Semiparametric Inference with Correlated Recurrence Time Data


We consider a study which monitors the occurrences of a recurrent event for n 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.


Mathematics and Statistics


The authors are grateful to the editor in chief and the referees for a number of suggestions for improvement. The authors thank Dr. John Singler for his careful reading of the manuscript. Dr. Akim Adekpedjou acknowledges research support from the Missouri Research Board (MRB) grant No. DEPTID R 6016058 MOCODE RC460 and Dr. Jonathan Quiton acknowledges research support from the Kentucky EPSCoR Research Startup Fund No. RSF-031-06 .

Keywords and Phrases

Correlated recurrence times; EM algorithm; Frailty model; Informative monitoring; Martingales

International Standard Serial Number (ISSN)


Document Type

Article - Journal

Document Version


File Type





© 2013 Elsevier, All rights reserved.

Publication Date

01 Jan 2013