Using mixed phase-type distributions to model patient pathways

Modeling length of stay (LOS) in hospital is an important aspect of developing integrated models that describe and predict movements of patients. However patient pathways and LOS distributions are highly heterogeneous, particularly with regard to patient diagnosis, age, gender and outcome. We here use a mixed Coxian phase-type distribution (MC-PH distribution) to describe such heterogeneity in terms of covariates, where a Coxian phase-type survival tree is used to estimate parameters for the MC-PH distribution. Multiple absorbing states (such as discharge to home, discharge to private nursing home, or death) are considered, and, based on the MC-PH distribution, expressions presented for key performance indicators of interest. The approach is illustrated using data for stroke patients from the Belfast City Hospital.