Causal Mediation Analysis with Multi-dimensional and Indirectly Observed Mediators
Abstract: Causal mediation analysis (CMA) is a powerful method to dissect the total effect of treatment into direct and mediated effects within the potential outcome framework. This is important in many scientific applications to identify the underlying mechanisms of a treatment effect. However, in many scientific applications, the mediator is unobserved, but there may exist related measurements. For example, we may want to identify how changes in brain activity or structure mediate an antidepressant's effect on behavior, but we may only have access to electrophysiological or imaging brain measurements. To date, most CMA methods assume the mediator is one-dimensional and observable, which oversimplifies such real-world scenarios. To overcome this limitation, we introduce a CMA framework that can handle complex and indirectly observed mediators based on the identifiable variational autoencoder (iVAE) architecture. We show the joint distribution over observed and latent variables is identifiable with our method both theoretically and empirically. In addition, our framework captures a disentangled representation of the indirectly observed mediator and yields an accurate estimation of the direct and mediated effects in synthetic and semi-synthetic experiments, providing evidence of its potential utility in real-world applications.
Submission Length: Regular submission (no more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=EvJ5b4x2QN
Changes Since Last Submission: Since the last submission, we have made the following changes:
1. We added an additional Section in the experiments (Section 5.1.2), in which we calculate the mean correlation coefficient (MCC) metric between the true and sampled latent distributions over different latent space dimensions and different numbers of training epochs. This serves as empirical evidence of the identifiability of our framework compared to conventional variational autoencoder (VAE).
2. We conducted an experiment on another electrophysiological dataset which was obtained from 10 mice during a free object social interaction test (FOSIT) with direct neurostimulation using optogenetic stimulation, serving as evidence of the efficacy of our framework in potential real-world scenarios.
3. To explore the choices of $g_{\boldsymbol{\gamma}}$, we re-generated the synthetic dataset in Section 5.1 using a nonlinear outcome model and repeated the experiment with different model architectures of $g_{\boldsymbol{\gamma}}$. The results are detailed in Appendix H.
4. We added some clarifying sentences after Theorem 1 to explain the required assumptions as well as their limitations and scopes.
5. The introductory paragraph has been rephrased to emphasize our contributions in the field of causal mediation analysis compared to previous studies, with the theoretical proof of identifiability being addressed as a minor point.
Assigned Action Editor: ~Blake_Aaron_Richards1
Submission Number: 2622
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