The Cox–Aalen Rate Model for Recurrent Events With an Informative Terminal Event

Recurrent event data arise frequently in many clinical and observational studies. In this article, we propose a Cox-Aalen rate model to analyze recurrent event data with a terminal event, where the covariate effects are additive, time-varying, and dependent on a latent variable nonparametrically. The association between recurrent and terminal events is fully nonparametric, and a proportional hazards model is specified for the terminal event. To estimate the model parameters, an estimating equation approach is developed and kernel-smoothing techniques are employed to estimate the conditional expectations in the estimating equation. The asymptotic properties of the proposed estimators are derived, and the finite sample performance is evaluated through simulation studies. An application to medical cost data for chronic heart failure patients is presented.