A Semiparametric Mixed Model for the Weighted Composite Endpoint of Recurrent and Terminal Events

Recurrent event data with a terminal event are commonly encountered in longitudinal follow-up studies. In this paper, we investigate regression analysis of the weighted composite endpoint of recurrent and terminal events with a semiparametric mixed model. Particularly, the weighted composite endpoint is constructed by the severity of all events while leaving the dependence structure among the recurrent and terminal events unspecified. The semiparametric mixed model is flexible since it allows the covariate effects on the rate function of the weighted composite endpoint to be proportional or convergent. For inference on the model parameters, the estimating equation approach and the inverse probability weighting technique are developed. The asymptotic properties of the resulting estimators are established and the finite sample performance of the proposed procedure is evaluated through Monte Carlo simulation studies. We apply the proposed method to a real data set on a medical cost study of chronic heart failure patients for illustration.