Title: State occupation probabilities in non-Markov models
Authors: Morten Overgaard - Aarhus University (Denmark) [presenting]
Abstract: In multi-state models, state occupation probabilities may well be of interest. When the multi-state process has the Markov property, estimates of the state occupation probabilities can be based on the Aalen--Johansen estimates of the transition probabilities. This estimate is consistent under an independent censoring assumption. The estimate remains consistent when the multi-state process does not have the Markov property. We will take a look at why that is. The approach will be through seeing the transition probabilities as interval functions and studying certain additive and multiplicative transforms related to these interval functions. Under a bounded variation requirement, an appropriate expression of the state occupation probability can then be given in terms of the initial distribution and a product integral of the transition hazards even without the Markov property. This expression matches what is estimated by the Aalen--Johansen-based estimator of the state occupation probabilities under the independent censoring assumption thus establishing the claim.