Lifetime Data Analysis

, Volume 25, Issue 1, pp 168–188 | Cite as

Mixture regression models for the gap time distributions and illness–death processes

  • Chia-Hui Huang


The aim of this study is to provide an analysis of gap event times under the illness–death model, where some subjects experience “illness” before “death” and others experience only “death.” Which event is more likely to occur first and how the duration of the “illness” influences the “death” event are of interest. Because the occurrence of the second event is subject to dependent censoring, it can lead to bias in the estimation of model parameters. In this work, we generalize the semiparametric mixture models for competing risks data to accommodate the subsequent event and use a copula function to model the dependent structure between the successive events. Under the proposed method, the survival function of the censoring time does not need to be estimated when developing the inference procedure. We incorporate the cause-specific hazard functions with the counting process approach and derive a consistent estimation using the nonparametric maximum likelihood method. Simulations are conducted to demonstrate the performance of the proposed analysis, and its application in a clinical study on chronic myeloid leukemia is reported to illustrate its utility.


Copula Dependent censoring Gap event time Illness–death model Semiparametric transformation 



The authors are grateful for the helpful comments from an associate editor and two referees. This research was supported by Taiwan Ministry of Science and Technology Grant 104-2118-M-305-003.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of StatisticsNational Taipei UniversityTaipeiTaiwan

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