Choice of Models for the Analysis and Forecasting of Hospital Beds
There is growing concern that current health care services are not sustainable. The compartmental flow model provides the opportunity for improved decision-making about bed occupancy decisions, particularly those of a strategic nature. This modelling can be applied to complement infrastructure and workforce-planning methods.
Discussion about appropriateness of the level of model complexity, the degree of fit and the ability to use compartmental flow models for generalization and forecasting has been lacking. The authors investigated model selection and assessment in relation to hospital bed compartment flow models.
A compartment model for a range of scenarios was created. The training and test data related to the 1998 and 1999 calendar years, respectively. The majority of scenarios tested were based upon commonly used periods that describe periods of time. The goodness-of-fit achieved by optimisation was measured against the training and test data.
Model fit improved with increasing complexity as expected. The analysis of model fit against the test data showed that increasing model complexity did result in over-fitting, and better prediction was achieved with a relatively simple model. In terms of generalisation, the seasonal models performed best.
Single day census type models, which have been used by Millard and his colleagues, were also generated. The performance of these models was similar, but inferior to that of the models generated from a full year of training data. The additional data make the models better able to capture the variation across the year in activity.
Keywordsoccupancy average length of stay beds modelling
Unable to display preview. Download preview PDF.
- 1. World Health Organisation, Active Ageing: A Policy Framework (World Health Organisation, Geneva, Switzerland, 2002).Google Scholar
- 2. OECD, A Disease-Based Comparison of Health Systems—What is Best and at What Cost? (OECD Publications, France, 2003).Google Scholar
- 3. Commission of the European Communities, Towards a Europe for All Ages—Promoting Prosperity and Intergenerational Solidarity (Commission of the European Communities, Brussels, 1999).Google Scholar
- 4. OECD, Health at a Glance (OECD Publications, France, 2001).Google Scholar
- 7. J. Pengelley, GP overflow ‘does not tax hospitals’, The Advertiser 23 (April 2004) 5.Google Scholar
- 8. Generational Health Review, Generational Health Review—Progress Report (Generational Health Review, Adelaide, Australia, 2003).Google Scholar
- 9. G. Hamel and C.K. Prahald, Competing for the Future (Harvard University Press, Boston, 1994).Google Scholar
- 10. I.J. Myung and M.A. Pitt, Applying Occam’s razor in modelling cognition: A bayesian approach, Psychonomic Bulletin and Review 1 (1997) 79–95.Google Scholar
- 11. H. Xiao-Ming, A planning model for requirement of emergency beds, IMA Journal of Mathematics Applied in Medicine & Biology 12 (1995) 345–353.Google Scholar
- 15. K.S. Bay and L.J Nestman, The use of bed distribution and service population indexes for hospital bed allocation, Health Services Research 19(2) (1984) 140–160.Google Scholar
- 16. J. Yates, Hospital Beds: A Problem for Diagnosis and Management (William Heinemann, London, 1982).Google Scholar
- 17. W.E. Sterk and E.G. Shyrock, Modern methods improve hospital forecasting, Healthcare Finance Manager 41(3) (1987) 96–98.Google Scholar
- 20. M. Mackay and P.H. Millard, Application and comparison of two modelling techniques for hospital bed management, Australian Healthcare Review 22 (1999) 118–143.Google Scholar
- 24. 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, ed. P.H. Millard and S.I. McClean, (Royal Society of Medicine, London, 1994).Google Scholar
- 25. S.I. McClean and P.H. Millard, Go with the flow: Modelling bed occupancy and patient flow through a geriatric department, OR Insight 7(3) (1994) 2–4.Google Scholar
- 26. 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 & Biology 12 (1995) 225–234.Google Scholar
- 28. F. Gorunescu, S.I. McClean and P.H. Millard, A queueing model for bed-occupancy management and planning of hospitals, Journal Operational Research Society 53 (2002) 19–24.Google Scholar
- 29. T.M. Mills, A mathematician goes to hospital, Australian Mathematical Society Gazette 31(5) (2004) 320–327.Google Scholar
- 31. K. Godfrey, Compartmental Models and Their Application (Academic Press Inc., London, 1983).Google Scholar
- 33. G. Taylor, S. McClean and P. Millard, Geriatric-patient flow-rate modeling, IMA Journal of Mathematics Applied in Medicine & Biology 13 (1996) 297–307.Google Scholar
- 35. S. MacStravic, Need new beds? Throw out your old formulas, Health Care Strategic Management 19(10) (2001) 16–19.Google Scholar
- 40. T. Hastie, R. Tibshirani and J. Friedman, The Elements of Statistical Learning; Data Mining, Inference and Prediction (Springer, Canada, 2001).Google Scholar
- 41. H. Kohler, Statistics for Business and Economics (Scott Foresman and Company, USA, 1985).Google Scholar
- 43. S. Karlin S (1983) cited by I.J. Myung, website http://quantrm2.psy.ohio-state.edu/injae/respub.html accessed Jan 2004.
- 44. U.S. Department of Health and Human Services, Active Aging: A Shift in the Paradigm (U.S. Department of Health and Human Services, United States of America, 1997).Google Scholar
- 45. Commission of the European Communities, Towards a Europe for All Ages—Promoting Prosperity and Intergenerational Solidarity (Commission of the European Communities, Brussels, 1999).Google Scholar
- 46. World Health Organisation, Active Ageing: A Policy Framework (World Health Organisation, Spain, 2002).Google Scholar