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.

翻译：针对多状态模型中转移概率的建模，已提出多种估计量，例如Aalen-Johansen估计量、landmark Aalen-Johansen估计量以及混合Aalen-Johansen估计量。尽管Aalen-Johansen估计量通常仅在较为严格的马尔可夫假设下具有一致性，但landmark Aalen-Johansen估计量能够处理非马尔可夫多状态模型。然而，landmark Aalen-Johansen估计量会导致严格的数据缩减，从而增加方差。混合Aalen-Johansen估计量作为一种折中方案，首先通过基于对数秩检验的方法验证马尔可夫假设是否成立；其次，仅在马尔可夫假设被拒绝时应用landmark方法。在本研究中，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模型替代基于对数秩的检验来验证马尔可夫假设。此外，我们通过广泛的模拟研究，在马尔可夫、半马尔可夫及不同类型的非马尔可夫设置下比较了这四种估计量。为深入评估估计量的性能，我们考虑了四个不同指标：偏差、方差、均方根误差和覆盖率。同时，还分析了影响估计量的其他因素，如非马尔可夫行为的形式与程度、不同转移过程以及起始时间。模拟研究的主要结果表明，混合Aalen-Johansen估计量在多种指标和设置下均表现出优越性能。