Health Care Management Science

, Volume 8, Issue 3, pp 213–220 | Cite as

Length of Stay-Based Patient Flow Models: Recent Developments and Future Directions

  • Adele Marshall
  • Christos Vasilakis
  • Elia El-Darzi
Article

Abstract

Modelling patient flow in health care systems is vital in understanding the system activity and may therefore prove to be useful in improving their functionality. An extensively used measure is the average length of stay which, although easy to calculate and quantify, is not considered appropriate when the distribution is very long-tailed. In fact, simple deterministic models are generally considered inadequate because of the necessity for models to reflect the complex, variable, dynamic and multidimensional nature of the systems. This paper focuses on modelling length of stay and flow of patients. An overview of such modelling techniques is provided, with particular attention to their impact and suitability in managing a hospital service.

Keywords

health stochastic models simulation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    P.H. Millard, Current measures and their defects, in Modelling Hospital Resource Use: A Different Approach to the Planning and Control of Health Care Systems, eds. P.H. Millard and S.I. McClean (Royal Society of Medicine, London, 1994.Google Scholar
  2. [2]
    P. Harper and A. Shahani, Modelling for the planning and management of bed capacities in hospitals, Journal of Operational Research Society 53 (2002) 11–18.Google Scholar
  3. [3]
    P. Harper, A framework for perational Modelling of Hospital Resources, Health Care Management Science 5 (2002) 165–173.CrossRefPubMedGoogle Scholar
  4. [4]
    P.C. Smith, and M. Goddard, Performance management and Operational Research: A marriage made in heaven?, Journal of Operational Research Society 53 (2002) 247–255.CrossRefGoogle Scholar
  5. [5]
    M.J. Cote, Understanding Patient Flow, Decision Line 31 (2000) 8–10.Google Scholar
  6. [6]
    I.K. Altinel and E. Ulas, Simulation modeling for emergency bed requirement planning, Annals of Operations Research 67 (1996) 183–210.Google Scholar
  7. [7]
    J.C. Lowery and J.B. Martin, Design and validation of a critical care simulation model, Journal of the Society for Health Systems 3 (1992) 15–36.PubMedGoogle Scholar
  8. [8]
    H.O. Davies and R. Davies, A simulation model for planning services of renal patients in Europe, Journal of Operational Research Society 38 (1997) 693–700.Google Scholar
  9. [9]
    R. Davies, D. Crabbe, P. Roderick, J.R. Goddard, J. Raftery and P. Patel, A Simulation to Evaluate Screening for Helicobacter Pylori Infection in the Prevention of Peptic Ulcers and Gastric Cancers, Health Care Management Science 5 (2002) 249–258.CrossRefPubMedGoogle Scholar
  10. [10]
    P.H. Millard, Throughput in a department of geriatric medicine: A problem of time space and behaviour, Health Trends 24 (1992) 20–24.PubMedGoogle Scholar
  11. [11]
    D. Snowden, Complex acts of knowing: Paradox and descriptive self-awareness, Journal of Knowledge Management 6 (2002) 100–11.CrossRefGoogle Scholar
  12. [12]
    I.J. Myung and M.A. Pitt, Applying Occam’s razor in modeling cognition: A bayesian approach, Psychonomic Bulletin & Review 4 (1997) 79–95.Google Scholar
  13. [13]
    P.H. Millard, Background to and potential Benefits of flow modelling medical and social services for an ageing population, in Go with the Flow: A Systems Approach to Healthcare Planning, eds. P.H. Millard and S.I. McClean (Royal Society of Medicine Press Limited, London, 1996).Google Scholar
  14. [14]
    S.D. Lapierre, D. Goldsman, R. Cochran and J. DuBow, Bed allocation techniques based on census data, Socio-Economic Planning Sciences 33 (1999) 25–38.CrossRefGoogle Scholar
  15. [15]
    D.J. Bartholomew, Stochastic Models for Social Processes (Wiley, London, 1982).Google Scholar
  16. [16]
    V. Irvine, S.I. McClean and P.H. Millard, Stochastic models for geriatric in-patient behaviour, IMA Journal of Mathematics Applied in Medicine and Biology 11 (1994) 207–216.Google Scholar
  17. [17]
    S.I. McClean, B. McAlea and P.H. Millard, Using a Markov reward model to estimate spend-down costs for a geriatric department, Journal of Operational Research Society 49 (1998) 1021–1025.CrossRefGoogle Scholar
  18. [18]
    G.J. Taylor, S.I. McClean and P.H. Millard, Continuous-time Markov model for geriatric patient behaviour, Applied Stochastic Models and Data Analysis 13 (1998) 315–323.CrossRefGoogle Scholar
  19. [19]
    G.J. Taylor, S.I. McClean and P.H. Millard, A Model to analyse the flow of elderly patients around departments of geriatric medicine and the community, in Go with the Flow: A Systems Approach to Healthcare Planning, eds. P.H. Millard and S.I. McClean (Royal Society of Medicine, London, 1996).Google Scholar
  20. [20]
    G.J. Taylor, S.I. McClean and P.H. Millard, Stochastic Models of Geriatric Patient Bed Occupancy Behaviour, Journal of The Royal Statistical Society Series A (2000) 1–10.Google Scholar
  21. [21]
    M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models (John Hopkins University Press, 1981).Google Scholar
  22. [22]
    M.J. Faddy, Examples of Fitting Structured Phase-Type Distributions, Applied Stochastic Models and Data Analysis 10 (1994) 247–55.Google Scholar
  23. [23]
    D.R. Cox, A Use of Complex Probabilities in the Theory of Stochastic Processes, Proceedings of the Camb. Phil. Soc. 51 (1955) 313–9.Google Scholar
  24. [24]
    M.J. Faddy and S.I. McClean, Analysing Data on Lengths of Stay of Hospital Patients Using Phase-type Distributions, Applied Stochastic Models in Business and Industry 15 (1999) 311–7.CrossRefGoogle Scholar
  25. [25]
    A.H. Marshall, S.I. McClean, C.M. Shapcott and P.H. Millard, Modelling Patient Duration of Stay to Facilitate Resource Management of Geriatric Hospitals, Health Care Management Science 5 (2002) 313–319.CrossRefPubMedGoogle Scholar
  26. [26]
    A.H. Marshall and S.I. McClean, Conditional phase-type distributions for modelling patient length of stay in hospital, International Transactions in Operational Research 10 (2003) 565–5576.CrossRefGoogle Scholar
  27. [27]
    A.H. Marshall, S.I. McClean, C.M. Shapcott, I.R. Hastie and P.H. Millard, Developing a Bayesian belief network for the management of geriatric hospital care, Health Care Management Science (2001) 25–30.Google Scholar
  28. [28]
    P.H. Millard, Geriatric medicine: A new method of measuring bed usage and a theory for planning (MD Thesis St. George’s Hospital Medical School, University of London, 1988).Google Scholar
  29. [29]
    P.H. Millard, Flow rate modelling: A method of comparing performance in departments of geriatric medicine (PhD thesis St George’s Hospital Medical School, University of London, 1992).Google Scholar
  30. [30]
    S.I. McClean and P.H. Millard, Patterns of length of stay after admission in geriatric medicine: An event history approach, The Statistician 42 (1993) 263–274.Google Scholar
  31. [31]
    S.I. McClean and P.H. Millard, Modelling in-patient bed usage behaviour in a department of geriatric medicine, Methods of Information in Medicine 32 (1993) 79–81.PubMedGoogle Scholar
  32. [32]
    G.W. Harrison and P.H. Millard, Balancing acute and long term care: The mathematics of throughput in departments of geriatric medicine, Methods of Information in Medicine 30 (1991) 221–228.PubMedGoogle Scholar
  33. [33]
    K. Godfrey, Compartmental models and their application (Academic Press, London, 1983).Google Scholar
  34. [34]
    G.W. Harrison, Compartmental models of hospital patient occupancy patterns, in Modelling Hospital Resource Use: A Different Approach to the Planning and Control of Health Care Systems, eds. P.H. Millard and S.I. McClean (Royal Society of Medicine, London, 1994).Google Scholar
  35. [35]
    G.J. Taylor, S.I. McClean and P.H. Millard, Geriatric patient flow-rate modelling, IMA Journal of Mathematics Applied in Medicine and Biology 13 (1996) 297–307.PubMedGoogle Scholar
  36. [36]
    S. Wyatt, The occupancy management and planning system (BOMPS), The Lancet 345 (1995) 243–244.Google Scholar
  37. [37]
    S.I. McClean and P.H. Millard, A decision support system for bed-occupancy management and planning hospitals, IMA Journal of Mathematics Applied in Medicine and Biology 12 (1995) 225–234.PubMedGoogle Scholar
  38. [38]
    P.H. Millard and S.I. McClean, Modelling Hospital Resource Use—A different approach to the planning and control of health care systems (Royal Society of Medicine Press, London, 1994).Google Scholar
  39. [39]
    P.H. Millard and S.I. McClean, Go with the flow: A systems approach to healthcare planning (Royal Society of Medicine Press Limited, London, 1996).Google Scholar
  40. [40]
    M. Mackay and P.H. Millard, Application and comparison of two modelling techniques for hospital bed management, Australian Health Review 22 (1999) 118–43.Google Scholar
  41. [41]
    P.H. Millard, M. Mackay, C. Vasilakis and G. Christodoulou, Measuring and modelling surgical bed usage, Annals of the Royal College of Surgeons of England 82 (2000) 75–82.PubMedGoogle Scholar
  42. [42]
    M. Mackay, Practical experience with bed occupancy management and planning systems: An Australian view, Health Care Management Science (2001) 47–56.Google Scholar
  43. [43]
    P.H. Millard, G. Christodoulou, C. Jagger, G.W. Harrison and S.I. McClean, Modelling hospital and social care bed occupancy and use by elderly people in an english health district, Health Care Management Science (2001) 57–62.Google Scholar
  44. [44]
    J.A. Garcia-Navaro and W.A. Thompson, Analysis of bed usage and occupancy following the introduction of geriatric rehabilitative care in a hospital in Huesca, Spain, Health Care Management Science 4 (2001) 63–66.CrossRefPubMedGoogle Scholar
  45. [45]
    M. Cottee and P.H. Millard, Performance Comparison in geriatric medicine: A study in one department, IMA Journal of Mathematics Applied in Medicine and Biology 12 (1995) 225–234.PubMedGoogle Scholar
  46. [46]
    M.A. Law and W.D. Kelton, Simulation Modelling & Analysis (McGraw-Hill, Singapore, 1991).Google Scholar
  47. [47]
    J.B. Jun, S.H. Jacobson and J.R. Swisher, Application of discrete-event simulation in health care clinics: A survey, Journal of Operational Research Society 50 (1999) 109–123.Google Scholar
  48. [48]
    E. El-Darzi, C. Vasilakis, T. Chaussalet and P.H. Millard, A Simulation Modelling Approach to Evaluating Length of Stay, Occupancy, Emptiness and Bed Blocking in a Hospital Geriatric Department, Health Care Management Science 1 (1998) 143–149.CrossRefPubMedGoogle Scholar
  49. [49]
    E. El-Darzi, C. Vasilakis, T. Chaussalet and P.H. Millard, A Simulation model to evaluate the interaction between acute, rehabilitation, long-stay care and the community, in Decision Making: Recent Developments and Worldwide Applications, eds. S.H. Zanakis, G. Doukidis and C. Zopounidis (Kluwer Academic Publishers, Dordrecht, 2000).Google Scholar
  50. [50]
    C. Vasilakis and E. El-Darzi, A simulation study of the winter bed crisis, Health Care Management Science 4 (2001) 31–36.CrossRefPubMedGoogle Scholar
  51. [51]
    C. Vasilakis, Simulating the flow of patients: An OLAP-enabled decision support framework (Ph.D. University of Westminster, 2003).Google Scholar
  52. [52]
    C. Vasilakis, E. El-Darzi and P. Chountas, Data cube modelling and OLAP algebra for hospital length of stay analysis, in Proceedings of The 1st MEDINF International Conference on Medical Informatics & Engineering (Craiova Medicala Journal, Romania, 2003).Google Scholar
  53. [53]
    C. Vasilakis, E. El-Darzi and P. Chountas, An OLAP-enabled environment for modelling patient flow, Journal of Computational Methods in Sciences and Engineering forthcoming (2004).Google Scholar
  54. [54]
    S. Walczak, W.E. Pofahl and R.J. Scorpio, A decision support tool for allocating hospital bed resources and determining required acuity of care, Decision Support Systems 34 (2003) 445–456.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Adele Marshall
    • 1
  • Christos Vasilakis
    • 2
  • Elia El-Darzi
    • 2
  1. 1.Department of Applied Mathematics and Theoretical PhysicsQueen’s University of BelfastBelfast Northern IrelandUK
  2. 2.Harrow School of Computer ScienceUniversity of WestminsterUK

Personalised recommendations