Asymptotic theory for the Cox semi-Markov illness-death model.
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.
Shu
Youyi
Y
Department of Biometrics and Reporting, Centocor, Inc., 200 Great Valley Parkway, Mailstop C-4-1, Malvern, PA 19355, USA. yshu@cntus.jnj.com
Klein
John P
JP
Zhang
Mei-Jie
MJ
D001699:Biometry / Q000379:methods; D003198:Computer Simulation; D006801:Humans; D016013:Likelihood Functions; D008390:Markov Chains; D009369:Neoplasms / Q000453:epidemiology / Q000401:mortality; D015995:Prevalence; D016016:Proportional Hazards Models; D016019:Survival Analysis