Multi-Absorbing Phase-Type Distributions for Right-Censored Competing Risks Data
Abstract
Phase-type (PH) distributions are versatile semi-parametric models for lifetime duration and can be used in survival and reliability analysis. In this paper we put forward methods and software for using PH distributions in a competing-risks model. The resulting multi-absorbing phase-type (MAPH) distribution records both the time until absorption and its cause. After formulating basic properties of this family, we develop an EM algorithm for parameter inference from exact event-time/cause observations and independently right-censored observations. For a censored subject, the E-step conditions on survival up to the censoring time and imputes both the latent transient path and its eventual cause of absorption; closed-form cause-resolved sufficient-statistic expectations are obtained from matrix exponentials. We illustrate applications and numerical properties and describe two accompanying Julia packages, in which both the exact-event and the censored E-step are implemented. Applied to intensive-care length-of-stay data in full, censored records included, the method attains a higher likelihood than the phase-type competing-risks fit previously published for those data.
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BibTeX
@misc{qiao2026multiabsorbing,
title = {{Multi-Absorbing Phase-Type Distributions for Right-Censored Competing Risks Data}},
author = {Zhihao Qiao and Budhi Surya and Azam Asanjarani and Yoni Nazarathy},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19921},
eprint = {2609.19921},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19921},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Multi-Absorbing Phase-Type Distributions for Right-Censored Competing Risks Data
AU - Zhihao Qiao
AU - Budhi Surya
AU - Azam Asanjarani
AU - Yoni Nazarathy
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19921
UR - https://arxiv.org/abs/2609.19921
AB - Phase-type (PH) distributions are versatile semi-parametric models for lifetime duration and can be used in survival and reliability analysis. In this paper we put forward methods and software for using PH distributions in a competing-risks model. The resulting multi-absorbing phase-type (MAPH) distribution records both the time until absorption and its cause. After formulating basic properties of this family, we develop an EM algorithm for parameter inference from exact event-time/cause observations and independently right-censored observations. For a censored subject, the E-step conditions on survival up to the censoring time and imputes both the latent transient path and its eventual cause of absorption; closed-form cause-resolved sufficient-statistic expectations are obtained from matrix exponentials. We illustrate applications and numerical properties and describe two accompanying Julia packages, in which both the exact-event and the censored E-step are implemented. Applied to intensive-care length-of-stay data in full, censored records included, the method attains a higher likelihood than the phase-type competing-risks fit previously published for those data.
ER -