General joint frailty model for recurrent event data with a dependent terminal event: Application to follicular lymphoma data.

Many biomedical studies focus on delaying disease relapses and on prolonging survival. Usual methods only consider one event, often the first recurrence or death. However, ignoring the other recurrences may lead to biased results. The whole history of the disease should be considered for each patient. In addition, some diseases involve recurrences that can increase the risk of death. In this case, the death time may be dependent on the recurrent event history. We propose a joint frailty model to analyze recurrences and death simultaneously. Two gamma-distributed frailties take into account both the inter-recurrences dependence and the dependence between the recurrences and the survival times. We estimate separate parameters for disease recurrent event times and survival times in the joint frailty model to distinguish treatment effects and prognostic factors on these two types of events. We show how maximum penalized likelihood estimation can be applied to semiparametric estimation of the continuous hazard functions in the proposed joint frailty model with right censoring. We also propose parametrical approach. We evaluate the model by simulation studies and illustrate through a study of patients with follicular lymphoma.