Joint model for recurrent event data with a cured fraction and a terminal event

In a longitudinal study where the recurrence of an event and a terminal event such as death are observed, a certain portion of the subjects may experience no event during a long follow-up period; this often denoted as the cure group which is assumed to be the risk-free from both recurrent events and death. However, this assumption ignores the possibility of death, which subjects in the cure group may experience. In the present study, such misspecification is investigated with the addition of a death hazard model to the cure group. We propose a joint model using a frailty effect, which reflects the association between a recurrent event and death. For the estimation, an expectation-maximization (EM) algorithm was developed and PROC NLMIXED in SAS was incorporated under a piecewise constant baseline. Simulation studies were performed to check the performance of the suggested method. The proposed method was applied to leukemia patients experiencing both infection and death after bone marrow transplant.