A General Additive-multiplicative Rates Model for Recurrent and Terminal Events

Recurrent events data with a terminal event(e.g. death) often arise in clinical and observational studies. Most of existing models assume multiplicative covariate effects and model the conditional recurrent event rate given survival. In this article, we propose a general additive-multiplicative rates model for recurrent event data in the presence of a terminal event, where the terminal event stop the further occurrence of recurrent events. Based on the estimating equation approach and the inverse probability weighting technique, we propose two procedures for estimating the regression parameters and the baseline mean function. The asymptotic properties of the resulting estimators are established. In addition, some graphical and numerical procedures are presented for model checking. The finite-sample behavior of the proposed methods is examined through simulation studies, and an application to a bladder cancer study is also illustrated.