Multi-Absorbing Phase-Type Distributions for Right-Censored Competing Risks Data

2026-09-17

AI Summary

本文提出了一种使用多吸收相型分布处理右删失竞争风险数据的方法，并通过EM算法进行参数推断，提高了对重症监护住院时间数据的拟合度。

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.

Problem

• Phase-type distributions
• Competing risks
• Right-censored data
• EM algorithm

Innovation

• Multi-Absorbing Phase-Type Distributions
• Competing Risks
• EM Algorithm
• Right-Censored Data
• Julia Packages