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.
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References
Population projections for the United Kingdom, Government Actuary’s Department, http://www.gad.gov.uk/
K. Kinsella and V.A. Velkoff, An Ageing World US Census Bureau, Series P95/01-1, US Government Printing Office, Washington, DC (2001).
J. Sorensen, Multi-phased bed modelling, Health Services Management Research 9 (1996) 61–67.
M.F. Neuts, Structured Stochastic Matrices of M/G/1 Type and Their Application (Marcel Dekker, New York, 1989).
M.J. Faddy, Examples of fitting structured phase-type distributions, Applied Stochastic Models and Data Analysis 10 (1994) 247–255.
M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models – An Algorithmic Approach (John Hopkins University Press, 1981).
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.
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.
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).
D.R. Cox, A use of complex probabilities in the theory of stochastic processes, Proceedings of the Camb. Phil. Soc. 51 (1955) 313–319.
D.R. Cox and H.D. Miller, The Theory of Stochastic Processes (Methuen, London, 1965).
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.
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.
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.
J.A. Nelder and R.A. Mead, Simplex method for function minimization, Computer Journal 7 (1965) 308–313.
MATLAB® Reference Guide, The MathsWorks Inc., Natick, MA (1992).
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).
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.
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).
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Marshall, A.H., McClean, S.I. Using Coxian Phase-Type Distributions to Identify Patient Characteristics for Duration of Stay in Hospital. Health Care Manage Sci 7, 285–289 (2004). https://doi.org/10.1007/s10729-004-7537-z
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DOI: https://doi.org/10.1007/s10729-004-7537-z