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Frailty models are essential tools in survival analysis for addressingunobserved heterogeneity and random effects in the data. These modelsincorporate a random effect, the frailty, which is assumed to impact the hazardrate multiplicatively. In this paper, we introduce a novel class of frailtymodels in both univariate and multivariate settings, using phase-typedistributions as the underlying frailty specification. We investigate theproperties of these phase-type frailty models and developexpectation-maximization algorithms for their maximum-likelihood estimation. Inparticular, we show that the resulting model shares similarities with the Gammafrailty model, has closed-form expressions for its functionals, and canapproximate any other frailty model. Through a series of simulated andreal-life numerical examples, we demonstrate the effectiveness and versatilityof the proposed models in addressing unobserved heterogeneity in survivalanalysis.

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