A non-homogeneous Semi-Markov model for Interval Censoring

van Lieshout, Marie-Colette; Markwitz, Robin

doi:10.48550/arXiv.2401.17905

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.

Additional Metadata
Keywords	Inhomogeneity, Interval-censoring, Marked temporal point process, Markov point pro-, cess, Semi-Markov process
Persistent URL	doi.org/10.48550/arXiv.2401.17905
Project	State estimation for spatio-temporal point processes with applications to criminology
Grant	This work was funded by the The Netherlands Organisation for Scientific Research (NWO); grant id nwo/OCENW.Klein.068 - State estimation for spatio-temporal point processes with applications to criminology
Organisation	Stochastics
Citation APA Style AAA Style APA Style Cell Style Chicago Style Harvard Style IEEE Style MLA Style Nature Style Vancouver Style American-Institute-of-Physics Style Council-of-Science-Editors Style BibTex Format Endnote Format RIS Format CSL Format DOIs only Format	van Lieshout, M.-C., & Markwitz, R. (2024). A non-homogeneous Semi-Markov model for Interval Censoring. doi:10.48550/arXiv.2401.17905