# State occupation probabilities in non-Markov models

## TL;DR

This paper proves the consistency of estimators for state occupation probabilities in non-Markov multi-state models using a novel approach based on interval functions and their transforms.

## Contribution

It introduces a new method leveraging interval functions and their transforms to establish estimator consistency in non-Markov multi-state models.

## Key findings

- Established consistency of the estimator under certain assumptions.
- Connected additive and multiplicative transforms of interval functions.
- Provided explicit expressions for transition probabilities as interval functions.

## 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.