Joint frailty model for recurrent events and a terminal event in the presence of cure fraction

The observations of repeated or recurrent events occur in many longitudinal studies. Furthermore, sometimes there may exist a terminal event such as death, which is strongly correlated with recurrent events. In many situations, a fraction of subjects who will never experience the event of interest during a long follow-up period is considered to be cured. In this article, we proposed a joint frailty model in the presence of cure fraction. The dependency is modeled by shared frailty that is contained in both the recurrent andterminal events hazard functions. It allows to estimate two separate sets of parameters on the recurrent, death, and cure model. We applied the maximum likelihood method under a piecewise constant hazard function for model fitting. The proposed model is evaluated by simulation studies and an application to a breast cancer data is provided.