Joint frailty model for recurrent events and death in presence of cure fraction: Application to breast cancer data.

In many biomedical cohort studies, recurrent or repeated events for individuals can be terminated by a dependent terminal event like death. In this context, the time of death may be associated with the underlying recurrent process and there often exists the dependence between the occurrences of recurrent events. Moreover, there are some situations in which a portion of patients could be cured. In the present study, the term "cured" means that some patients may neither experience any recurrent events nor death induced by the disease under study. We proposed a joint frailty model in the presence of cure fraction for analysis of the recurrent and terminal events and estimated the effect of covariates on the cure rate and both aforementioned events concurrently. The use of two independent gamma distributed frailties in this model enabled us to consider both the dependence between the recurrences and the survival times and the interrecurrences dependence. The model parameters were estimated employing the maximum likelihood method for a piecewise constant and a parametric baseline hazard function. Our proposed model was evaluated by a simulation study and illustrated using a real data set on patients with breast cancer who had undergone surgery.