Multiply robust estimation of natural indirect effects with multiple ordered mediators

Multiple mediation analysis is a powerful methodology to assess causal effects in the presence of multiple mediators. Several methodologies, such as G-computation and inverse-probability-weighting, have been widely used to draw inferences about natural indirect effects (NIEs). However, a limitation of these methods is their potential for model misspecification. Although powerful semiparametric methods with high robustness and consistency have been developed for inferring average causal effects and for analyzing the effects of a single mediator, a comparably robust method for multiple mediation analysis is still lacking. Therefore, this theoretical study proposes a method of using multiply robust estimators of NIEs in the presence of multiple ordered mediators. We show that the proposed estimators not only enjoy the multiply robustness to model misspecification, they are also consistent and asymptotically normal under regular conditions. We also performed simulations for empirical comparisons of the finite-sample properties between our multiply robust estimators and existing methods. In an illustrative example, a dataset for liver disease patients in Taiwan is used to examine the mediating roles of liver damage and liver cancer in the pathway from hepatitis B/C virus infection to mortality. The model is implemented in the open-source R package "MedMR."