Mediation analysis for mixture Cox proportional hazards cure models.

Mediation analysis aims to decompose a total effect into specific pathways and investigate the underlying causal mechanism. Although existing methods have been developed to conduct mediation analysis in the context of survival models, none of these methods accommodates the existence of a substantial proportion of subjects who never experience the event of interest, even if the follow-up is sufficiently long. In this study, we consider mediation analysis for the mixture of Cox proportional hazards cure models that cope with the cure fraction problem. Path-specific effects on restricted mean survival time and survival probability are assessed by introducing a partially latent group indicator and applying the mediation formula approach in a three-stage mediation framework. A Bayesian approach with P-splines for approximating the baseline hazard function is developed to conduct analysis. The satisfactory performance of the proposed method is verified through simulation studies. An application of the Alzheimer's disease (AD) neuroimaging initiative dataset investigates the causal effects of APOE-