Semiparametric Additive-Multiplicative Rates Model for Recurrent Events in Multi-Regional Studies in the Presence of a Terminal Event

We propose a general additive-multiplicative rate model for recurrent event data with a terminal event, enhancing flexibility by incorporating both additive and multiplicative effects on the rate function. To address regional heterogeneity often present in large-scale medical studies, cluster-specific baseline rate and hazard functions are utilized for recurrent and terminal events, respectively. Parameter estimation is performed using the inverse probability survival weighting approach. Theoretical results establish the asymptotic properties of the estimators, and simulation studies are conducted to assess finite-sample performance. Results demonstrate that the proposed method yields unbiased estimators and effectively characterizes region-specific heterogeneity. The practical value of the model is illustrated by applying it to cardiovascular disease data from diabetic patients.