedings{Shpitser2006,
	title        = {Identification of Conditional Interventional Distributions},
	author       = {Shpitser, Ilya and Pearl, Judea},
	year         = 2006,
	booktitle    = {Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence},
	location     = {Cambridge, MA, USA},
	publisher    = {AUAI Press},
	address      = {Arlington, Virginia, USA},
	series       = {Uai'06},
	pages        = {437--444},
	isbn         = {0974903922},
	abstract     = {The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting distributions on post-action outcomes given a set of measurements. We provide a necessary and sufficient graphical condition for the cases where such distributions can be uniquely computed from the available information, as well as an algorithm which performs this computation whenever the condition holds. Furthermore, we use our results to prove completeness of do-calculus [Pearl, 1995] for the same identification problem, and show applications to sequential decision making.},
	numpages     = 8
}
@inproceedings{shpitserATT,
	title        = {Effects of treatment on the treated: Identification and generalization},
	author       = {Shpitser, Ilya and Pearl, Judea},
	year         = 2009,
	booktitle    = {Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence, UAI 2009},
	pages        = {514--521},
	organization = {AUAI Press}
}
@inproceedings{ShpitserPearl06,
	title        = {Identification of Joint Interventional Distributions in Recursive Semi-{M}arkovian Causal Models},
	author       = {Shpitser, Ilya and Pearl, Judea},
	year         = 2006,
	booktitle    = {Proceedings of the 21st National Conference on Artificial Intelligence - Volume 2},
	location     = {Boston, Massachusetts},
	publisher    = {AAAI Press},
	series       = {Aaai'06},
	pages        = {1219--1226},
	isbn         = 9781577352815,
	abstract     = {This paper is concerned with estimating the effects of actions from causal assumptions, represented concisely as a directed graph, and statistical knowledge, given as a probability distribution. We provide a necessary and sufficient graphical condition for the cases when the causal effect of an arbitrary set of variables on another arbitrary set can be determined uniquely from the available information, as well as an algorithm which computes the effect whenever this condition holds. Furthermore, we use our results to prove completeness of do-calculus [Pearl, 1995], and a version of an identification algorithm in [Tian, 2002] for the same identification problem. Finally, we derive a complete characterization of semi-{M}arkovian models in which all causal effects are identifiable.},
	numpages     = 8
}
@inproceedings{ShpitserRobin10,
	title        = {On the Validity of Covariate Adjustment for Estimating Causal Effects},
	author       = {Shpitser, Ilya and VanderWeele, Tyler and Robins, James},
	year         = 2010,
	booktitle    = {Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence},
	location     = {Catalina Island, CA},
	publisher    = {AUAI Press},
	address      = {Arlington, Virginia, USA},
	series       = {Uai'10},
	pages        = {527--536},
	isbn         = 9780974903965,
	abstract     = {Identifying effects of actions (treatments) on outcome variables from observational data and causal assumptions is a fundamental problem in causal inference. This identification is made difficult by the presence of con-founders which can be related to both treatment and outcome variables. Confounders are often handled, both in theory and in practice, by adjusting for covariates, in other words considering outcomes conditioned on treatment and covariate values, weighed by probability of observing those covariate values. In this paper, we give a complete graphical criterion for covariate adjustment, which we term the adjustment criterion, and derive some interesting corollaries of the completeness of this criterion.},
	numpages     = 10
}
@article{ShpitserVanderWeele_2011,
	title        = {A Complete Graphical Criterion for the Adjustment Formula in Mediation Analysis},
	author       = {Ilya Shpitser and Tyler VanderWeele},
	year         = 2011,
	journal      = {The International Journal of Biostatistics},
	volume       = 7,
	number       = 1,
	doi          = {doi:10.2202/1557-4679.1297},
	url          = {https://doi.org/10.2202/1557-4679.1297},
	lastchecked  = {2023-03-24},
	bdsk-url-1   = {https://doi.org/10.2202/1557-4679.1297}
}
@article{sl2018,
	title        = {Stacked generalization: an introduction to super learning},
	author       = {Naimi, Ashley I. and Balzer, Laura B.},
	year         = 2018,
	journal      = {European Journal of Epidemiology},
	volume       = 33,
	number       = 5,
	pages        = {459--464},
	doi          = {10.1007/s10654-018-0390-z},
	isbn         = {1573-7284},
	url          = {https://doi.org/10.1007/s10654-018-0390-z},
	abstract     = {Stacked generalization is an ensemble method that allows researchers to combine several different prediction algorithms into one. Since its introduction in the early 1990s, the method has evolved several times into a host of methods among which is the ``Super Learner''. Super Learner uses V-fold cross-validation to build the optimal weighted combination of predictions from a library of candidate algorithms. Optimality is defined by a user-specified objective function, such as minimizing mean squared error or maximizing the area under the receiver operating characteristic curve. Although relatively simple in nature, use of Super Learner by epidemiologists has been hampered by limitations in understanding conceptual and technical details. We work step-by-step through two examples to illustrate concepts and address common concerns.},
	date         = {2018/05/01},
	date-added   = {2023-10-17 11:10:23 +0200},
	date-modified = {2023-10-17 11:10:23 +0200},
	id           = {Naimi2018},
	bdsk-url-1   = {https://doi.org/10.1007/s10654-018-0390-z}
}
@article{smith2019bounding,
	title        = {Bounding bias due to selection},
	author       = {Smith, Louisa and VanderWeele, Tyler},
	year         = 2019,
	journal      = {Epidemiology (Cambridge, Mass.)},
	publisher    = {Wolters Kluwer Health},
	volume       = 30,
	number       = 4,
	pages        = 509
}
@article{Smith2023,
	title        = {Application of targeted maximum likelihood estimation in public health and epidemiological studies: a systematic review},
	author       = {Matthew Smith and Rachael Phillips and Miguel Luque-Fernandez and Camille Maringe},
	year         = 2023,
	journal      = {Annals of Epidemiology},
	volume       = 86,
	pages        = {34--48.e28},
	doi          = {https://doi.org/10.1016/j.annepidem.2023.06.004},
	issn         = {1047-2797},
	url          = {https://www.sciencedirect.com/science/article/pii/S1047279723001151},
	abstract     = {Purpose The targeted maximum likelihood estimation (TMLE) statistical data analysis framework integrates machine learning, statistical theory, and statistical inference to provide a least biased, efficient, and robust strategy for estimation and inference of a variety of statistical and causal parameters. We describe and evaluate the epidemiological applications that have benefited from recent methodological developments. Methods We conducted a systematic literature review in PubMed for articles that applied any form of TMLE in observational studies. We summarized the epidemiological discipline, geographical location, expertize of the authors, and TMLE methods over time. We used the Roadmap of Targeted Learning and Causal Inference to extract key methodological aspects of the publications. We showcase the contributions to the literature of these TMLE results. Results Of the 89 publications included, 33\% originated from the University of California at Berkeley, where the framework was first developed by Professor Mark van der Laan. By 2022, 59\% of the publications originated from outside the United States and explored up to seven different epidemiological disciplines in 2021--2022. Double-robustness, bias reduction, and model misspecification were the main motivations that drew researchers toward the TMLE framework. Through time, a wide variety of methodological, tutorial, and software-specific articles were cited, owing to the constant growth of methodological developments around TMLE. Conclusions There is a clear dissemination trend of the TMLE framework to various epidemiological disciplines and to increasing numbers of geographical areas. The availability of R packages, publication of tutorial papers, and involvement of methodological experts in applied publications have contributed to an exponential increase in the number of studies that understood the benefits and adoption of TMLE.},
	keywords     = {Targeted Maximum Likelihood Estimation (TMLE), Epidemiology, Observational studies, Causal inference, Systematic review},
	bdsk-url-1   = {https://www.sciencedirect.com/science/article/pii/S1047279723001151},
	bdsk-url-2   = {https://doi.org/10.1016/j.annepidem.2023.06.004}
}
@article{song2014local,
	title        = {Local asymptotic minimax estimation of nonregular parameters with translation-scale equivariant maps},
	author       = {Song, Kyungchul},
	year         = 2014,
	journal      = {Journal of Multivariate Analysis},
	publisher    = {Elsevier},
	volume       = 125,
	pages        = {136--158}
}
@misc{song2021,
	title        = {The Missing Covariate Indicator Method is Nearly Valid Almost Always},
	author       = {Mingyang Song and Xin Zhou and Mathew Pazaris and Donna Spiegelman},
	year         = 2021,
	url          = {https://arxiv.org/abs/2111.00138},
	eprint       = {2111.00138},
	archiveprefix = {arXiv},
	primaryclass = {stat.AP}
}
@article{Soo,
	title        = {Sharp bounds on the distribution of treatment effects and their statistical inference},
	author       = {Fan, Yanqin and Park, Sang},
	year         = 2010,
	journal      = {Econometric Theory},
	volume       = 26,
	number       = 3,
	pages        = {931--951},
	url          = {https://EconPapers.repec.org/RePEc:cup:etheor:v:26:y:2010:i:03:p:931-951\%5F99},
	abstract     = {In this paper, we propose nonparametric estimators of sharp bounds on the distribution of treatment effects of a binary treatment and establish their asymptotic distributions. We note the possible failure of the standard bootstrap with the same sample size and apply the fewer-than-n bootstrap to making inferences on these bounds. The finite sample performances of the confidence intervals for the bounds based on normal critical values, the standard bootstrap, and the fewer-than-n bootstrap are investigated via a simulation study. Finally we establish sharp bounds on the treatment effect distribution when covariates are available.},
	bdsk-url-1   = {https://EconPapers.repec.org/RePEc:cup:etheor:v:26:y:2010:i:03:p:931-951_99}
}
@article{specEduNorway,
	title        = {Effects of special education on academic achievement and task motivation: a propensity-score and fixed-effects approach},
	author       = {Marianne Kvande and Oda Bj{\o}rklund and Stian Lydersen and Jay Belsky and Lars Wichstr{\o}m},
	year         = 2019,
	journal      = {European Journal of Special Needs Education},
	publisher    = {Routledge},
	volume       = 34,
	number       = 4,
	pages        = {409--423},
	doi          = {10.1080/08856257.2018.1533095},
	url          = {https://doi.org/10.1080/08856257.2018.1533095},
	eprint       = {https://doi.org/10.1080/08856257.2018.1533095},
	bdsk-url-1   = {https://doi.org/10.1080/08856257.2018.1533095}
}
@article{spencer2022social,
	title        = {Social gradients in ADHD by household income and maternal education exposure during early childhood: findings from birth cohort studies across six countries},
	author       = {Spencer, Nick and Reijneveld, Sijmen and Totsika, Vasiliki and Fouad, Farrah and others},
	year         = 2022,
	journal      = {PLoS ONE},
	publisher    = {Public Library of Science},
	volume       = 17,
	number       = 3,
	pages        = {e0264709}
}
@book{Spirtes2000,
	title        = {Causation, Prediction, and Search},
	author       = {Spirtes, P. and Glymour, C. and Scheines, R.},
	year         = 2000,
	publisher    = {MIT press},
	added-at     = {2009-09-12t19:19:34.000+0200},
	biburl       = {https://www.bibsonomy.org/bibtex/2e2b107e8fd3469c8b0e944ca37a559f3/mozaher},
	edition      = {2nd},
	interhash    = {559e17fcd12a76214629ba6c4efe3f9a},
	intrahash    = {e2b107e8fd3469c8b0e944ca37a559f3},
	keywords     = {imported},
	owner        = {Mozaherul Hoque},
	review       = {PC algorithm},
	timestamp    = {2009-09-12t19:19:43.000+0200}
}
@article{spotify,
	title        = {Estimating categorical counterfactuals via deep twin networks},
	author       = {Vlontzos, Athanasios and Kainz, Bernhard and Gilligan-Lee, Ciar{\'a}n},
	year         = 2023,
	journal      = {Nature Machine Intelligence},
	volume       = 5,
	number       = 2,
	pages        = {159--168},
	doi          = {10.1038/s42256-023-00611-x},
	url          = {https://doi.org/10.1038/s42256-023-00611-x},
	abstract     = {Counterfactual inference is a powerful tool, capable of solving challenging problems in high-profile sectors. To perform counterfactual inference, we require knowledge of the underlying causal mechanisms. However, causal mechanisms cannot be uniquely determined from observations and interventions alone. This raises the question of how to choose the causal mechanisms so that the resulting counterfactual inference is trustworthy in a given domain. This question has been addressed in causal models with binary variables, but for the case of categorical variables, it remains unanswered. We address this challenge by introducing for causal models with categorical variables the notion of counterfactual ordering, a principle positing desirable properties that causal mechanisms should possess and prove that it is equivalent to specific functional constraints on the causal mechanisms. To learn causal mechanisms satisfying these constraints, and perform counterfactual inference with them, we introduce deep twin networks. These are deep neural networks that, when trained, are capable of twin network counterfactual inference---an alternative to the abduction--action--prediction method. We empirically test our approach on diverse real-world and semisynthetic data from medicine, epidemiology and finance, reporting accurate estimation of counterfactual probabilities while demonstrating the issues that arise with counterfactual reasoning when counterfactual ordering is not enforced},
	date         = {2023-02-01},
	date-added   = {2024-05-13},
	date-modified = {2024-05-13},
	id           = {Vlontzos2023},
	bdsk-url-1   = {https://doi.org/10.1038/s42256-023-00611-x}
}
@article{stableIPW,
	title        = {Stable inverse probability weighting estimation for longitudinal studies},
	author       = {Avagyan, Vahe and Vansteelandt, Stijn},
	year         = 2021,
	journal      = {Scandinavian Journal of Statistics},
	volume       = 48,
	number       = 3,
	pages        = {1046--1067},
	doi          = {https://doi.org/10.1111/sjos.12542},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12542},
	abstract     = {Abstract We consider estimation of the average effect of time-varying dichotomous exposure on outcome using inverse probability weighting (IPW) under the assumption that there is no unmeasured confounding of the exposure--outcome association at each time point. Despite the popularity of IPW, its performance is often poor due to instability of the estimated weights. We develop an estimating equation-based strategy for the nuisance parameters indexing the weights at each time point, aimed at preventing highly volatile weights and ensuring the stability of IPW estimation. Our proposed approach targets the estimation of the counterfactual mean under a chosen treatment regime and requires fitting a separate propensity score model at each time point. We discuss and examine extensions to enable the fitting of marginal structural models using one propensity score model across all time points. Extensive simulation studies demonstrate adequate performance of our approach compared with the maximum likelihood propensity score estimator and the covariate balancing propensity score estimator.},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/sjos.12542},
	keywords     = {calibration estimation, covariate balancing, inverse probability weighting, propensity score},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.1111/sjos.12542},
	bdsk-url-2   = {https://doi.org/10.1111/sjos.12542}
}
@article{stensrud2024optimal,
	title        = {Optimal regimes for algorithm-assisted human decision-making},
	author       = {Stensrud, Mats and Laurendeau, JD and Sarvet, Aaron},
	year         = 2024,
	journal      = {Biometrika},
	publisher    = {Oxford University Press},
	pages        = {asae016}
}
@article{Stern2018,
	title        = {Karl Pearson and the Logic of Science: Renouncing Causal Understanding (the Bride) and Inverted Spinozism.},
	author       = {Julio Stern},
	year         = 2018,
	journal      = {South American Journal of Logic},
	volume       = 4,
	number       = 1,
	pages        = {219--252}
}
@article{Stijn,
	title        = {{Structural Nested Models and G-estimation: The Partially Realized Promise}},
	author       = {Stijn Vansteelandt and Marshall Joffe},
	year         = 2014,
	journal      = {Statistical Science},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 29,
	number       = 4,
	pages        = {707 -- 731},
	doi          = {10.1214/14-sts493},
	url          = {https://doi.org/10.1214/14-STS493},
	keywords     = {causal effect, confounding, direct effect, instrumental variable, mediation, time-varying confounding},
	bdsk-url-1   = {https://doi.org/10.1214/14-STS493}
}
@article{stochasticThreshold,
	title        = {Nonparametric estimation of the causal effect of a stochastic threshold-based intervention},
	author       = {van der Laan, Lars and Zhang, Wenbo and Gilbert, Peter},
	year         = 2023,
	journal      = {Biometrics},
	volume       = 79,
	number       = 2,
	pages        = {1014--1028},
	doi          = {https://doi.org/10.1111/biom.13690},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1111/biom.13690},
	abstract     = {Abstract Identifying a biomarker or treatment-dose threshold that marks a specified level of risk is an important problem, especially in clinical trials. In view of this goal, we consider a covariate-adjusted threshold-based interventional estimand, which happens to equal the binary treatment--specific mean estimand from the causal inference literature obtained by dichotomizing the continuous biomarker or treatment as above or below a threshold. The unadjusted version of this estimand was considered in Donovan et al.. Expanding upon Stitelman et al., we show that this estimand, under conditions, identifies the expected outcome of a stochastic intervention that sets the treatment dose of all participants above the threshold. We propose a novel nonparametric efficient estimator for the covariate-adjusted threshold-response function for the case of informative outcome missingness, which utilizes machine learning and targeted minimum-loss estimation (TMLE). We prove the estimator is efficient and characterize its asymptotic distribution and robustness properties. Construction of simultaneous 95\% confidence bands for the threshold-specific estimand across a set of thresholds is discussed. In the Supporting Information, we discuss how to adjust our estimator when the biomarker is missing at random, as occurs in clinical trials with biased sampling designs, using inverse probability weighting. Efficiency and bias reduction of the proposed estimator are assessed in simulations. The methods are employed to estimate neutralizing antibody thresholds for virologically confirmed dengue risk in the CYD14 and CYD15 dengue vaccine trials.},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/biom.13690},
	keywords     = {causal inference, nonparametric efficient estimation, stochastic intervention, targeted minimum-loss estimation, threshold estimation, vaccine trials},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.1111/biom.13690},
	bdsk-url-2   = {https://doi.org/10.1111/biom.13690}
}
@article{Storebo2015dz,
	title        = {Methylphenidate for attention-deficit/hyperactivity disorder in children and adolescents: {C}ochrane systematic review with meta-analyses and trial sequential analyses of randomised clinical trials},
	author       = {Storeb{\o}, Ole and Krogh, Helle and Ramstad, Erica and Moreira-Maia, Carlos and Holmskov, Mathilde and Skoog, Maria and Nilausen, Trine  and Magnusson, Frederik and Zwi, Morris and Gillies, Donna and Rosendal, Susanne and Groth, Camilla and Rasmussen, Kirsten and Gauci, Dorothy and Kirubakaran, Richard and Forsb{\o}l, Bente and Simonsen, Erik and Gluud, Christian},
	year         = 2015,
	month        = nov,
	journal      = {British Medical Journal},
	publisher    = {British Medical Journal Publishing Group},
	volume       = 351,
	pages        = {h5203},
	doi          = {10.1136/bmj.h5203},
	issn         = {0959-8138, 1756-1833},
	url          = {http://www.bmj.com/content/351/bmj.h5203},
	language     = {en},
	pmid         = 26608309,
	bdsk-url-1   = {http://www.bmj.com/content/351/bmj.h5203},
	bdsk-url-2   = {https://doi.org/10.1136/bmj.h5203}
}
@article{superlearner2007,
	title        = {Super Learner},
	author       = {Mark {van der Laan} and Eric Polley and Alan Hubbard},
	year         = 2007,
	journal      = {Statistical Applications in Genetics and Molecular Biology},
	volume       = 6,
	number       = 1,
	doi          = {doi:10.2202/1544-6115.1309},
	url          = {https://doi.org/10.2202/1544-6115.1309},
	lastchecked  = {2023-10-17},
	bdsk-url-1   = {https://doi.org/10.2202/1544-6115.1309}
}
@article{superlearners2023,
	title        = {{Practical considerations for specifying a super learner}},
	author       = {Phillips, Rachael and {van der Laan}, Mark  and Lee, Hana and Gruber, Susan},
	year         = 2023,
	month        = {03},
	journal      = {International Journal of Epidemiology},
	volume       = 52,
	number       = 4,
	pages        = {1276--1285},
	doi          = {10.1093/ije/dyad023},
	issn         = {0300-5771},
	url          = {https://doi.org/10.1093/ije/dyad023},
	abstract     = {{Common tasks encountered in epidemiology, including disease incidence estimation and causal inference, rely on predictive modelling. Constructing a predictive model can be thought of as learning a prediction function (a function that takes as input covariate data and outputs a predicted value). Many strategies for learning prediction functions from data (learners) are available, from parametric regressions to machine learning algorithms. It can be challenging to choose a learner, as it is impossible to know in advance which one is the most suitable for a particular dataset and prediction task. The super learner (SL) is an algorithm that alleviates concerns over selecting the one `right' learner by providing the freedom to consider many, such as those recommended by collaborators, used in related research or specified by subject-matter experts. Also known as stacking, SL is an entirely prespecified and flexible approach for predictive modelling. To ensure the SL is well specified for learning the desired prediction function, the analyst does need to make a few important choices. In this educational article, we provide step-by-step guidelines for making these decisions, walking the reader through each of them and providing intuition along the way. In doing so, we aim to empower the analyst to tailor the SL specification to their prediction task, thereby ensuring their SL performs as well as possible. A flowchart provides a concise, easy-to-follow summary of key suggestions and heuristics, based on our accumulated experience and guided by SL optimality theory.}},
	eprint       = {https://academic.oup.com/ije/article-pdf/52/4/1276/51027197/dyad023.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/ije/dyad023}
}
@article{superStensrud,
	title        = {Optimal regimes for algorithm-assisted human decision-making},
	author       = {Stensrud, M and Laurendeau, J and Sarvet, A},
	year         = 2024,
	month        = {03},
	journal      = {Biometrika},
	volume       = 111,
	number       = 4,
	pages        = {1089--1108},
	doi          = {10.1093/biomet/asae016},
	issn         = {1464-3510},
	url          = {https://doi.org/10.1093/biomet/asae016},
	abstract     = {We consider optimal regimes for algorithm-assisted human decision-making. Such regimes are decision functions of measured pre-treatment variables and, by leveraging natural treatment values, enjoy a superoptimality property whereby they are guaranteed to outperform conventional optimal regimes. When there is unmeasured confounding, the benefit of using superoptimal regimes can be considerable. When there is no unmeasured confounding, superoptimal regimes are identical to conventional optimal regimes. Furthermore, identification of the expected outcome under superoptimal regimes in nonexperimental studies requires the same assumptions as identification of value functions under conventional optimal regimes when the treatment is binary. To illustrate the utility of superoptimal regimes, we derive identification and estimation results in a common instrumental variable setting. We use these derivations to analyse examples from the optimal regimes literature, including a case study of the effect of prompt intensive care treatment on survival.},
	eprint       = {https://academic.oup.com/biomet/article-pdf/111/4/1089/60783717/asae016.pdf}
}
@article{Tang2024,
	title        = {Efficient covariate balancing for the average treatment effect with missing outcome},
	author       = {Shengfang Tang and Mingfeng Zhan and Qingshan Jiang and Tong Zhang},
	year         = 2024,
	journal      = {Economics Letters},
	pages        = 111961,
	doi          = {https://doi.org/10.1016/j.econlet.2024.111961},
	issn         = {0165-1765},
	url          = {https://www.sciencedirect.com/science/article/pii/S0165176524004452},
	abstract     = {This paper develops an empirical balancing approach for the estimation of treatment effects under the framework of outcomes being suffered from missing. We first represent the parameter of interest as a weighted expectation of the observed outcome by introducing two auxiliary binary variables and then estimate the weighting functions using covariate balancing methods. By tailoring the loss function for the weighting functions, the resulting treatment effect estimates are automatically weight-normalized and exhibit both low bias and reduced variance in finite samples when compared to conventional inverse probability weighting methods. Under some regularity conditions, we show that the proposed estimator is consistent, asymptotically normally distributed with the asymptotic variance achieving the semiparametric efficiency bound. Finite-sample performance of the proposed method is evaluated via Monte Carlo simulations.},
	keywords     = {Average treatment effect, Covariate balancing, Missing outcome, Semiparametric efficiency bound},
	bdsk-url-1   = {https://www.sciencedirect.com/science/article/pii/S0165176524004452},
	bdsk-url-2   = {https://doi.org/10.1016/j.econlet.2024.111961}
}
@article{tanskanen2015prescription,
	title        = {From prescription drug purchases to drug use periods--a second generation method ({PRE2DUP})},
	author       = {Tanskanen, Antti and Taipale, Heidi and Koponen, Marjaana and Tolppanen, Anna-Maija and Hartikainen, Sirpa and Ahonen, Riitta and Tiihonen, Jari},
	year         = 2015,
	journal      = {{BMC} medical informatics and decision making},
	publisher    = {BioMed Central},
	volume       = 15,
	number       = 1,
	pages        = {1--13}
}
@article{teacherSpecialEd,
	title        = {Effects of teachers' aides on students with special needs},
	author       = {Andersen, Simon and Beuchert, Louise and Nielsen, Helena},
	year         = 2024,
	journal      = {The Scandinavian Journal of Economics},
	doi          = {10.1111/sjoe.12579},
	url          = {https://onlinelibrary.wiley.com/doi/abs/10.1111/sjoe.12579},
	keywords     = {Randomized controlled trial, segregated classes, special class, special school},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/sjoe.12579},
	abstract     = {Abstract This study investigates the effect of increasing educational support in regular classes on students with special education needs (SEN). We exploit previous randomized controlled trials that added teachers' aides to Danish grade 6 classes combined with rich register data informative about SEN and school assignment. There were three types of teachers' aides: a co-teacher with a teaching degree, a teaching assistant without a teaching degree, and a coach. We find that the treatments increased inclusion of SEN students in regular classes, by 7–8 percentage points, and that SEN students gained academically. Long-term follow-up data indicate that while the academic gains evaporated over time, the treated students were able to stay in regular classes throughout compulsory education and largely followed the same progression as their counterparts in the control group when they moved to upper secondary education. Finally, we show that the costs of the teachers' aides are outweighed by the saved costs of special education.}
}
@article{Tengberg2017,
	title        = {National reading tests in Denmark, Norway, and Sweden: A comparison of construct definitions, cognitive targets, and response formats},
	author       = {Tengberg, Michael},
	year         = 2017,
	journal      = {Language testing},
	publisher    = {SAGE Publications},
	address      = {London, England},
	volume       = 34,
	number       = 1,
	pages        = {83--100},
	issn         = {0265-5322},
	copyright    = {The Author(s) 2015},
	abstract     = {Reading comprehension tests are often assumed to measure the same, or at least similar, constructs. Yet, reading is not a single but a multidimensional form of processing, which means that variations in terms of reading material and item design may emphasize one aspect of the construct at the cost of another. The educational systems in Denmark, Norway, and Sweden share a number of traits, and in the recent decade, the development of national test instruments, especially for reading, has been highly influenced by international surveys of student achievement. In this study, national tests of L1 reading comprehension in secondary school in the three Scandinavian countries are compared in order to reveal the present range of diversity/commonality within the three test domains. The analysis employs both qualitative and quantitative aspects of data, including frameworks, text samples, task samples, and scoring guidelines from 2011 to 2014. Findings indicate that the three tests differ substantially from each other, not only in terms of the intentional and operative constructs of reading to be measured, but also in terms of testing methods and stability over time. Implications for the future development of reading comprehension assessment are discussed.},
	language     = {eng},
	keywords     = {Achievement tests ; Comparative Analysis ; Definitions ; Education ; Foreign Countries ; National Competency Tests ; Pedagogik ; Qualitative Research ; Reading ; Reading achievement ; Reading Comprehension ; Reading Materials ; Reading Tests ; Secondary Schools ; Statistical Analysis ; Test Format ; Test Items}
}
@inproceedings{testability1,
	title        = {On the Testability of Models with Missing Data},
	author       = {Mohan, Karthika and Pearl, Judea},
	year         = 2014,
	month        = 4,
	booktitle    = {Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics},
	publisher    = {Pmlr},
	address      = {Reykjavik, Iceland},
	series       = {Proceedings of Machine Learning Research},
	volume       = 33,
	pages        = {643--650},
	url          = {https://proceedings.mlr.press/v33/mohan14.html},
	editor       = {Kaski, Samuel and Corander, Jukka},
	pdf          = {http://proceedings.mlr.press/v33/mohan14.pdf},
	abstract     = {Graphical models that depict the process by which data are lost are helpful in recovering information from missing data. We address the question of whether any such model can be submitted to a statistical test given that the data available are corrupted by missingness. We present sufficient conditions for testability in missing data applications and note the impediments for testability when data are contaminated by missing entries. Our results strengthen the available tests for MCAR and MAR and further provide tests in the category of MNAR. Furthermore, we provide sufficient conditions to detect the existence of dependence between a variable and its missingness mechanism. We use our results to show that model sensitivity persists in    almost all models typically categorized as MNAR.}
}
@inproceedings{testability2,
	title        = {On Testability and Goodness of Fit Tests in Missing Data Models},
	author       = {Nabi, Razieh and Bhattacharya, Rohit},
	year         = 2023,
	month        = 7,
	booktitle    = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence},
	publisher    = {Pmlr},
	series       = {Proceedings of Machine Learning Research},
	volume       = 216,
	pages        = {1467--1477},
	url          = {https://proceedings.mlr.press/v216/nabi23a.html},
	editor       = {Evans, Robin J. and Shpitser, Ilya},
	pdf          = {https://proceedings.mlr.press/v216/nabi23a/nabi23a.pdf},
	abstract     = {Significant progress has been made in developing identification and estimation techniques for missing data problems where modeling assumptions can be described via a directed acyclic graph. The validity of results using such techniques rely on the assumptions encoded by the graph holding true; however, verification of these assumptions has not received sufficient attention in prior work. In this paper, we provide new insights on the testable implications of three broad classes of missing data graphical models, and design goodness-of-fit tests for them. The classes of models explored are: sequential missing-at-random and  missing-not-at-random models which can be used for modeling longitudinal studies with dropout/censoring, and a  no self-censoring model which can be applied to cross-sectional studies and surveys.}
}
@article{tikka2021causal,
	title        = {Causal Effect Identification from Multiple Incomplete Data Sources: A General Search-Based Approach},
author={Tikka, Santtu and Hyttinen, Antti and Karvanen, Juha},
	year         = 2021,
	journal      = {Journal of Statistical Software},
	volume       = 99,
	pages        = {1--40}
}
@inproceedings{TikkaNeurips,
	title        = {Identifying Causal Effects via Context-specific Independence Relations},
	author       = {Tikka, Santtu and Hyttinen, Antti and Karvanen, Juha},
	year         = 2019,
	booktitle    = {Advances in Neural Information Processing Systems},
	publisher    = {Curran Associates, Inc.},
	volume       = 32,
	url          = {https://papers.nips.cc/paper_files/paper/2019/hash/d88518acbcc3d08d1f18da62f9bb26ec-Abstract.html},
	editor       = {H. Wallach and H. Larochelle and A. Beygelzimer and F. d\textquotesingle Alch\'{e}-Buc and E. Fox and R. Garnett}
}
@book{TMLEbook1,
	title        = {Targeted Learning: Causal Inference for Observational and Experimental Data},
	author       = {{van der Laan}, Mark and Rose, Sherri},
	year         = 2011,
	publisher    = {Springer New York},
	series       = {Springer Series in Statistics},
	isbn         = 9781441997821,
	url          = {https://books.google.no/books?id=RGnSX5aCAgQC},
	lccn         = 2011930854,
	bdsk-url-1   = {https://books.google.no/books?id=RGnSX5aCAgQC}
}
@book{TMLEbook2,
	title        = {Targeted Learning in Data Science: Causal Inference for Complex Longitudinal Studies},
	author       = {{van der Laan}, Mark and Rose, Sherri},
	year         = 2018,
	publisher    = {Springer Publishing Company, Incorporated},
	isbn         = 3319653032,
	abstract     = {This textbook for graduate students in statistics, data science, and public health dealswith the practical challenges that come with big, complex, and dynamic data. It presentsa scientific roadmap to translate real-world data science applications into formal statisticalestimation problems by using the general template of targeted maximum likelihoodestimators. These targeted machine learning algorithms estimate quantities of interestwhile still providing valid inference. Targeted learning methods within data science area critical component for solving scientific problems in the modern age. The techniquescan answer complex questions including optimal rules for assigning treatment basedon longitudinal data with time-dependent confounding, as well as other estimands independent data structures, such as networks. Included in Targeted Learning in Data Science are demonstrations with soft ware packages and real data sets that present acase that targeted learning is crucial for the next generation of statisticians and datascientists. Th is book is a sequel to the first textbook on machine learning for causalinference, Targeted Learning, published in 2011. Mark van der Laan, PhD, is Jiann-Ping Hsu/Karl E. Peace Professor of Biostatistics and Statistics at UC Berkeley. His research interests include statistical methods in genomics, survival analysis, censored data, machine learning, semiparametric models, causalinference, and targeted learning. Dr. van der Laan received the 2004 Mortimer Spiegelman Award, the 2005 Van Dantzig Award, the 2005 COPSS Snedecor Award, the 2005 COPSS Presidential Award, and has graduated over 40 PhD students in bio statistics and statistics. Sherri Rose, PhD, is Associate Professor of Health Care Policy (Biostatistics) at Harvard Medical School. Her work is centered on developing and integrating innovative statistical approaches to advance human health. Dr. Roses methodological research focuseson nonparametric machine learning for causal inference and prediction. She co-leadsthe Health Policy Data Science Lab and currently serves as an associate editor for the Journal of the American Statistical Association and Biostatistics.},
	edition      = {1st}
}
@article{Tobias,
	title        = {What would have happened? Counterfactuals, hypotheticals and causal judgements},
	author       = {Gerstenberg, Tobias},
	year         = 2022,
	journal      = {Philosophical Transactions of the Royal Society B: Biological Sciences},
	volume       = 377,
	number       = 1866,
	pages        = 20210339,
	doi          = {10.1098/rstb.2021.0339},
	url          = {https://royalsocietypublishing.org/doi/abs/10.1098/rstb.2021.0339},
	abstract     = {How do people make causal judgements? In this paper, I show that counterfactual simulations are necessary for explaining causal judgements about events, and that hypotheticals do not suffice. In two experiments, participants viewed video clips of dynamic interactions between billiard balls. In Experiment 1, participants either made hypothetical judgements about whether ball B would go through the gate if ball A were not present in the scene, or counterfactual judgements about whether ball B would have gone through the gate if ball A had not been present. Because the clips featured a block in front of the gate that sometimes moved and sometimes stayed put, hypothetical and counterfactual judgements came apart. A computational model that evaluates hypotheticals and counterfactuals by running noisy physical simulations accurately captured participants' judgements. In Experiment 2, participants judged whether ball A caused ball B to go through the gate. The results showed a tight fit between counterfactual and causal judgements, whereas hypotheticals did not predict causal judgements. I discuss the implications of this work for theories of causality, and for studying the development of counterfactual thinking in children. This article is part of the theme issue `Thinking about possibilities: mechanisms, ontogeny, functions and phylogeny'.},
	eprint       = {https://royalsocietypublishing.org/doi/pdf/10.1098/rstb.2021.0339},
	bdsk-url-1   = {https://royalsocietypublishing.org/doi/abs/10.1098/rstb.2021.0339},
	bdsk-url-2   = {https://doi.org/10.1098/rstb.2021.0339}
}
@article{TP,
	title        = {Probabilities of causation: Bounds and identification},
	author       = {Tian, Jin and Pearl, Judea},
	year         = 2000,
	journal      = {Annals of Mathematics and Artificial Intelligence},
	volume       = 28,
	number       = 1,
	pages        = {287--313},
	doi          = {10.1023/a:1018912507879},
	url          = {https://doi.org/10.1023/A:1018912507879},
	abstract     = {This paper deals with the problem of estimating the probability of causation, that is, the probability that one event was the real cause of another, in a given scenario. Starting from structural-semantical definitions of the probabilities of necessary or sufficient causation (or both), we show how to bound these quantities from data obtained in experimental and observational studies, under general assumptions concerning the data-generating process. In particular, we strengthen the results of Pearl {$[$}39{$]$} by presenting sharp bounds based on combined experimental and nonexperimental data under no process assumptions, as well as under the mild assumptions of exogeneity (no confounding) and monotonicity (no prevention). These results delineate more precisely the basic assumptions that must be made before statistical measures such as the excess-risk-ratio could be used for assessing attributional quantities such as the probability of causation.},
	date         = {2000-10-01},
	date-added   = {2024-02-04},
	date-modified = {2024-02-04},
	id           = {Tian2000},
	bdsk-url-1   = {https://doi.org/10.1023/A:1018912507879}
}

@article{TreatmentMed,
	title        = {Does methylphenidate improve academic performance? A systematic review and meta-analysis},
	author       = {Kortekaas-Rijlaarsdam, Anne and Luman, Marjolein and Sonuga-Barke, Edmund and Oosterlaan, Jaap},
	year         = 2019,
	journal      = {European Child \& Adolescent Psychiatry},
	volume       = 28,
	number       = 2,
	pages        = {155--164},
	doi          = {10.1007/s00787-018-1106-3},
	url          = {https://doi.org/10.1007/s00787-018-1106-3},
	abstract     = {Academic improvement is amongst the most common treatment targets when prescribing stimulants to children with ADHD. Previous reviews on stimulant-related academic improvements are inconclusive and focus on task engagement. Recent literature suggests outcome-domain-specific medication effects that are larger for productivity than for accuracy. The aims of this study are quantifying methylphenidate effects on academic productivity and accuracy for math, reading, spelling; exploring the mediating or moderating effects of symptom improvements, demographic-, design- and disorder-related variables. PubMed, EMBASE, ERIC and PsycINFO were searched for articles reporting methylphenidate effects on academic productivity and accuracy. Thirty-four studies met entry criteria. Methylphenidate improved math productivity (7.8{\%} increase, p < .001); math accuracy (3.0{\%} increase, p = .001); increased reading speed (SMD .47, p < .001) but not reading accuracy. None of the mediators or moderators tested affected methylphenidate efficacy. Academic improvements were small compared to symptom improvements; qualitative changes limited to math. Clinicians should take this discrepancy into account when prescribing medication for ADHD.},
	date         = {2019-02-01},
	date-added   = {2025-01-01},
	date-modified = {2025-01-01},
	id           = {Kortekaas-Rijlaarsdam2019},
	bdsk-url-1   = {https://doi.org/10.1007/s00787-018-1106-3}
}
@book{Tsiatis2007,
	title        = {Semiparametric Theory and Missing Data},
	author       = {Tsiatis, A.},
	year         = 2007,
	publisher    = {Springer New York},
	series       = {Springer Series in Statistics},
	isbn         = 9780387373454,
	url          = {https://books.google.no/books?id=xqZFi2EMB40C},
	lccn         = 2006921164,
	bdsk-url-1   = {https://books.google.no/books?id=xqZFi2EMB40C}
}
@book{tsiatisDTR,
	title        = {Dynamic Treatment Regimes: Statistical Methods for Precision Medicine},
	author       = {Tsiatis, A. and Davidian, M. and Holloway, S. and Laber, E.},
	year         = 2019,
	publisher    = {CRC Press},
	series       = {Chapman \& Hall/CRC Monographs on Statistics \& Applied Probability},
	isbn         = 9781498769785,
	url          = {https://books.google.no/books?id=FD0PEAAAQBAJ},
	lccn         = 2019038385
}
@misc{udir2022eigthninth,
	title        = {Analyse av nasjonale pr\o ver for 8. og 9. trinn 2022. [{Analysis of national tests for 8th and 9th grade 2022}]},
	author       = {Utdanningsdirektoratet},
	year         = 2022,
	url          = {https://www.udir.no/tall-og-forskning/statistikk/statistikk-grunnskole/analyser/analyse-av-nasjonale-prover-8.-trinn/},
	shortauthor  = {{Udir}},
	bdsk-url-1   = {https://www.udir.no/tall-og-forskning/statistikk/statistikk-grunnskole/analyser/analyse-av-nasjonale-prover-8.-trinn/}
}
@misc{udir2022fifth,
	title        = {Analyse av nasjonale pr\o ver for 5. trinn 2022. [{Analysis of national tests for 5th grade 2022}]},
	author       = {Utdanningsdirektoratet},
	year         = 2022,
	url          = {https://www.udir.no/tall-og-forskning/statistikk/statistikk-grunnskole/analyser/analyse-av-nasjonale-prover-5.-trinn/},
	shortauthor  = {{Udir}},
	bdsk-url-1   = {https://www.udir.no/tall-og-forskning/statistikk/statistikk-grunnskole/analyser/analyse-av-nasjonale-prover-5.-trinn/}
}
@misc{udir2023exemption,
	title        = {Administrere nasjonale pr\o ver [{Administer national tests}]},
	author       = {Utdanningsdirektoratet},
	year         = 2023,
	url          = {https://www.udir.no/eksamen-og-prover/prover/nasjonale-prover/administrere-nasjonale-prover2},
	shortauthor  = {{Udir}},
	bdsk-url-1   = {https://www.udir.no/eksamen-og-prover/prover/nasjonale-prover/administrere-nasjonale-prover2}
}
@misc{udir2023stats5,
	title        = {Nasjonale pr\o ver 5. trinn -- resultater. [{National tests 5th grade - results}]},
	author       = {Utdanningsdirektoratet},
	year         = 2023,
	url          = {https://www.udir.no/tall-og-forskning/statistikk/statistikk-grunnskole/nasjonale-prover-5.-trinn/},
	shortauthor  = {{Udir}},
	bdsk-url-1   = {https://www.udir.no/tall-og-forskning/statistikk/statistikk-grunnskole/nasjonale-prover-5.-trinn/}
}
@misc{udir2023stats89,
	title        = {Nasjonale pr\o ver 8. og 9. trinn -- resultater. [{National tests 8th and 9th grade - results}]},
	author       = {Utdanningsdirektoratet},
	year         = 2023,
	url          = {https://www.udir.no/tall-og-forskning/statistikk/statistikk-grunnskole/nasjonale-prover-8.-og-9.-trinn/},
	shortauthor  = {{Udir}},
	bdsk-url-1   = {https://www.udir.no/tall-og-forskning/statistikk/statistikk-grunnskole/nasjonale-prover-8.-og-9.-trinn/}
}
@book{van1995efficient,
	title        = {Efficient and Inefficient Estimation in Semiparametric Models},
	author       = {{van der Laan}, Mark},
	year         = 1995,
	publisher    = {Centrum voor Wiskunde en Informatica},
	series       = {CWI Tract - Centrum voor Wiskunde en Informatica},
	isbn         = 9789061964612,
	url          = {https://books.google.com/books?id=ZwjvAAAAMAAJ},
	bdsk-url-1   = {https://books.google.com/books?id=ZwjvAAAAMAAJ}
}
@book{van1996weak,
	title        = {Weak Convergence and Empirical Processes: With Applications to Statistics},
	author       = {{van der Vaart}, A. and Wellner, J.},
	year         = 1996,
	publisher    = {Springer},
	series       = {Springer Series in Statistics},
	isbn         = 9780387946405,
	url          = {https://books.google.no/books?id=OCenCW9qmp4C},
	lccn         = 95049099,
	bdsk-url-1   = {https://books.google.no/books?id=OCenCW9qmp4C}
}
@book{van2000,
	title        = {Asymptotic Statistics},
	author       = {{van der Vaart}, A.},
	year         = 2000,
	publisher    = {Cambridge University Press},
	series       = {Asymptotic Statistics},
	isbn         = 9780521784504,
	url          = {https://books.google.com/books?id=UEuQEM5RjWgC},
	lccn         = 98015176,
	bdsk-url-1   = {https://books.google.com/books?id=UEuQEM5RjWgC}
}
@techreport{van2014online,
	title        = {Online targeted learning},
	author       = {{van der Laan}, Mark and Lendle, Samuel},
	year         = 2014,
	month        = 9,
	institution  = {University of California in Berkeley -- Division of Biostatistics},
	publisher    = {Institute of Mathematical Statistics},
	series       = {Working Paper 330},
	url          = {https://biostats.bepress.com/ucbbiostat/paper330},
	bdsk-url-1   = {https://biostats.bepress.com/ucbbiostat/paper330}
}
@inbook{vanderLaanChapter,
	title        = {CV-TMLE for Nonpathwise Differentiable Target Parameters},
	author       = {{van der Laan}, Mark and Bibaut, Aur{\'e}lien and Luedtke, Alexander},
	year         = 2018,
	booktitle    = {Targeted Learning in Data Science: Causal Inference for Complex Longitudinal Studies},
	publisher    = {Springer International Publishing},
	address      = {Cham},
	pages        = {455--481},
	doi          = {10.1007/978-3-319-65304-4_25},
	isbn         = {978-3-319-65304-4},
	url          = {https://doi.org/10.1007/978-3-319-65304-4\%5F25},
	abstract     = {TMLE has been developed for the construction of efficient substitution estimators of pathwise differentiable target parameters. Many parameters are nonpathwise differentiable such as a density or regression curves at a single point in a nonparametric model. In these cases one often uses a specific estimator under a specific smoothness assumptions for which it is possible to establish a limit distribution and thereby provide statistical inference. However, such estimators do not adapt to the true unknown smoothness of the data density and, as a consequence, can be easily outperformed by an adaptive estimator that is able to adapt to the underlying true smoothness.van der Laan, M.J.Luedtke, A.},
	bdsk-url-1   = {https://doi.org/10.1007/978-3-319-65304-4_25}
}
@article{vanderLaanNuisance,
	title        = {Targeted Estimation of Nuisance Parameters to Obtain Valid Statistical Inference},
	author       = {Mark {van der Laan}},
	year         = 2014,
	journal      = {The International Journal of Biostatistics},
	volume       = 10,
	number       = 1,
	pages        = {29--57},
	doi          = {doi:10.1515/ijb-2012-0038},
	url          = {https://doi.org/10.1515/ijb-2012-0038},
	lastchecked  = {2023-09-18},
	bdsk-url-1   = {https://doi.org/10.1515/ijb-2012-0038}
}
@article{vanderLaanRubin2006,
	title        = {Targeted Maximum Likelihood Learning},
	author       = {Mark {van der Laan} and Daniel Rubin},
	year         = 2006,
	journal      = {The International Journal of Biostatistics},
	volume       = 2,
	number       = 1,
	doi          = {doi:10.2202/1557-4679.1043},
	url          = {https://doi.org/10.2202/1557-4679.1043},
	lastchecked  = {2023-09-25},
	bdsk-url-1   = {https://doi.org/10.2202/1557-4679.1043}
}
@article{vanderVaart1991,
	title        = {On differentiable functionals},
	author       = {{van der Vaart}, A.},
	year         = 1991,
	journal      = {The Annals of Statistics},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 19,
	number       = 3,
	pages        = {178--204},
	doi          = {10.1214/aos/1176348366}
}
@article{vanderweele2013d,
	title        = {On the definition of a confounder},
	author       = {VanderWeele, Tyler and Shpitser, Ilya},
	year         = 2013,
	journal      = {Annals of Statistics},
	publisher    = {Institute of Mathematical Statistics},
	volume       = 41,
	number       = 1,
	pages        = {196--220}
}
@article{vanderweele2017sensitivity,
	title        = {Sensitivity analysis in observational research: introducing the E-value},
	author       = {VanderWeele, Tyler and Ding, Peng},
	year         = 2017,
	journal      = {Annals of internal medicine},
	publisher    = {American College of Physicians},
	volume       = 167,
	number       = 4,
	pages        = {268--274}
}
@inproceedings{vanderzander2014,
	title        = {Constructing separators and adjustment sets in ancestral graphs},
	author       = {{van der Zander}, Benito and Li\'{s}kiewicz, Maciej and Textor, Johannes},
	year         = 2014,
	booktitle    = {Proceedings of the UAI 2014 Conference on Causal Inference: Learning and Prediction - Volume 1274},
	location     = {Quebec City, Canada},
	publisher    = {CEUR-WS.org},
	address      = {Aachen, DEU},
	series       = {Ci'14},
	pages        = {11--24},
	abstract     = {Ancestral graphs (AGs) are graphical causal models that can represent uncertainty about the presence of latent confounders, and can be inferred from data. Here, we present an algorithmic framework for efficiently testing, constructing, and enumerating m-separators in AGs. Moreover, we present a new constructive criterion for covariate adjustment in directed acyclic graphs (DAGs) and maximal ancestral graphs (MAGs) that characterizes adjustment sets as m-separators in a subgraph. Jointly, these results allow to find all adjustment sets that can identify a desired causal effect with multivariate exposures and outcomes in the presence of latent confounding. Our results generalize and improve upon several existing solutions for special cases of these problems.},
	numpages     = 14
}
@article{VESTHEIM20161,
	title        = {A study of Norwegian schools achieving good national test results},
	author       = {Ole Vestheim and Kitt Lyngsnes},
	year         = 2016,
	journal      = {International Journal of Educational Research},
	volume       = 79,
	pages        = {1--9},
	doi          = {https://doi.org/10.1016/j.ijer.2016.06.005},
	issn         = {0883-0355},
	url          = {https://www.sciencedirect.com/science/article/pii/S0883035515301841},
	abstract     = {This article presents a qualitative case study of seven Norwegian schools that over a period of at least three years have achieved good results on national tests. The schools are situated in socioeconomic areas where one statistically would not expect such results. This article sheds light on how national tests influence various elements of practice in these schools: specifically how school leaders, teachers, and pupils talk about the tests; how they prepare their pupils for the tests; and how they use the test results. We found there is a gap between the participants' opinions of national tests and their practice when applying the tests results.}
}
@article{vim,
	title        = {Collaborative targeted maximum likelihood estimation for variable importance measure: Illustration for functional outcome prediction in mild traumatic brain injuries},
	author       = {Romain Pirracchio and John K Yue and Geoffrey T Manley and Mark {van der Laan} and Alan E Hubbard and Wayne A Gordon and Hester F Lingsma and Andrew IR Maas and Pratik Mukherjee and David O Okonkwo, David M Schnyer and Alex B Valadka and Esther L Yuh},
	year         = 2018,
	journal      = {Statistical Methods in Medical Research},
	volume       = 27,
	number       = 1,
	pages        = {286--297},
	doi          = {10.1177/0962280215627335},
	url          = {https://doi.org/10.1177/0962280215627335},
	note         = {Pmid: 27363429},
	abstract     = {Standard statistical practice used for determining the relative importance of competing causes of disease typically relies on ad hoc methods, often byproducts of machine learning procedures (stepwise regression, random forest, etc.). Causal inference framework and data-adaptive methods may help to tailor parameters to match the clinical question and free one from arbitrary modeling assumptions. Our focus is on implementations of such semiparametric methods for a variable importance measure (VIM). We propose a fully automated procedure for VIM based on collaborative targeted maximum likelihood estimation (cTMLE), a method that optimizes the estimate of an association in the presence of potentially numerous competing causes. We applied the approach to data collected from traumatic brain injury patients, specifically a prospective, observational study including three US Level-1 trauma centers. The primary outcome was a disability score (Glasgow Outcome Scale - Extended (GOSE)) collected three months post-injury. We identified clinically important predictors among a set of risk factors using a variable importance analysis based on targeted maximum likelihood estimators (TMLE) and on cTMLE. Via a parametric bootstrap, we demonstrate that the latter procedure has the potential for robust automated estimation of variable importance measures based upon machine-learning algorithms. The cTMLE estimator was associated with substantially less positivity bias as compared to TMLE and larger coverage of the 95\% CI. This study confirms the power of an automated cTMLE procedure that can target model selection via machine learning to estimate VIMs in complicated, high-dimensional data.},
	eprint       = {https://doi.org/10.1177/0962280215627335},
	bdsk-url-1   = {https://doi.org/10.1177/0962280215627335}
}
@article{visually,
	title        = {Visually Communicating and Teaching Intuition for Influence Functions},
	author       = {Aaron Fisher and Edward Kennedy},
	year         = 2021,
	journal      = {The American Statistician},
	publisher    = {ASA Website},
	volume       = 75,
	number       = 2,
	pages        = {162--172},
	doi          = {10.1080/00031305.2020.1717620},
	url          = {https://doi.org/10.1080/00031305.2020.1717620},
	eprint       = {https://doi.org/10.1080/00031305.2020.1717620},
	bdsk-url-1   = {https://doi.org/10.1080/00031305.2020.1717620}
}
@article{wachter2017,
	title        = {Counterfactual explanations without opening the black box: Automated decisions and the GDPR},
	author       = {Wachter, Sandra and Mittelstadt, Brent and Russell, Chris},
	year         = 2018,
	journal      = {Harvard Journal of Law and Technology},
	volume       = 31,
	number       = 2,
	doi          = {10.2139/ssrn.3063289},
	url          = {https://ssrn.com/abstract=3063289},
	bdsk-url-1   = {https://ssrn.com/abstract=3063289},
	bdsk-url-2   = {https://doi.org/10.2139/ssrn.3063289}
}
@incollection{Walsh,
	title        = {{Counterfactual and generative accounts of causal attribution}},
	author       = {Walsh, Clare R. and Sloman, Steven A.},
	year         = 2011,
	month        = {03},
	booktitle    = {{Causality in the Sciences}},
	publisher    = {Oxford University Press},
	doi          = {10.1093/acprof:oso/9780199574131.003.0009},
	isbn         = 9780199574131,
	url          = {https://doi.org/10.1093/acprof:oso/9780199574131.003.0009},
	abstract     = {{Causal attribution is central to people's ability to understand and make sense of the world. It is necessary to explain why events occurred, to predict the consequences of actions as well as other events, and to assign credit and blame. The question this chapter aims to address is how people make these attributions. Interest is in the explanation of single events, for example, how someone explains what caused this particular window to break, rather than general occurrences, such as what kinds of things usually cause windows to break. This question has been studied for millennia and yet the answer remains elusive. The chapter reviews some of the existing research and offer a bit of new evidence about how people make causal attributions. The chapter's review will focus on two major types of theory: counterfactual and generative theories.}},
	eprint       = {https://academic.oup.com/book/0/chapter/144344947/chapter-ag-pdf/45014633/book_3313_section_144344947.ag.pdf},
	bdsk-url-1   = {https://doi.org/10.1093/acprof:oso/9780199574131.003.0009}
}
@article{wasserman,
	title        = {Discussion of "On {B}ayesian estimation of marginal structural models"},
	author       = {Robins, James and Hern{\'a}n, Miguel and Wasserman, Larry},
	year         = 2015,
	month        = {06},
	journal      = {Biometrics},
	volume       = 71,
	number       = 2,
	pages        = {296--299},
	doi          = {10.1111/biom.12273},
	isbn         = {1541-0420; 0006-341x},
	url          = {https://pubmed.ncbi.nlm.nih.gov/25652314},
	an           = 25652314,
	date         = {2015/06/},
	date-added   = {2022-04-02 21:29:05 +0200},
	date-modified = {2022-04-02 21:29:05 +0200},
	db           = {PubMed},
	edition      = {2015/02/04},
	j2           = {Biometrics},
	keywords     = {\textasteriskcenteredBayes Theorem; Humans},
	l2           = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4667748/},
	la           = {eng},
	u1           = {25652314{$[$}pmid{$]$}},
	u2           = {PMC4667748{$[$}pmcid{$]$}},
	bdsk-url-1   = {https://pubmed.ncbi.nlm.nih.gov/25652314},
	bdsk-url-2   = {https://doi.org/10.1111/biom.12273}
}
@article{Wei2022,
	title        = {Doubly robust estimation in causal inference with missing outcomes: With an application to the Aerobics Center Longitudinal Study},
	author       = {Kecheng Wei and Guoyou Qin and Jiajia Zhang and Xuemei Sui},
	year         = 2022,
	journal      = {Computational Statistics and Data Analysis},
	volume       = 168,
	pages        = 107399,
	doi          = {https://doi.org/10.1016/j.csda.2021.107399},
	issn         = {0167-9473},
	url          = {https://www.sciencedirect.com/science/article/pii/S0167947321002334},
	abstract     = {Estimation of the average treatment effect (ATE) and the average treatment effect on the treated (ATT) are two important topics of causal inference. However, when using the observational data for causal inference, two main problems including unbalanced covariates and missing outcomes should be tackled. In order to handle these two challenges and provide protection against model misspecification, the doubly robust estimators are developed, which remain consistent when the propensity score model and the selection probability model are correctly specified concurrently, or the outcome regression model is correctly specified. Under regularity conditions, the asymptotic normality of the estimators is established. Simulation studies confirm the desirable finite-sample performance of the proposed methods. Based on the Aerobics Center Longitudinal Study, the significant positive causal effect of physical activity levels on health status is discovered.},
	keywords     = {Average treatment effect, Average treatment effect on the treated, Causal inference, Missing data, Propensity score, Double robustness},
	bdsk-url-1   = {https://www.sciencedirect.com/science/article/pii/S0167947321002334},
	bdsk-url-2   = {https://doi.org/10.1016/j.csda.2021.107399}
}
@article{westreich2012,
	title        = {Berkson's bias, selection bias, and missing data},
	author       = {Westreich, Daniel},
	year         = 2012,
	journal      = {Epidemiology},
	publisher    = {Lippincott Williams and Wilkins},
	volume       = 23,
	number       = 1,
	pages        = {159--164},
	doi          = {10.1097/EDE.0b013e31823b6296},
	note         = {Pmid: 22081062; Pmcid: Pmc3237868},
	bdsk-url-1   = {https://doi.org/10.1097/EDE.0b013e31823b6296}
}
@misc{who0000ddd,
	title        = {Defined Daily Dose ({DDD}). Definition and general considerations},
	author       = {World Health Organization},
	year         = {n.d.},
	howpublished = {\url{https://www.who.int/tools/atc-ddd-toolkit/about-ddd}}
}
@misc{WHO2003Introduction,
	title        = {Introduction to Drug Utilization Research},
	author       = {{WHO International Working Group for Drug Statistics Methodology and WHO Collaborating Centre for Drug Statistics Methodology and WHO Collaborating Centre for Drug Utilization Research and Clinical Pharmacological Services}},
	year         = 2003,
	publisher    = {World Health Organization},
	howpublished = {\url{https://iris.who.int/handle/10665/42627}}
}
@article{xu2023disentangled,
	title        = {Disentangled Representation for Causal Mediation Analysis},
	author       = {Xu, Ziqi and Cheng, Debo and Li, Jiuyong and Liu, Jixue and Liu, Lin and Wang, Ke},
	year         = 2023,
	journal      = {arXiv preprint arXiv:2302.09694}
}
@inproceedings{Zhang,
	title        = {Designing Optimal Dynamic Treatment Regimes: A Causal Reinforcement Learning Approach},
	author       = {Zhang, Junzhe and Bareinboim, Elias},
	year         = 2020,
	month        = {13--18 Jul},
	booktitle    = {Proceedings of the 37th International Conference on Machine Learning},
	publisher    = {Pmlr},
	series       = {Proceedings of Machine Learning Research},
	volume       = 119,
	pages        = {11012--11022},
	url          = {https://proceedings.mlr.press/v119/zhang20a.html},
	editor       = {III, Hal Daum\'{e} and Singh, Aarti},
	pdf          = {http://proceedings.mlr.press/v119/zhang20a/zhang20a.pdf},
	abstract     = {A dynamic treatment regime (DTR) consists of a sequence of decision rules, one per stage of intervention, that dictates how to determine the treatment assignment to patients based on evolving treatments and covariates' history. These regimes are particularly effective for managing chronic disorders and is arguably one of the critical ingredients underlying more personalized decision-making systems. All reinforcement learning algorithms for finding the optimal DTR in online settings will suffer O(\sqrt{\vert{}D_{X, S}\vert{}T}) regret on some environments, where T is the number of experiments, and D_{X, S} is the domains of treatments X and covariates S. This implies T = O (\vert{}D_{X, S}\vert{}) trials to generate an optimal DTR. In many applications, domains of X and S could be so enormous that the time required to ensure appropriate learning may be unattainable. We show that, if the causal diagram of the underlying environment is provided, one could achieve regret that is exponentially smaller than D_{X, S}. In particular, we develop two online algorithms that satisfy such regret bounds by exploiting the causal structure underlying the DTR; one is based on the principle of optimism in the face of uncertainty (OFU-DTR), and the other uses the posterior sampling learning (PS-DTR). Finally, we introduce efficient methods to accelerate these online learning procedures by leveraging the abundant, yet biased observational (non-experimental) data.}
}
@inproceedings{zhang2022partial,
	title        = {Partial counterfactual identification from observational and experimental data},
	author       = {Zhang, Junzhe and Tian, Jin and Bareinboim, Elias},
	year         = 2022,
	booktitle    = {International Conference on Machine Learning},
	pages        = {26548--26558},
	organization = {Pmlr}
}
@article{ZhengvanderLaan2012,
	title        = {Targeted Maximum Likelihood Estimation of Natural Direct Effects},
	author       = {Wenjing Zheng and Mark {van der Laan}},
	year         = 2012,
	journal      = {The International Journal of Biostatistics},
	volume       = 8,
	number       = 1,
	pages        = {1--40},
	doi          = {doi:10.2202/1557-4679.1361},
	url          = {https://doi.org/10.2202/1557-4679.1361},
	lastchecked  = {2023-09-19},
	bdsk-url-1   = {https://doi.org/10.2202/1557-4679.1361}
}
@inproceedings{zhou2023domain,
	title        = {Domain adaptation under missingness shift},
	author       = {Zhou, Helen and Balakrishnan, Sivaraman and Lipton, Zachary},
	year         = 2023,
	booktitle    = {International Conference on Artificial Intelligence and Statistics},
	pages        = {9577--9606},
	url          = {https://proceedings.mlr.press/v206/zhou23b/zhou23b.pdf},
	organization = {Pmlr}
}
%%%%%%%%%%%%%%%%%%%%%%%
@article{peters2016causal,
	title        = {Causal inference by using invariant prediction: identification and confidence intervals},
	author       = {Peters, Jonas and B{\"u}hlmann, Peter and Meinshausen, Nicolai},
	year         = 2016,
	journal      = {Journal of the Royal Statistical Society Series B: Statistical Methodology},
	publisher    = {Oxford University Press},
	volume       = 78,
	number       = 5,
	pages        = {947--1012}
}
@inproceedings{agentBased,
	title        = {Causal {ABM}s: Learning Plausible Causal Models using Agent-based Modeling},
	author       = {Valogianni, Konstantina and Padmanabhan, Balaji},
	year         = 2022,
	month        = 8,
	booktitle    = {Proceedings of The KDD'22 Workshop on Causal Discovery},
	publisher    = {Pmlr},
	series       = {Proceedings of Machine Learning Research},
	volume       = 185,
	pages        = {3--29},
	url          = {https://proceedings.mlr.press/v185/valogianni22a.html},
	editor       = {Le, Thuc-Duy and Liu, Lin and K\i{}c\i{}man, Emre and Triantafyllou, Sofia and Liu, Huan},
	pdf          = {https://proceedings.mlr.press/v185/valogianni22a/valogianni22a.pdf},
	abstract     = {We present Causal ABM, a methodology to derive causal structures describing complex underlying behavioral phenomena. Agent-based models (ABMs) have powerful advantages for causal modeling that have not been explored sufficiently. Unlike traditional causal estimation approaches which often result in ``one best'' causal structure that is learned, two properties of ABMs - equifinality (the ability of different sets of conditions or model representations to yield the same outcome) and mutlifinality (the same ABM might yield different outcomes) - can be exploited to learn multiple diverse ``plausible causal models'' from data. Using an illustrative example of news sharing on social networks we show how this idea can be applied to learn such causal sets. We also show how genetic algorithms can be used as a estimation technique to learn multiple plausible causal models from data due to their parallel search structure. However, significant computational challenges remain before this can be generally applied, and we, therefore, highlight specific key issues that need to be addressed in future work.}
}
@article{MurrayAgent,
	title        = {Emulating Target Trials to Improve Causal Inference From Agent-Based Models},
	author       = {Murray, Eleanor and Marshall, Brandon and Buchanan, Ashley},
	year         = 2021,
	month        = 2,
	journal      = {American Journal of Epidemiology},
	volume       = 190,
	number       = 8,
	pages        = {1652--1658},
	doi          = {10.1093/aje/kwab040},
	issn         = {0002-9262},
	url          = {https://doi.org/10.1093/aje/kwab040},
	abstract     = {Agent-based models are a key tool for investigating the emergent properties of population health settings, such as infectious disease transmission, where the exposure often violates the key ``no interference'' assumption of traditional causal inference under the potential outcomes framework. Agent-based models and other simulation-based modeling approaches have generally been viewed as a separate knowledge-generating paradigm from the potential outcomes framework, but this can lead to confusion about how to interpret the results of these models in real-world settings. By explicitly incorporating the target trial framework into the development of an agent-based or other simulation model, we can clarify the causal parameters of interest, as well as make explicit the assumptions required for valid causal effect estimation within or between populations. In this paper, we describe the use of the target trial framework for designing agent-based models when the goal is estimation of causal effects in the presence of interference, or spillover.},
	eprint       = {https://academic.oup.com/aje/article-pdf/190/8/1652/40491678/kwab040.pdf}
}
@article{MarshallAgent,
	title        = {Formalizing the Role of Agent-Based Modeling in Causal Inference and Epidemiology},
	author       = {Marshall, Brandon and Galea, Sandro},
	year         = 2014,
	month        = 12,
	journal      = {American Journal of Epidemiology},
	volume       = 181,
	number       = 2,
	pages        = {92--99},
	doi          = {10.1093/aje/kwu274},
	issn         = {0002-9262},
	url          = {https://doi.org/10.1093/aje/kwu274},
	abstract     = {Calls for the adoption of complex systems approaches, including agent-based modeling, in the field of epidemiology have largely centered on the potential for such methods to examine complex disease etiologies, which are characterized by feedback behavior, interference, threshold dynamics, and multiple interacting causal effects. However, considerable theoretical and practical issues impede the capacity of agent-based methods to examine and evaluate causal effects and thus illuminate new areas for intervention. We build on this work by describing how agent-based models can be used to simulate counterfactual outcomes in the presence of complexity. We show that these models are of particular utility when the hypothesized causal mechanisms exhibit a high degree of interdependence between multiple causal effects and when interference (i.e., one person's exposure affects the outcome of others) is present and of intrinsic scientific interest. Although not without challenges, agent-based modeling (and complex systems methods broadly) represent a promising novel approach to identify and evaluate complex causal effects, and they are thus well suited to complement other modern epidemiologic methods of etiologic inquiry.},
	eprint       = {https://academic.oup.com/aje/article-pdf/181/2/92/17342562/kwu274.pdf}
}

@article{evans2014markovian,
  title={Markovian acyclic directed mixed graphs for discrete data},
  author={Evans, Robin J and Richardson, Thomas S},
  journal={The Annals of Statistics},
  volume={42},
  number={4},
  pages={1452--1482},
  year={2014}
}

@article{horvitz1952generalization,
  author    = {Horvitz, D. and Thompson, D.},
  title     = {A Generalization of Sampling Without Replacement from a Finite Population},
  journal   = {Journal of the American Statistical Association},
  volume    = {47},
  number    = {260},
  pages     = {663--685},
  year      = {1952},
  publisher = {Taylor \& Francis},
  doi       = {10.1080/01621459.1952.10483446}
}

@misc{tchetgen2024nudge,
  title={The Nudge Average Treatment Effect},
  author={Eric Tchetgen-Tchetgen},
	year         = 2024,
	url          = {https://doi.org/10.48550/arXiv.2410.23590},
	eprint       = {2410.23590},
	archiveprefix = {arXiv},
	primaryclass = {stat.ME}
}
@article{logicalCSI,
    title = {A logical approach to context-specific independence},
    journal = {Annals of Pure and Applied Logic},
    volume = 170,
    number = 9,
    pages = {975-992},
    year = {2019},
    note = {The 23rd Workshop on Logic, Language, Information and Computation},
    issn = {0168-0072},
    doi = {https://doi.org/10.1016/j.apal.2019.04.004},
    url = {https://www.sciencedirect.com/science/article/pii/S0168007219300326},
    author = {Jukka Corander and Antti Hyttinen and Juha Kontinen and Johan Pensar and Jouko Väänänen},
    keywords = {Directed acyclic graph, Graphical model, Context-specific independence, Implication problem, Team semantics},
    abstract = {Directed acyclic graphs (DAGs) constitute a qualitative representation for conditional independence (CI) properties of a probability distribution. It is known that every CI statement implied by the topology of a DAG is witnessed over it under a graph-theoretic criterion of d-separation. Alternatively, all such implied CI statements are derivable from the local independencies encoded by a DAG using the so-called semi-graphoid axioms. We consider Labeled Directed Acyclic Graphs (LDAGs) modeling graphically scenarios exhibiting context-specific independence (CSI). Such CSI statements are modeled by labeled edges, where labels encode contexts in which the edge vanishes. We study the problem of identifying all independence statements implied by the structure and the labels of an LDAG. We show that this problem is coNP-hard for LDAGs and formulate a sound extension of the semi-graphoid axioms for the derivation of such implied independencies. Finally we connect our study to certain qualitative versions of independence ubiquitous in database theory and teams semantics.}
}

@book{koller2009probabilistic,
  title     = {Probabilistic Graphical Models: Principles and Techniques},
  author    = {Daphne Koller and Nir Friedman},
  year      = {2009},
  publisher = {MIT Press},
  address   = {Cambridge, MA},
  isbn      = {978-0-262-01319-2}
}