Estimation with right‐censored observations under a semi‐Markov model |
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Authors: | Lihui Zhao X. Joan Hu |
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Affiliation: | 1. Department of Preventive Medicine, Northwestern University, Chicago, IL 60611, USA;2. Department of Statistics and Actuarial Science, Simon Fraser University, Burnaby, BC, Canada V5A1S6 |
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Abstract: | The semi‐Markov process often provides a better framework than the classical Markov process for the analysis of events with multiple states. The purpose of this paper is twofold. First, we show that in the presence of right censoring, when the right end‐point of the support of the censoring time is strictly less than the right end‐point of the support of the semi‐Markov kernel, the transition probability of the semi‐Markov process is nonidentifiable, and the estimators proposed in the literature are inconsistent in general. We derive the set of all attainable values for the transition probability based on the censored data, and we propose a nonparametric inference procedure for the transition probability using this set. Second, the conventional approach to constructing confidence bands is not applicable for the semi‐Markov kernel and the sojourn time distribution. We propose new perturbation resampling methods to construct these confidence bands. Different weights and transformations are explored in the construction. We use simulation to examine our proposals and illustrate them with hospitalization data from a recent cancer survivor study. The Canadian Journal of Statistics 41: 237–256; 2013 © 2013 Statistical Society of Canada |
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Keywords: | Case fatality ratio confidence band identifiability multi‐state process semi‐Markov kernel semi‐Markov process Sojourn time distribution transition probability MSC 2010: Primary 62M09 secondary 62N01 |
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