Modeling hospital length of stay by Coxian phase-type regression with heterogeneity

Xiaoqin Tang, Zhehui Luo and Joseph Gardiner have a new paper in Statistics in Medicine. This considers modelling right-censored length-of-stay data by using Coxian phase-type distributions, which are distributions defined by the times to absorption of a class of acyclic finite-state time homogeneous Markov processes. Coxian phase-type distributions have been used quite extensively to model right-censored survival data , particularly length-of-stay, see e.g. Marshall and Zenga. The novelty of the current paper is in the estimation of the model. Phase-type distributions suffer from being over parameterized and as a result suffer identifiability issues that in turn cause poor behaviour of optimization procedures. A further issue is the choice of the number of phases of the phase-type distribution. In the current paper a Bayesian reversible jump MCMC approach is taken.

Any acyclic Markov chain can be represented by a Coxian distribution in which the absolute values of the diagonal of the subgenerator matrix are decreasing. If parameters are unrestricted then there are inherent identifiability problems which would hamper the MCMC procedure. To avoid this the authors parameterize based on the first diagonal element and then the ratio (between 0 and 1) of the second element to the first, and so on, with the hazard of absorption from each phase being determined by a proportion (again between 0 and 1) of the diagonal element.