Estimation with right-censored observations under a semi-Markov model

Lihui Zhao*, X. Joan Hu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)237-256
Number of pages20
JournalCanadian Journal of Statistics
Volume41
Issue number2
DOIs
StatePublished - Jun 1 2013

Keywords

  • Case fatality ratio
  • Confidence band
  • Identifiability
  • Multi-state process
  • Semi-Markov kernel
  • Semi-Markov process
  • Sojourn time distribution
  • Transition probability

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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