Identification and multiply robust estimation in causal mediation analysis across principal strata

We consider assessing causal mediation in the presence of a post-treatment event (examples include noncompliance, a clinical event, or death). We identify natural mediation effects for the entire study population and for each principal stratum characterized by the joint potential values of the post-treatment event. We derive the efficient influence function for each mediation estimand, which motivates a set of multiply robust estimators for inference. The multiply robust estimators are consistent under four types of misspecifications and are efficient when all nuisance models are correctly specified. We also develop a nonparametric efficient estimator that leverages data-adaptive machine learners to achieve efficient inference and discuss sensitivity methods to address key identification assumptions. We illustrate our methods via simulations and two real data examples.