• clustered survival data;
  • Cox proportional hazards model;
  • Kaplan–Meier estimator;
  • log-rank test;
  • multiple outputation;
  • multivariate survival times


The gap times between recurrent events are often of primary interest in medical and epidemiology studies. The observed gap times cannot be naively treated as clustered survival data in analysis because of the sequential structure of recurrent events. This paper introduces two important building blocks, the averaged counting process and the averaged at-risk process, for the development of the weighted risk-set (WRS) estimation methods. We demonstrate that with the use of these two empirical processes, existing risk-set based methods for univariate survival time data can be easily extended to analyze recurrent gap times. Additionally, we propose a modified within-cluster resampling (MWCR) method that can be easily implemented in standard software. We show that the MWCR estimators are asymptotically equivalent to the WRS estimators. An analysis of hospitalization data from the Danish Psychiatric Central Register is presented to illustrate the proposed methods. Copyright © 2010 John Wiley & Sons, Ltd.