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 behavior. 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 behavior does not persist, or is not uniform in nature across patient time.

中文翻译：

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多状态模型中马尔可夫性质的一般检验

用于事件历史分析的多状态模型通常假设过程是马尔可夫。本文考虑适用于一般多状态模型的马尔可夫假设检验。考虑使用现有方法的两种方法；一种基于将进入每个状态的时间作为转换强度 Cox 模型中的协变量的简单方法，以及一种涉及通过分层 Commenges-Andersen 检验检测共同脆弱性的方法。此外，使用马尔可夫过程下过程的未来转移率有时|$t > s$|的原理。不应该受到当时所占据的状态的影响|$s$|⁠，通过考虑对数秩统计家族的摘要，开发了一类新的一般测试，其中患者按不同初始时间占据的状态进行分组|$s$|⁠. 还导出了适用于以观察到的协变量为条件的马尔可夫模型的扩展形式的检验。建议的测试统计数据的零分布通过使用野引导抽样来近似。在模拟中比较了这些方法，并将其应用于睡眠行为数据集。尽管基于 Cox 的方法在广泛的场景中保持良好的能力，但最强大的测试取决于与马尔可夫过程的特定偏离。所提出的基于对数秩统计的测试类别在非马尔可夫行为不持续或在整个患者时间内本质上不统一的情况下最有用。