Mediation analysis for survival data using semiparametric probit models

Causal mediation modeling has become a popular approach for studying the effect of an exposure on an outcome through mediators. Currently, the literature on mediation analyses with survival outcomes largely focused on settings with a single mediator and quantified the mediation effects on the hazard, log hazard and log survival time (Lange and Hansen 2011; VanderWeele 2011). In this article, we propose a multi-mediator model for survival data by employing a flexible semiparametric probit model. We characterize path-specific effects (PSEs) of the exposure on the outcome mediated through specific mediators. We derive closed form expressions for PSEs on a transformed survival time and the survival probabilities. Statistical inference on the PSEs is developed using a nonparametric maximum likelihood estimator under the semiparametric probit model and the functional Delta method. Results from simulation studies suggest that our proposed methods perform well in finite sample. We illustrate the utility of our method in a genomic study of glioblastoma multiforme survival.