Bayesian tree-based heterogeneous mediation analysis with a time-to-event outcome

Mediation analysis aims at quantifying and explaining the underlying causal mechanism between an exposure and an outcome of interest. In the context of survival analysis, mediation models have been widely used to achieve causal interpretation for the direct and indirect effects on the survival of interest. Although heterogeneity in treatment effect is drawing increasing attention in biomedical studies, none of the existing methods have accommodated the presence of heterogeneous causal pathways pointing to a time-to-event outcome. In this study, we consider a heterogeneous mediation analysis for survival data based on a Bayesian tree-based Cox proportional hazards model with shared topologies. Under the potential outcomes framework, individual-specific conditional direct and indirect effects are derived on the scale of the logarithm of hazards, survival probability, and restricted mean survival time. A Bayesian approach with efficient sampling strategies is developed to estimate the conditional causal effects through the Monte Carlo implementation of the mediation formula. Simulation studies show the satisfactory performance of the proposed method. The proposed model is then applied to an HIV dataset extracted from the ACTG175 study to demonstrate its usage in detecting heterogeneous causal pathways.