Bayesian mediation analysis for time-to-event outcome: Investigating racial disparity in breast cancer survival

Mediation analysis is conducted to make inferences on the effects of mediators that intervene in the relationship between an exposure variable and an outcome. Bayesian mediation analysis (BMA) naturally considers the hierarchical structure of the effects from the exposure variable to mediators and then to the outcome. We propose three BMA methods on survival outcomes, where mediation effects are measured in terms of hazard rate, survival time, or log of survival time respectively. In addition, we allow setting a limited survival time in the time-to-event analysis. The methods are validated by comparing the estimation precision at different scenarios through simulations. The three methods all give effective estimates. Finally, the methods are applied to the Surveillance, Epidemiology, and End Results Program (SEER) supported special studies to explore the racial disparity in breast cancer survival. The included variable completely explained the observed racial disparities. We provide visual aids to help with the result interpretations.