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

Dobler, Dennis and Titman, Andrew Charles (2020) Dynamic inference for non-Markov transition probabilities under random right-censoring. Scandinavian Journal of Statistics. ISSN 0303-6898

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Abstract

The main contribution of this article is the verification of} weak convergence of the general non-Markov state transition probability estimator by Titman (2015) which has not yet been done for any other general non-Markov 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 the two-sample liver cirrhosis data-set by Andersen et al (1993) 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 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 Aalen-Johansen estimator in this data example. The reliability of these results is assessed in a simulation study.

Item Type:
Journal Article
Journal or Publication Title:
Scandinavian Journal of Statistics
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/1800/1804
Subjects:
ID Code:
138489
Deposited By:
Deposited On:
31 Oct 2019 09:55
Refereed?:
Yes
Published?:
Published
Last Modified:
05 Apr 2020 04:43