Presmoothed estimators of the state occupation probabilities in multi-state survival data

Abstract

The progress of a disease can be analyzed using multistate models. These models focus on two key parameters of interest: the transition hazard and the state occupation probabilities. The state occupation probabilities have been consistently estimated by the Aalen-Johansen estimator. This estimator is particularly well-suited for handling censoring and benefits from the Markov assumption in the underlying stochastic process. In some cases, these estimators may lead to estimators with higher variability. To mitigate this issue we propose alternative estimators that incorporate a preliminary estimation approach. We introduce also practical estimation techniques for the state occupation probabilities, considering covariate measures. We explore the finite sample behavior of the estimators through simulations. An application to breast cancer is included.