State occupation probabilities in non-Markov models

Abstract

The consistency of the Aalen--Johansen-derived estimator of state occupation probabilities in non-Markov multi-state settings is studied and established via a new route. This new route is based on interval functions and relies on a close connection between additive and multiplicative transforms of interval functions, which is established. Under certain assumptions, the consistency follows from explicit expressions of the additive and multiplicative transforms related to the transition probabilities as interval functions, which are obtained, in combination with certain censoring and positivity assumptions.

References in corpus (2)

• On the assumption of independent right censoring
• Counting processes in $p$-variation with applications to recurrent events

Cited by in corpus (1)

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