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Bayesian Inference for Mediation Effects Using Principal Stratification

Investigations in the social and health sciences often aim to understand causal relationships between an exposure and outcome. Given the multitude of pathways through which an exposure may affect the outcome, there is also interest on decomposing the effect of exposure into ``direct'' and ``mediated'' effects. Building on the potential outcome framework, we consider estimating direct and mediating effects with dichotomous mediators and outcomes, which is challenging as many parameters cannot be fully identified. Since likelihood theory is not well-developed for non-identifiable parameters, we consider a Bayesian approach that allows direct and mediated effects to be expressed as the posterior distributions of the parameters of interest. These distributions can be tightened by making further assumptions that can be encoded as prior distributions. We perform sensitivity analysis using several prior distributions that make weaker assumptions than monotonicity or the exclusion restriction. The methodology is illustrated using both real and simulated examples.