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.

中文翻译：

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随机右删失下非马尔可夫转移概率的动态推理

本文的主要贡献是Titman对一般非马尔可夫（NM）状态转移概率估计器弱收敛性的验证，这是其他任何一般NM估计器尚未完成的。为引导程序显示了类似的定理，为统计函数产生基于重采样的推理方法。详细介绍了所涉及的协方差函数的公式。特定应用包括在特定状态下的条件预期停留时间，给定过去另一个状态的职业，以及为转换概率构建时间同步置信带。比较了两个样本肝硬化数据集中的预期停留时间，并构建了它们差异的置信区间。与安慰剂组相比，具有临界意义，鉴于较早的疾病状态职业，治疗组在健康状态下的预期停留时间延长。相比之下，依赖于马尔可夫假设的基于 Aalen-Johansen (AJ) 估计量的置信区间会导致截然不同的结论。此外，转移概率的置信区间的图形说明证明了该数据示例中 AJ 估计量的偏差。在模拟研究中评估了这些结果的可靠性。转移概率的置信区间的图形说明证明了该数据示例中 AJ 估计量的偏差。在模拟研究中评估了这些结果的可靠性。转移概率的置信区间的图形说明证明了该数据示例中 AJ 估计量的偏差。在模拟研究中评估了这些结果的可靠性。