Fitting phase-type frailty models

Frailty models are survival analysis models which account for heterogeneity and random effects in the data. In these models, the random effect (the frailty) is assumed to have a multiplicative effect on the hazard. In this paper, we present frailty models using phase-type distributions as the frailties. We explore the properties of the proposed frailty models and derive expectation-maximization algorithms for maximum-likelihood estimation. The algorithms' performance is illustrated in several numerical examples of practical significance.