Asymptotic theory for the Cox semi-Markov illness-death model |
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Authors: | Youyi Shu John P Klein Mei-Jie Zhang |
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Institution: | (1) Department of Biometrics and Reporting, Centocor, Inc., 200 Great Valley Parkway, Mailstop C-4-1, Malvern, PA 19355, USA;(2) Division of Biostatistics, Medical College of Wisconsin, 8701 Watertown Plank Road, Milwaukee, WI 53226, USA |
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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. |
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Keywords: | Cox model Illness-death process Prevalence function Probability of being in response function Semi-Markov model |
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