Bayesian Semiparametric Joint Dynamic Model for Multitype Recurrent Events and a Terminal Event

In many biomedical research, recurrent events such as myocardial infraction, stroke, and heart failure often result in a terminal outcome such as death. Understanding the relationship among the multi-type recurrent events and terminal event is essential for developing interventions to prolong the terminal event such as death. This study introduces a Bayesian semiparametric joint dynamic model for type-specific hazards that quantifies how the type-specific event history dynamically changes the intensities of each recurrent event type and the terminal event over calendar time. The framework jointly captures unmeasured heterogeneity through a shared frailty term, cumulative effects of past recurrent events on themselves and terminal events, and the effects of covariates. Gamma process priors (GPP) are used as a nonparametric prior for the baseline cumulative hazard function (CHF) and parametric priors for covariates and frailty. For a more accurate risk assessment, this model provides an analytical closed-form estimator of cumulative hazard functions (CHF) and frailties. The Breslow-Aalen-type estimators of CHFs are special cases of our estimators when the precision parameters are set to zero. We evaluate the performance of the model through extensive simulations and apply the method to the Antihypertensive and Lipid-Lowering Treatment to Prevent Heart Attack Trial (ALLHAT). The analysis offers a practical past event effect based risk assessment for acute and chronic cardiovascular recurrent events with a terminal end point death and provides new information to support the prevention and treatment of cardiovascular disease to clinicians.