Dynamic inference for non-Markov transition probabilities under random right censoring

Dennis Dobler*, Andrew Titman

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

The main contribution of this article is the verification of weak convergence of a general non-Markov (NM) state transition probability estimator by Titman, which has not yet been done for any other general NM estimator. A similar theorem is shown for the bootstrap, yielding resampling-based inference methods for statistical functionals. Formulas of the involved covariance functions are presented in detail. Particular applications include the conditional expected length of stay in a specific state, given occupation of another state in the past, and the construction of time-simultaneous confidence bands for the transition probabilities. The expected lengths of stay in a two-sample liver cirrhosis dataset are compared and confidence intervals for their difference are constructed. With borderline significance and in comparison to the placebo group, the treatment group has an elevated expected length of stay in the healthy state given an earlier disease state occupation. In contrast, the Aalen-Johansen (AJ) estimator-based confidence interval, which relies on a Markov assumption, leads to a drastically different conclusion. Also, graphical illustrations of confidence bands for the transition probabilities demonstrate the biasedness of the AJ estimator in this data example. The reliability of these results is assessed in a simulation study.

Original languageEnglish
Pages (from-to)572-586
Number of pages15
JournalScandinavian Journal of Statistics
Volume47
Issue number2
Early online date14 Jan 2020
DOIs
Publication statusPublished - 1 Jun 2020

Keywords

  • confidence bands
  • Markov assumption
  • multistate model
  • restricted conditional expected length of stay
  • right censoring
  • weak convergence

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