Decomposition, identification and multiply robust estimation of natural mediation effects with multiple mediators

Summary

Natural mediation effects are desirable estimands for studying causal mechanisms in a population, but complications arise in defining and estimating natural indirect effects through multiple mediators with an unspecified causal ordering. We propose a decomposition of the natural indirect effect of multiple mediators into individual components, termed exit indirect effects, and a remainder interaction term, and study the similarities to and differences from existing natural and interventional effects in the literature. We provide a set of identification assumptions for estimating all components of the proposed natural effect decomposition and derive the semiparametric efficiency bounds for the effects. The efficient influence functions contain conditional densities that are variationally dependent, which is uncommon in existing problems and may lead to model incompatibility. By ensuring model compatibility through a reparameterization based on copulas, our estimator is quadruply robust, which means that it remains consistent and asymptotically normal under four types of possible misspecification, and also is locally semiparametric efficient. We further propose a stabilized quadruply robust estimator to improve practical performance under possibly misspecified models, as well as a nonparametric extension based on sample splitting.