Phase-type Models for Competing Risks

We extend the phase-type methodology for modeling of lifetime distributions to the case of competing risks. This is done by considering finite state Markov chains in continuous time with more than one absorbing state, letting each absorbing state correspond to a particular risk. We study statistical estimation from (possibly censored) competing risks data modeled by the phase-type approach. Using results from the literature we consider estimation via the EM algorithm as well as Bayesian estimation using Markov chain Monte Carlo methods. Treatment of covariates in competing risks data is also be discussed.