Multi-state models are increasingly being used to model complex epidemiological and clinical outcomes over time. It is common to assume that the models are Markov, but the assumption can often be unrealistic. The Markov assumption is seldomly checked and violations can lead to biased estimation of many parameters of interest. This is a well known problem for the standard Aalen-Johansen estimator of transition probabilities and several alternative estimators, not relying on the Markov assumption, have been suggested. A particularly simple approach known as landmarking have resulted in the Landmark-Aalen-Johansen estimator. Since landmarking is a stratification method a disadvantage of landmarking is data reduction, leading to a loss of power. This is problematic for “less traveled” transitions, and undesirable when such transitions indeed exhibit Markov behaviour. Introducing the concept of partially non-Markov multi-state models, we suggest a hybrid landmark Aalen-Johansen estimator for transition probabilities. We also show how non-Markov transitions can be identified using a testing procedure. The proposed estimator is a compromise between regular Aalen-Johansen and landmark estimation, using transition specific landmarking, and can drastically improve statistical power. We show that the proposed estimator is consistent, but that the traditional variance estimator can underestimate the variance of both the hybrid and landmark estimator. Bootstrapping is therefore recommended. The methods are compared in a simulation study and in a real data application using registry data to model individual transitions for a birth cohort of 184 951 Norwegian men between states of sick leave, disability, education, work and unemployment.

随着时间的推移，多状态模型越来越多地被用来模拟复杂的流行病学和临床结果。通常假设模型是马尔可夫模型，但这种假设通常是不切实际的。马尔可夫假设很少被检查，违反可能导致对许多感兴趣参数的估计出现偏差。对于转移概率的标准 Aalen-Johansen 估计量来说，这是一个众所周知的问题，并且已经提出了几种不依赖于马尔可夫假设的替代估计量。一种称为地标的特别简单的方法产生了 Landmark-Aalen-Johansen 估计器。由于地标是一种分层方法，地标的缺点是数据减少，从而导致功率损失。这对于“较少旅行”的转换来说是有问题的，并且当这种转换确实表现出马尔可夫行为时，这是不希望的。引入部分非马尔可夫多状态模型的概念，我们提出了一种用于转移概率的混合地标 Aalen-Johansen 估计器。我们还展示了如何使用测试程序来识别非马尔可夫转移。所提出的估计器是常规 Aalen-Johansen 和界标估计之间的折衷方案，使用特定于转换的界标，并且可以显着提高统计功效。我们证明所提出的估计器是一致的，但是传统的方差估计器可以低估混合估计器和界标估计器的方差。因此建议使用引导程序。在模拟研究和真实数据应用中对这些方法进行了比较，使用登记数据对 184 951 名挪威男性出生队列的病假、残疾、教育、工作和失业状态之间的个人转变进行建模。