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Primary Submission Category: Causal Inference and Bias/Discrimination

Causal Inference with Hidden Mediators

Authors: AmirEmad Ghassami, Alan Yang, Ilya Shpitser, Eric Tchetgen Tchetgen,

Presenting Author: AmirEmad Ghassami*

Proximal causal inference was recently proposed as a framework to identify causal effects from observational data in the presence of hidden confounders. In this work, we extend the proximal causal inference approach to settings where identification of causal effects hinges upon a set of mediators which are not observed, yet error prone proxies of the hidden mediators are measured. Specifically, (i) We establish causal hidden mediation analysis, which extends classical causal mediation analysis methods for identifying direct and indirect effects to a setting where the mediator of interest is hidden. (ii) We establish hidden front-door criterion, which extends the classical front-door criterion to allow for hidden mediators. (iii) We show that the identification of a certain causal effect called population intervention indirect effect remains possible with hidden mediators in settings where challenges in (i) and (ii) might co-exist. We view (i)-(iii) as important steps towards the practical application of front-door criteria and mediation analysis as mediators are almost always measured with error and thus, the most one can hope for in practice is that the measurements are at best proxies of mediating mechanisms. We propose three identification approaches for the parameters of interest in our considered models. For the estimation aspect, we propose an influence function-based estimation method and provide an analysis for the robustness the estimators.