Semiparametric Transformation Models for Interventional Path-Specific Effects with Multiple Time-to-Event Mediators

Abstract

Disease progression is often characterized by a sequence of time-to-event milestones subject to right censoring and structural dependence, where terminal events may preclude the subsequent occurrence or observation of intermediate events. For instance, in the progression from hepatitis B or C infection to mortality, patients may experience intermediate events such as liver cirrhosis and hepatocellular carcinoma. Quantifying causal effects along specific pathways is scientifically important yet methodologically challenging, as multiple time-to-event mediators are correlated and constrained by an event-ordering structure. Although recent nonparametric approaches have addressed interventional path-specific effects (iPSEs) in this context, they often rely on stratification for confounding adjustment, which can lead to substantial efficiency loss, particularly when confounders are continuous or high-dimensional. To balance robustness and efficiency, we propose a semiparametric approach based on a family of transformation models that allows data-adaptive model selection while accommodating covariate adjustment. Under the identification formula, the target interventional hazard is represented as a weighted combination of state-specific hazards for the terminal event, with weights determined by mediator-state probabilities. We model the state-specific hazards using semiparametric transformation models and the mediator-state probabilities using time-specific logistic regressions. The resulting iPSE estimators are constructed by plugging the estimated model components into the identification formula. We further establish uniform consistency of the proposed estimators and weak convergence of the estimated iPSE processes to tight mean-zero Gaussian processes. Simulation studies show that the proposed approach achieves substantially smaller variance than the nonparametric estimator and accurately recovers the target iPSEs when the selected transformation models are correctly specified. In an analysis of the motivating REVEAL cohort, we investigate the effects of hepatitis B and C on mortality through pathways involving liver cirrhosis and liver cancer. The conclusions are consistent with prior nonparametric results but are supported by smaller standard errors and stronger statistical evidence, demonstrating the practical gains of data-adaptive semiparametric modeling.

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