Predicting elderly patient length of stay in hospital and community care using a series of conditional Coxian phase-type distributions, further conditioned on a survival tree

Abstract

Increasing demand on hospital resources by an ageing population is impacting significantly on the number of beds available and, in turn, the length of time that elderly patients must wait for a bed before being admitted to hospital. This research presents a new methodology that models patient pathways and allows the accurate prediction of patient length of stay in hospital, using a phase-type survival tree to cluster patients based on their covariates and length of stay in hospital. A type of Markov model, called the conditional Coxian phase-type distribution is then implemented, with the probability density function for the time spent at a particular stage of care, for example, the first community discharge, conditioned on the length of stay experienced at the previous stage, namely the initial hospital admission. This component of the methodology is subsequently applied to each cohort of patients over a number of hospital and community stages in order to build up the profile of patient readmissions and associated timescales for each cohort. It is then possible to invert the methodology, so that the length of stay for an observation representing a new patient admission may be estimated at each stage of care, based on the assigned cohort at the initial hospital stage. This approach provides hospital managers with an accurate understanding of the rates with which different groups of patients move between hospital and community care, which may be used to reduce the negative effects of bed-blocking and the premature discharge of patients without a required period of convalescence. This has the benefit of assisting hospital managers with the effective allocation of vital healthcare resources. The approach presented is different to previous research in that it allows the inclusion of patient covariate information into the methodology describing patient transitions between hospital and community care stages in an aggregate Markov process. A data set containing hospital readmission data for elderly patients from the Abruzzo region of Italy is used as a case study in the application of the presented methodology.