  In this paper we present a new methodology to model patient transitions and
length of stay in the emergency department using a series of conditional Coxian
phase-type distributions, with covariates. We reformulate the Coxian models
(standard Coxian, Coxian with multiple absorbing states, joint Coxian, and
conditional Coxian) to take into account heterogeneity in patient
characteristics such as arrival mode, time of admission and age. The approach
differs from previous research in that it reduces the computational time, and
it allows the inclusion of patient covariate information directly into the
model. The model is applied to emergency department data from University
Hospital Limerick in Ireland.
