A non-homogeneous Semi-Markov model for Interval Censoring

TL;DR

This paper introduces a non-homogeneous semi-Markov model for interval-censored data, allowing for time-dependent censoring mechanisms and underlying distributions, improving flexibility over traditional homogeneous models.

Contribution

It proposes a novel non-homogeneous semi-Markov framework for interval censoring, including a new censoring mechanism and a Markov point process model for occurrence times.

Findings

Model accommodates time-dependent censoring and occurrence distributions

Derived the conditional distribution of occurrence times given intervals

Compared non-homogeneous model to homogeneous approaches with positive results

Abstract

Previous approaches to modelling interval-censored data have often relied on assumptions of homogeneity in the sense that the censoring mechanism, the underlying distribution of occurrence times, or both, are assumed to be time-invariant. In this work, we introduce a model which allows for non-homogeneous behaviour in both cases. In particular, we outline a censoring mechanism based on semi-Markov processes in which interval generation is assumed to be time-dependent and we propose a Markov point process model for the underlying occurrence time distribution. We prove the existence of this process and derive the conditional distribution of the occurrence times given the intervals. We provide a framework within which the process can be accurately modelled, and subsequently compare our model to homogeneous approaches by way of a parametric example.