A hybrid landmark Aalen-Johansen estimator for transition probabilities in partially non-Markov multi-state models

TL;DR

This paper introduces a hybrid estimator for transition probabilities in multi-state models that balances the assumptions of Markov models with the robustness of landmark methods, improving statistical power in complex epidemiological data.

Contribution

It proposes a novel hybrid landmark Aalen-Johansen estimator for transition probabilities in partially non-Markov multi-state models, enhancing power while accommodating non-Markovian features.

Findings

The hybrid estimator outperforms traditional methods in simulations.

Application to Norwegian registry data demonstrates practical utility.

The method effectively captures complex transition dynamics.

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 for many parameters of interest. As argued by Datta and Satten (2001), the Aalen-Johansen estimator of occupation probabilities is consistent also in the non-Markov case. Putter and Spitoni (2018) exploit this fact to construct a consistent estimator of state transition probabilities, the landmark Aalen-Johansen estimator, which does not rely on the Markov assumption. 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. Using a framework of partially non-Markov multi-state models we suggest a hybrid landmark Aalen-Johansen estimator for transition probabilities. The proposed estimator is a compromise between regular Aalen-Johansen and landmark estimation, using transition specific landmarking, and can drastically improve statistical power. The methods are compared in a simulation study and in a real data application modelling individual transitions between states of sick leave, disability, education, work and unemployment. In the application, a birth cohort of 184951 Norwegian men are followed for 14 years from the year they turn 21, using data from national registries.