%\documentclass{uai2024} % for initial submission
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\title{Detecting critical treatment effect bias in small subgroups}

% The standard author block has changed for UAI 2024 to provide
% more space for long author lists and allow for complex affiliations
%
% All author information is authomatically removed by the class for the
% anonymous submission version of your paper, so you can already add your
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% Add authors
\author[]{Piersilvio De Bartolomeis}
\author[]{Javier Abad}
\author[]{Konstantin Donhauser}
\author[]{Fanny Yang}
\affil[]{Department of Computer Science, ETH Zürich}

  
  \begin{document}
\maketitle

\begin{abstract}
 Randomized trials are considered the gold standard for making informed decisions in medicine, yet they often lack generalizability to the patient populations in clinical practice.  Observational studies, on the other hand, cover a broader patient population but are prone to various biases. Thus, before using an observational study for decision-making, it is crucial to \emph{benchmark} its treatment effect estimates against those derived from a randomized trial. 
We propose a novel strategy to benchmark observational studies beyond the average treatment effect. First, we design a statistical test for the null hypothesis that the treatment effects estimated from the two studies, conditioned on a set of relevant features, differ up to some tolerance. We then estimate an asymptotically valid lower bound on the maximum bias strength for any subgroup in the observational study.  Finally, we validate our benchmarking strategy in a real-world setting and show that it leads to conclusions that align with established medical knowledge.
\end{abstract}

\section{Introduction}
\input{content/intro}


\section{Problem setting}
\label{sec:setting}
\input{content/setting}

\section{Methodology}
\label{sec:test}
\input{content/test}

\section{Semi-synthetic experiments}
\label{sec:exp}
\input{content/experiments.tex}
\section{Real-world experiments}
\label{sec:rwexp}
\input{content/confounding.tex}
\section{Related work}
\input{content/related_work}

\section{Limitations and future work}
\input{content/conclusion.tex}

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\bibliography{main}

\newpage

\onecolumn

\title{Detecting critical treatment effect bias in small subgroups\\(Supplementary Material)}
\maketitle


The following appendices provide deferred proofs, experiment details, and ablation studies.


\appendix
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\end{document}
