标题： 多状态模型在潜在非马尔可夫过程中的估计量比较 显示英文标题

标题： Comparison of Estimators for Multi-State Models in Potentially Non-Markov Processes

摘要： 针对多状态模型中转换概率的建模，已经提出了各种估计量，例如Aalen-Johansen估计量、地标的Aalen-Johansen估计量以及混合的Aalen-Johansen估计量。虽然Aalen-Johansen估计量通常仅在较为严格的马尔可夫假设下是一致的，但地标的Aalen-Johansen估计量可以处理非马尔可夫的多状态模型。然而，地标的Aalen-Johansen估计量会导致严格的数据缩减，从而导致方差增加。混合的Aalen-Johansen估计量通过首先使用基于对数秩检验的检验来检查马尔可夫假设是否满足，作为折中方案。其次，只有在拒绝马尔可夫假设时才应用地标法。在本工作中，我们提出了一种新的混合Aalen-Johansen估计量，该估计量在第一步中使用Cox模型代替基于对数秩检验的检验来检查马尔可夫假设。此外，我们在马尔可夫、半马尔可夫和不同的非马尔可夫设置中进行了广泛的模拟研究，比较了四种估计量。为了深入了解估计量的表现，我们考虑了四个不同的指标：偏差、方差、均方根误差和覆盖率。此外，还分析了对估计量有进一步影响的因素，如非马尔可夫行为的形式和程度、不同的转换以及起始时间。模拟研究的主要结果是，混合的Aalen-Johansen估计量在各种指标和设置中都表现出良好的结果。 显示英文摘要

摘要： Various estimators for modelling the transition probabilities in multi-state models have been proposed, e.g., the Aalen-Johansen estimator, the landmark Aalen-Johansen estimator, and a hybrid Aalen-Johansen estimator. While the Aalen-Johansen estimator is generally only consistent under the rather restrictive Markov assumption, the landmark Aalen-Johansen estimator can handle non-Markov multi-state models. However, the landmark Aalen-Johansen estimator leads to a strict data reduction and, thus, to an increased variance. The hybrid Aalen-Johansen estimator serves as a compromise by, firstly, checking with a log-rank-based test whether the Markov assumption is satisfied. Secondly, landmarking is only applied if the Markov assumption is rejected. In this work, we propose a new hybrid Aalen-Johansen estimator which uses a Cox model instead of the log-rank-based test to check the Markov assumption in the first step. Furthermore, we compare the four estimators in an extensive simulation study across Markov, semi-Markov, and distinct non-Markov settings. In order to get deep insights into the performance of the estimators, we consider four different measures: bias, variance, root mean squared error, and coverage rate. Additionally, further influential factors on the estimators such as the form and degree of non-Markov behaviour, the different transitions, and the starting time are analysed. The main result of the simulation study is that the hybrid Aalen-Johansen estimators yield favourable results across various measures and settings.