A hybrid landmark Aalen-Johansen estimator for transition probabilities in partially non-Markov multi-state models
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Violations of the Markov assumption in multi-state models are not uncommon, and problematic for estimation of many parameters of interest. The assumption is seldomly checked, which may lead to biased estimation. However, 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 so-called landmark Aalen-Johansen estimator, which does not rely on the Markov assumption. A consequence 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 of transition probabilities. The proposed estimator is a compromise between regular Aalen-Johansen and landmark estimation, using transition specific landmarking. Inspired by the Markov test of Titman and Putter (2020) we suggest a transition specific Markov-test as a possible selection criterion to obtain an estimator utilizing a larger sample than the traditional landmark method. The methods are applied in a three-state simulation study and to real world data on individual transitions between states of sick leave, disability, education, work and unemployment. The latter dataset includes information from various national registries on 184 951 Norwegian men born between 1971 and 1976, followed up from July 1st the year subjects turned 21 (1992-1997) until December 31st, 14 years later. The results show that the hybrid approach can drastically improve statistical power.
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