An estimator for state occupation probabilities in non-Markov multistate models

Abstract

In medical research, the progress of a disease can be modelled using multistate models. Quantities of interest are the transition hazard and the state occupation probabilities. In this thesis, we consider estimators of the integrated transition hazard and state occupation probabilities, with the possibility of right-censoring, in multistate models that are not necessarily Markov. We focus on deriving the Nelson-Aalen estimator and the Aalen-Johansen estimator, and show that these are consistent, by correcting the proofs in [1]. We work out the variance for the distribution of the latter estimator, and propose an estimator for this variance. The contribution of this manuscript is purely theoretical, without data simulations.