  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.
