Causal Mediation Analysis of Survival Outcome with Multiple Mediators

Mediation analyses have been a popular approach to investigate the effect of an exposure on an outcome through a mediator. Mediation models with multiple mediators have been proposed for continuous and dichotomous outcomes. However, development of multimediator models for survival outcomes is still limited.

We present methods for multimediator analyses using three survival models: Aalen additive hazard models, Cox proportional hazard models, and semiparametric probit models. Effects through mediators can be characterized by path-specific effects, for which definitions and identifiability assumptions are provided. We derive closed-form expressions for path-specific effects for the three models, which are intuitively interpreted using a causal diagram.

Mediation analyses using Cox models under the rare-outcome assumption and Aalen additive hazard models consider effects on log hazard ratio and hazard difference, respectively; analyses using semiparametric probit models consider effects on difference in transformed survival time and survival probability. The three models were applied to a hepatitis study where we investigated effects of hepatitis C on liver cancer incidence mediated through baseline and/or follow-up hepatitis B viral load. The three methods show consistent results on respective effect scales, which suggest an adverse estimated effect of hepatitis C on liver cancer not mediated through hepatitis B, and a protective estimated effect mediated through the baseline (and possibly follow-up) of hepatitis B viral load.

Causal mediation analyses of survival outcome with multiple mediators are developed for additive hazard and proportional hazard and probit models with utility demonstrated in a hepatitis study.