Joint Frailty Mixing Model for Recurrent Event Data with an Associated Terminal Event: Application to Hospital Readmission Data

Recurrent events like repeated hospitalization, cancer tumour recurrences, and many others occur frequently. The follow-up on recurrent events may be stopped by a terminal event like death. It is obvious that if the frequencies of recurrent events are more, then it may lead to a terminal event and in this case terminal event becomes ‘dependent’. In this article, we study a joint modelling and analysis of recurrent events with a dependent terminal event. Here, the proportional intensity model for the recurrent events process and the proportional hazard model for the terminal event time are taken. To account for the association between recurrent events and terminal events, mixing frailty or random effect is studied rather than available pure frailty. In our case, the distribution of frailty is introduced as a mixture of folded normal distribution and gamma distribution rather than using pure gamma distribution. An estimation procedure in the joint frailty model is applied to estimate the parameters of the model. This method is close to the method of minimum chi-square rather than a complicated one. An extensive simulation study has been performed to estimate the model parameters and the performances are evaluated based on bias and MSE criteria. Further from an application point of view, the method is illustrated to a hospital readmission data for colorectal cancer patients.