Causal inference with a mediated proportional hazards regression model

The natural direct and indirect effects in causal mediation analysis with survival data having one mediator is addressed by VanderWeele. He derived an approach for (1) accelerated failure time regression model general cases (2) a proportional hazards when the time-to-event outcome rare. If not rare, then VanderWeele did derive simple closed-form expression log-natural because baseline cumulative hazard function does zero. We develop two approaches to extend VanderWeele’s approach, which assumption of rare required. obtain specific points through numerical integration after we calculate applying Breslow method Cox estimate unspecified hazard; assuming piecewise constant model, yielding parametric hazard. conduct simulation studies compare our other methods illustrate them from ASsessment, Serial Evaluation, Subsequent Sequelae Acute Kidney Injury (ASSESS-AKI) Consortium.