Bayesian inference for causal mediation effects using principal stratification with dichotomous mediators and outcomes

Most investigations in the social and health sciences aim to understand the directional or causal relationship between a treatment or risk factor and outcome. Given the multitude of pathways through which the treatment or risk factor may affect the outcome, there is also an interest in decomposing the effect of a treatment of risk factor into "direct" and "mediated" effects. For example, child's socioeconomic status (risk factor) may have a direct effect on the risk of death (outcome) and an effect that may be mediated through the adulthood socioeconomic status (mediator). Building on the potential outcome framework for causal inference, we develop a Bayesian approach for estimating direct and mediated effects in the context of a dichotomous mediator and dichotomous outcome, which is challenging as many parameters cannot be fully identified. We first define principal strata corresponding to the joint distribution of the observed and counterfactual values of the mediator, and define associate, dissociative, and mediated effects as functions of the differences in the mean outcome under differing treatment assignments within the principal strata. We then develop the likelihood properties and calculate nonparametric bounds of these causal effects assuming randomized treatment assignment. Because likelihood theory is not well developed for nonidentifiable parameters, we consider a Bayesian approach that allows the direct and mediated effects to be expressed in terms of the posterior distribution of the population parameters of interest. This range can be reduced by making further assumptions about the parameters that can be encoded in prior distribution assumptions. We perform sensitivity analyses by using several prior distributions that make weaker assumptions than monotonicity or the exclusion restriction. We consider an application that explores the mediating effects of adult poverty on the relationship between childhood poverty and risk of death.