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    Rights statement: This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biostatistics following peer review. The definitive publisher-authenticated version Andrew C Titman, Hein Putter, General tests of the Markov property in multi-state models, Biostatistics, 23, 2: 380-396 is available online at: https://academic.oup.com/biostatistics/article/23/2/380/5906124

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General tests of the Markov property in multi-state models

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Published
<mark>Journal publication date</mark>30/04/2022
<mark>Journal</mark>Biostatistics
Issue number2
Volume23
Number of pages17
Pages (from-to)380-396
Publication StatusPublished
Early online date16/09/20
<mark>Original language</mark>English

Abstract

Multi-state models for event history analysis most commonly assume the process is Markov. This article considers tests of the Markov assumption that are applicable to general multi-state models. Two approaches using existing methodology are considered; a simple method based on including time of entry into each state as a covariate in Cox models for the transition intensities and a method involving detecting a shared frailty through a stratified Commenges-Andersen test. In addition, using the principle that under a Markov process the future rate of transitions of the process at times t > s should not be influenced by the state occupied at time s, a new class of general tests is developed by considering summaries from families of log-rank statistics where patients are grouped by the state occupied at varying initial time s. An extended form of the test applicable to models that are Markov conditional on observed covariates is also derived. The null distribution of the proposed test statistics are approximated by using wild bootstrap sampling. The approaches are compared in simulation and applied to a dataset on sleeping behaviour. The most powerful test depends on the particular departure from a Markov process, although the Cox-based method maintained good power in a wide range of scenarios. The proposed class of log-rank statistic based tests are most useful in situations where the non-Markov behaviour does not persist, or is not uniform in nature across patient time.

Bibliographic note

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Biostatistics following peer review. The definitive publisher-authenticated version Andrew C Titman, Hein Putter, General tests of the Markov property in multi-state models, Biostatistics, 23, 2: 380-396 is available online at: https://academic.oup.com/biostatistics/article/23/2/380/5906124