Causal mediation analysis for survival outcome with unobserved mediator–outcome confounders

The indirect effect of the treatment on the survival outcome through the mediate variable and the direct effect of the treatment on the survival outcome are described. The relationships between the direct and indirect effects and the parameters of three models for survival analysis are provided. The conditions for identifying the direct and indirect effects of the treatment on the survival outcome with an unobserved mediator–outcome confounder vector are presented. Further the identifiability is illustrated via a simulation study. Finally, the proposed approaches are applied to a real data set to illustrate the methodology.