Consider a recurrent event data where frailty models are used to account for correlations among the inter-event times within each unit under study. In this talk we consider the problem of semiparametric estimation of the inter-event time distribution under informative monitoring and the Gamma frailty model. We propose a semiparametric estimator of the baseline survivor function. We show that the estimator under the i.i.d. setting is inconsistent in the presence of frailty. We present results of simulaiton study where we discuss the performence of our proposed estimator to that derived under the i.i.d. setting. Finally, these estimators will be demonstrated by applying to biomedical and engineering data sets
