Phase-Type Survival Trees to Model a Delayed Discharge and Its Effect in a Stroke Care Unit

Lalit Grag, Sally I McClean, Brian Meenan, Maria Barton, Ken Fullerton, Sandra Buttigieg, Alexander Micallef

Research output: Contribution to journalArticlepeer-review

20 Downloads (Pure)


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.
Original languageEnglish
Article number414
Pages (from-to)1-24
Number of pages24
Issue number11
Early online date5 Nov 2022
Publication statusPublished online - 5 Nov 2022

Bibliographical note

Funding Information:
This research was partially funded by the Engineering and Physical Sciences Research Council (Grant Number EP/E019900/1 and GR/S29874/01) and the University of Malta Internal Research Grants Programme’s Research Excellence Fund (Grant Number NICE-Healthcare). Any views or opinions presented herein are those of the authors and do not necessarily represent those of funders, their associates or their sponsors.

Publisher Copyright:
© 2022 by the authors.


  • Markov processes
  • OR in health services
  • bed blocking
  • delayed discharge
  • discharge delay
  • healthcare costing
  • hospital length of stay
  • phase-type survival trees
  • simulation


Dive into the research topics of 'Phase-Type Survival Trees to Model a Delayed Discharge and Its Effect in a Stroke Care Unit'. Together they form a unique fingerprint.

Cite this