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Title: Phase-type survival trees to model a delayed discharge and its effect in a stroke care unit
Authors: Garg, Lalit
McClean, Sally
Meenan, Brian
Barton, Maria
Fullerton, Ken
Buttigieg, Sandra C.
Micallef, Alexander
Keywords: Hospitals -- Admission and discharge -- Data processing
Hospitals -- Admission and discharge -- Simulation methods
Hospital utilization -- Length of stay
Hospital utilization -- Data processing
Markov processes -- Mathematical models
Issue Date: 2022
Publisher: MDPI AG
Citation: Garg, L., McClean, S., Meenan, B., Barton, M., Fullerton, K., Buttigieg, S. C., & Micallef, A. (2022). Phase-Type Survival Trees to Model a Delayed Discharge and Its Effect in a Stroke Care Unit. Algorithms, 15(11), 414.
Abstract: The problem of hospital patients’ delayed discharge or ‘bed blocking’ has long been a challenge for healthcare managers and policymakers. It negatively affects the hospital performance metrics and has other severe consequences for the healthcare system, such as affecting patients’ health. In our previous work, we proposed the phase-type survival tree (PHTST)-based analysis to cluster patients into clinically meaningful patient groups and an extension of this approach to examine the relationship between the length of stay in hospitals and the destination on discharge. This paper describes how PHTST-based clustering can be used for modelling delayed discharge and its effects in a stroke care unit, especially the extra beds required, additional cost, and bed blocking. The PHTST length of stay distribution of each group of patients (each PHTST node) is modelled separately as a finite state continuous-time Markov chain using Coxian-phase-type distributions. Delayed discharge patients waiting for discharge are modelled as the Markov chain, called the ‘blocking state’ in a special state. We can use the model to recognise the association between demographic factors and discharge delays and their effects and identify groups of patients who require attention to resolve the most common delays and prevent them from happening again. The approach is illustrated using five years of retrospective data of patients admitted to the Belfast City Hospital with a stroke diagnosis.
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