Frailty Models for Recurrent Events with Short Term Dependence

Recurrent events are one type of the multivariate survival data. Correlation between observations on each subject is the most important feature of this type of data. This feature does not allow using the ordinary survival models. Frailty models are one of the main approaches to the analysis of recurrent events. Ordinary Frailty models assumed the frailty is constant over time, that is not realistic in many applications. In this paper we introduce a time-dependent frailty model. The introduced model is based on piecewise semiparametric proportional hazard and frailty variable followed a Gamma distribution. The frailty variable in the model has a gamma process that is constant during each interval and has independent increments in the beginning of each interval. We found a close form function for integrated likelihood function and estimated parameters of model. The efficiency of introduced model was compared with an ordinary constant gamma model by a simulation study.