Phase-type frailty models: A flexible approach to modeling unobserved heterogeneity in survival analysis

TL;DR

This paper introduces a new class of frailty models using phase-type distributions to better capture unobserved heterogeneity in survival analysis, with efficient estimation algorithms and demonstrated versatility.

Contribution

The paper presents a novel phase-type frailty model framework, including properties, estimation methods, and its ability to approximate other frailty models.

Findings

Model shares similarities with Gamma frailty model

Closed-form expressions for functionals

Effective in simulated and real data examples

Abstract

Frailty models are essential tools in survival analysis for addressing unobserved heterogeneity and random effects in the data. These models incorporate a random effect, the frailty, which is assumed to impact the hazard rate multiplicatively. In this paper, we introduce a novel class of frailty models in both univariate and multivariate settings, using phase-type distributions as the underlying frailty specification. We investigate the properties of these phase-type frailty models and develop expectation-maximization algorithms for their maximum-likelihood estimation. In particular, we show that the resulting model shares similarities with the Gamma frailty model, has closed-form expressions for its functionals, and can approximate any other frailty model. Through a series of simulated and real-life numerical examples, we demonstrate the effectiveness and versatility of the proposed models in addressing unobserved heterogeneity in survival analysis.