Causal Mediation for Survival Data: A Unifying Approach via GLM

Mediation analysis has been receiving much attention from the scientific community in the last years, mainly due to its ability to disentangle causal pathways from exposures to outcomes. Particularly, causal mediation analysis for time-to-event outcomes has been widely discussed using accelerated failures times, Cox and Aalen models, with continuous or binary mediator. We derive general expressions for the Natural Direct Effect and Natural Indirect Effect for the time-to-event outcome when the mediator is modeled using generalized linear models, which includes existing procedures as particular cases. We also define a responsiveness measure to assess the variations in continuous exposures in the presence of  ediation. We consider a community-based prospective cohort study that investigates the mediation of hepatitis B in the relationship between hepatitis C and liver cancer. We fit different models as well as distinct distributions and link functions associated to the mediator. We also notice that estimation of NDE and NIE using different models leads to non-contradictory conclusions despite their effect scales. The survival models provide a compelling framework that is appropriate to answer many research questions involving causal mediation analysis. The extensions through GLMs for the mediator may encompassa broad field of medical research, allowing the often necessary control for confounding.