Semiparametric inference with correlated recurrence time data

We consider a study which monitors the occurrences of a recurrent event for nn subjects or units. Recurrent event data have many features which are worth looking into in the estimation process. In this manuscript, we consider the problem of estimating the distribution function of the inter-event times by taking into account two of these features: correlation among the inter-event times and the dependence and informative aspect of the right-censoring random variables. The parametric approach to the problem has been dealt with in Zamba and Adekpedjou (2011) [25]. The semiparametric approach is considered in this article. We derive a Kaplan–Meier type estimator of the distribution function under the gamma frailty model and an informative monitoring model for recurrent events by extending an approach due to Sellke (1988) [20]. The sampling distribution properties of the proposed estimators are examined through simulation studies. Furthermore, the performance of our proposed estimator is assessed with respect to the existing ones. The procedures are applied to a recurrent event dataset.