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

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.