Mediation analysis with causally ordered mediators using Cox proportional hazards model

Causal mediation analysis aims to investigate the mechanism linking an exposure and an outcome. However, studies regarding mediation effects on survival outcomes are limited, particularly in multi-mediator settings. The existing multi-mediator analyses for survival outcomes are either performed under special model specifications such as probit models or additive hazard models, or they assume a rare outcome. Here, we propose a novel multi-mediation analysis based on the widely used Cox proportional hazards model without the rare outcome assumption. We develop a methodology under a counterfactual framework to identify path-specific effects (PSEs) of the exposure on the outcome through the mediator(s) and derive the closed-form formula for PSEs on a transformed survival time. Moreover, we show that the convolution of an extreme value and Gaussian random variables converges to another Gaussian, provided that the variance of the original Gaussian gets large. Based on that, we further derive closed-form expressions for PSEs on survival probabilities. Asymptotic properties are established for both estimators. Extensive simulation is conducted to evaluate the finite sample performance of our proposed estimators and to compare with existing methods. The utility of the proposed method is illustrated in a hepatitis study of liver cancer risk.