Causal mediation of semicompeting risks

Abstract

The semi-competing risks problem arises when one is interested in the effect of an exposure or treatment on both intermediate (e.g., having cancer) and primary events (e.g., death) where the intermediate event may be censored by the primary event, but not vice versa. Here we propose a nonparametric approach casting the semi-competing risks problem in the framework of causal mediation modeling. We set up a mediation model with the intermediate and primary events, respectively as the mediator and the outcome, and define an indirect effect as the effect of the exposure on the primary event mediated by the intermediate event and a direct effect as that not mediated by the intermediate event. A nonparametric estimator with time-varying weights is proposed for direct and indirect effects where the counting process at time t of the primary event $N_{2n_1}\left(t\right)$ and its compensator $A_{n_1}\left(t\right)$ are both defined conditional on the status of the intermediate event right before t, $N_1\left(t^{-}\right)=n_1$ . We show that $N_{2n_1}\left(t\right)-A_{n_1}\left(t\right)$ is a zero-mean martingale. Based on this, we further establish theoretical properties for the proposed estimators. Simulation studies are presented to illustrate the finite sample performance of the proposed method. Its advantage in causal interpretation over existing methods is also demonstrated in a hepatitis study.

Keywords: Nelson-Aalen estimator; causal inference; causal mediation model; martingale; semi-competing risk.