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Lifetime Data Analysis

, Volume 13, Issue 1, pp 91–117 | Cite as

Asymptotic theory for the Cox semi-Markov illness-death model

  • Youyi Shu
  • John P. Klein
  • Mei-Jie Zhang
Article

Abstract

Irreversible illness-death models are used to model disease processes and in cancer studies to model disease recovery. In most applications, a Markov model is assumed for the multistate model. When there are covariates, a Cox (1972, J Roy Stat Soc Ser B 34:187–220) model is used to model the effect of covariates on each transition intensity. Andersen et al. (2000, Stat Med 19:587–599) proposed a Cox semi-Markov model for this problem. In this paper, we study the large sample theory for that model and provide the asymptotic variances of various probabilities of interest. A Monte Carlo study is conducted to investigate the robustness and efficiency of Markov/Semi-Markov estimators. A real data example from the PROVA (1991, Hepatology 14:1016–1024) trial is used to illustrate the theory.

Keywords

Cox model Illness-death process Prevalence function Probability of being in response function Semi-Markov model 

Notes

Acknowledgements

This research was supported by a grant from the National Cancer Institute. The first author is indebted to Professor Per Kragh Andersen of the University of Copenhagen for suggesting this problem as a dissertation topic and for providing the PROVA trial data.

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Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Biometrics and ReportingCentocor, Inc.MalvernUSA
  2. 2.Division of BiostatisticsMedical College of WisconsinMilwaukeeUSA

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