Joint modeling of interval counts of recurrent events and death

When a recurrent event process is ended by death, this may imply dependent censoring if the two processes are associated. Such dependent censoring would have to be modeled to obtain a valid inference. Moreover, the dependence between the recurrence process and the terminal event may be the primary topic of interest. Joint frailty models for recurrent events and death, which include a separate dependence parameter, have been proposed for exactly observed recurrence times. However, in many situations, only the number of events experienced during consecutive time intervals are available. We propose a method for estimating a joint frailty model based on such interval counts and observed or independently censored terminal events. The baseline rates of the two processes are modeled by piecewise constant functions, and Gaussian quadrature is used to approximate the marginal likelihood. Covariates can be included in a proportional rates setting. The observation intervals for the recurrent event counts can differ between individuals. Furthermore, we adapt a score test for the association between recurrent events and death to the setting in which only individual interval counts are observed. We study the performance of both approaches via simulation studies, and exemplify the methodology in a biodemographic study of the dependence between budding rates and mortality in the species Eleutheria dichotoma.