Mediation Analysis With Bayesian Nonlinear Joint Models: Evaluation of the Treatment Causal Pathways Between Tumor Growth Kinetics and Overall Survival

Understanding the mechanisms through which anti-cancer treatments influence survival is central to improving drug development and evaluation. In this work, we develop a Bayesian joint modeling framework for mediation analysis to quantify the extent to which tumor size dynamics mediate the effect of treatment on overall survival (OS). Our model integrates a nonlinear longitudinal sub-model describing tumor growth inhibition (TGI) with a parametric survival model, and supports several biologically motivated link functions between tumor size and survival. We explore alternative parameterizations of the treatment effect on tumor shrinkage and regrowth rates and assess their impact on mediation quantities. The approach is implemented using a Bayesian hierarchical joint model. Marginal effects are computed to characterize the proportion of treatment effect (PTE), natural direct effect (NDE), and natural indirect effect (NIE) over time. Through simulations under varying mediation levels and sample sizes, we evaluate bias, coverage, and identifiability of mediation quantities. Application to the IMBrave150 Phase III study suggests that the mediated proportion of the treatment effect varies over time, indicating that tumor dynamics partially but not fully capture the treatment mechanism of action. This framework provides a robust tool to investigate mediation mechanisms in oncology and may contribute to the validation of tumor size as a surrogate endpoint for survival.