Lifetime Data Analysis

, Volume 12, Issue 1, pp 53–67 | Cite as

Nonparametric Estimation of Sojourn Time Distributions for Truncated Serial Event Data—a Weight-adjusted Approach



In follow-up studies, survival data often include subjects who have had a certain event at recruitment and may potentially experience a series of subsequent events during the follow-up period. This kind of survival data collected under a cross-sectional sampling criterion is called truncated serial event data. The outcome variables of interest in this paper are serial sojourn times between successive events. To analyze the sojourn times in truncated serial event data, we need to confront two potential sampling biases arising simultaneously from a sampling criterion and induced informative censoring. In this study, nonparametric estimation of the joint probability function of serial sojourn times is developed by using inverse probabilities of the truncation and censoring times as weight functions to accommodate these two sampling biases under various situations of truncation and censoring. Relevant statistical properties of the proposed estimators are also discussed. Simulation studies and two real data are presented to illustrate the proposed methods.


Bivariate distribution Informative censoring Multiple events Nonparametric estimation Recurrent events Truncation 



We are very grateful to Associate Editor and two referees for their constructive comments that led to a significant improvement of this paper. We thank Dr. Mau-Roung Lin at Taipei Medical University Institute of Injury Prevention and Control for providing the anonymous motorcycle crash data. We also thank the Department of Health, Taiwan, R.O.C. for providing the Taiwan Cancer registry and Death registry data. Part of this work was supported by NSC-91-2118-M-002-003 from National Science Council in Taiwan.


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Copyright information

© Springer Science + Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Division of Biostatistics, Graduate Institute of Epidemiology, College of Public HealthNational Taiwan UniversityTaipeiTaiwan
  2. 2.Department of Agronomy, College of AgricultureNational Chiayi UniversityChiayiTaiwan

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