Abstract
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.
Highlights
Multi-state models are increasingly being used to model complex epidemiological and clinical outcomes over time
The idea behind the hybrid landmark Aalen-Johansen (HAJ) estimator is to utilize the interpretation of transition probabilities as a functional of transition specific rates and provide a framework for analyzing how specific transitions affect the estimation of transition probabilities
This sensitivity analysis point of view is useful when modelling non-Markov multi-state data. It frames the problem of non-Markov behaviour as a more familiar problem of bias-variance trade-off by considering the HAJ estimator as a compromise between the AJ and the landmark Aalen-Johansen (LMAJ) estimators
Summary
Multi-state models are increasingly being used to model complex epidemiological and clinical outcomes over time. Several methods have been proposed for estimating transition probabilities in general semi- and non-Markov multi-state models based on subsampling (de Uña-Álvarez and Meira-Machado 2015; Allignol et al 2014; Titman 2015; Putter and Spitoni 2018). They differ in that they are valid for models of different level of complexity. The landmark Aalen-Johansen (LMAJ) method of Putter and Spitoni (2018) is based on analysing a subset of the population being in a specific state at a specific time point. In this paper we suggest an alternative approach, the hybrid landmark Aalen-Johansen (HAJ) estimator, for models consisting of Markov and non-Markov transitions. R code for implementation and reproduction of the simulation study is available on GitHub (see Supporting Information)
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