A discrete conditional phase-type model utilising a survival tree for the identification of elderly patient cohorts and their subsequent prediction of length of stay in hospital

Health care providers continue to feel the pressure in providing adequate care for an increasing elderly population. If length of stay patterns for elderly patients in care can be captured through analytical modelling, then accurate predictions may be made on when they are expected to leave hospital. The Discrete Conditional Phase-type (DC-Ph) model is an effective technique through which length of stay in hospital can be modelled and consists of both a conditional and a process component. This research expands the DC-Ph model by introducing a survival tree as the conditional component, whereby covariates are used to partition patients into cohorts based on their distribution of length of stay in hospital. The Coxian phase-type distribution is then used to model the length of stay for patients belonging to each cohort. A demonstration of how patient length of stay may be predicted for new admissions using this methodology is then given. This tool has the benefit of providing an aid to the decision making processes undertaken by hospital managers and has the potential to result in the more effective allocation of hospital resources. Hospital admission data from the Lombardy region of Italy is used as a case-study.