Health Care Management Science

, Volume 7, Issue 4, pp 285–289 | Cite as

Using Coxian Phase-Type Distributions to Identify Patient Characteristics for Duration of Stay in Hospital

Article

Abstract

Coxian phase-type distributions are a special type of Markov model that describes duration until an event occurs in terms of a process consisting of a sequence of latent phases. This paper considers the use of Coxian phase-type distributions for modelling patient duration of stay for the elderly in hospital and investigates the potential for using the resulting distribution as a classifying variable to identify common characteristics between different groups of patients according to their (anticipated) length of stay in hospital. The identification of common characteristics for patient length of stay groups would offer hospital managers and clinicians possible insights into the overall management and bed allocation of the hospital wards.

Keywords

stochastic modelling Coxian phase-type distributions Markov models survival analysis geriatric medicine 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Population projections for the United Kingdom, Government Actuary’s Department, http://www.gad.gov.uk/
  2. [2]
    K. Kinsella and V.A. Velkoff, An Ageing World US Census Bureau, Series P95/01-1, US Government Printing Office, Washington, DC (2001). Google Scholar
  3. [3]
    J. Sorensen, Multi-phased bed modelling, Health Services Management Research 9 (1996) 61–67. Google Scholar
  4. [4]
    M.F. Neuts, Structured Stochastic Matrices of M/G/1 Type and Their Application (Marcel Dekker, New York, 1989). Google Scholar
  5. [5]
    M.J. Faddy, Examples of fitting structured phase-type distributions, Applied Stochastic Models and Data Analysis 10 (1994) 247–255. Google Scholar
  6. [6]
    M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models – An Algorithmic Approach (John Hopkins University Press, 1981). Google Scholar
  7. [7]
    P. Fazekas, S. Imre and M. Telek, Modeling and analysis of broadband cellular networks with multimedia connections, Telecommunications Systems 19(3–4), (2002) 263–288. Google Scholar
  8. [8]
    M.J. Faddy, On inferring the number of phases in a coxian phase-type distribution, Communications of the Statistician – Stochastic Models 14(1–2) (1998) 407–417. Google Scholar
  9. [9]
    M.J. Faddy and S.I. McClean, Analysing data on lengths of stay of hospital patients using phase-type distributions, Applied Stochastic Models and Data Analysis (2000). Google Scholar
  10. [10]
    D.R. Cox, A use of complex probabilities in the theory of stochastic processes, Proceedings of the Camb. Phil. Soc. 51 (1955) 313–319. CrossRefGoogle Scholar
  11. [11]
    D.R. Cox and H.D. Miller, The Theory of Stochastic Processes (Methuen, London, 1965). Google Scholar
  12. [12]
    P.H. Millard, G. Christodoulou and S.I. McClean, Survival in long-term care – discussion document on the interactions and costs between health and social care, submitted to the Royal Commission on Long Term Care, Department of Geriatric Medicine, St George’s Hospital Medical School, London (1998) 1–30. Google Scholar
  13. [13]
    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) 565–576. Google Scholar
  14. [14]
    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 Journal 4 (2001) 23–28. Google Scholar
  15. [15]
    J.A. Nelder and R.A. Mead, Simplex method for function minimization, Computer Journal 7 (1965) 308–313. Google Scholar
  16. [16]
    MATLAB® Reference Guide, The MathsWorks Inc., Natick, MA (1992). Google Scholar
  17. [17]
    G.W. Harrison, Compartmental Models of 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 Press, 1994). Google Scholar
  18. [18]
    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 Journal 5 (2002) 313–319. Google Scholar
  19. [19]
    C. Vasilakis and A.H. Marshall, Modelling nationwide hospital length of stay: Opening the black box, Journal of the Operational Research Society Practice Notes (2004). Google Scholar

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Department of Applied Mathematics and Theoretical Physics, David Bates BuildingQueen’s University of BelfastBelfastUK
  2. 2.School of Computing and Information Engineering, Faculty of InformaticsUniversity of UlsterUK

Personalised recommendations