Sharp Mediation Analysis With Recanting Witnesses

ALEXANDER LEVIS – PERELMAN SCHOOL OF MEDICINE, UNIVERSITY OF PENNSYLVANIA 

ABSTRACT

Causal mediation analysis invariably relies on strong untestable identifying assumptions. The standard approach for point identifying natural direct and indirect effects assumes that there are no “recanting witnesses”, that is, post-treatment confounders of the mediator-outcome relationship. Alternatives include replacing estimands with less interpretable but identifiable randomized analogues, or assuming the treatment decomposes into components that do not simultaneously affect the same post-treatment confounders. Here, we pursue partial identification of true mediation quantities: natural path-specific effects under a nonparametric equation model with independent errors.  We show that sharp bounds arise as solutions to a challenging optimal transport problem. We provide a general solution by regularizing the bound functionals using entropic optimal transport, and derive flexible, nonparametric efficient estimators for the smoothed bounds. Further, we present preliminary results for separable effect estimands under a weaker structural model. In this case, we assume that the treatment can be decomposed into two distinct components, but allow both components to arbitrarily impact the same set of post-treatment confounders. Finally, we demonstrate the proposed methods in simulations and empirical examples.