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A continuous time Markov model for the length of stay of elderly people in institutional long‐term care

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  • H. Xie
  • T. J. Chaussalet
  • P. H. Millard

Abstract

Summary. The paper develops a Markov model in continuous time for the length of stay of elderly people moving within and between residential home care and nursing home care. A procedure to determine the structure of the model and to estimate parameters by maximum likelihood is presented. The modelling approach was applied to 4 years’ placement data from the social services department of a London borough. The results in this London borough suggest that, for residential home care, a single‐exponential distribution with mean 923 days is adequate to provide a good description of the pattern of the length of stay, whereas, for nursing home care, a mixed exponential distribution with means 59 days (short stay) and 784 days (long stay) is required, and that 64% of admissions to nursing home care will become long‐stay residents. The implications of these findings and the advantages of the proposed modelling approach in the general context of long‐term care are discussed.

Suggested Citation

  • H. Xie & T. J. Chaussalet & P. H. Millard, 2005. "A continuous time Markov model for the length of stay of elderly people in institutional long‐term care," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 51-61, January.
    • Handle: RePEc:bla:jorssa:v:168:y:2005:i:1:p:51-61
    DOI: 10.1111/j.1467-985X.2004.00335.x
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    References listed on IDEAS

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    1. Gordon Taylor & Sally McClean & Peter Millard, 1997. "Continuous‐time Markov models for geriatric patient behaviour," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 13(3‐4), pages 315-323, September.
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    Cited by:

    1. Adam Steventon & Adam Roberts, 2015. "Estimating Lifetime Costs of Social Care: A Bayesian Approach Using Linked Administrative Datasets from Three Geographical Areas," Health Economics, John Wiley & Sons, Ltd., vol. 24(12), pages 1573-1587, December.
    2. Bruce Jones & Sally McClean & David Stanford, 2019. "Modelling mortality and discharge of hospitalized stroke patients using a phase-type recovery model," Health Care Management Science, Springer, vol. 22(4), pages 570-588, December.
    3. Andrew S. Gordon & Adele H. Marshall & Mariangela Zenga, 2018. "Predicting elderly patient length of stay in hospital and community care using a series of conditional Coxian phase-type distributions, further conditioned on a survival tree," Health Care Management Science, Springer, vol. 21(2), pages 269-280, June.
    4. Mark Fackrell, 2009. "Modelling healthcare systems with phase-type distributions," Health Care Management Science, Springer, vol. 12(1), pages 11-26, March.
    5. Wanlu Gu & Neng Fan & Haitao Liao, 2019. "Evaluating readmission rates and discharge planning by analyzing the length-of-stay of patients," Annals of Operations Research, Springer, vol. 276(1), pages 89-108, May.
    6. Noa Zychlinski & Avishai Mandelbaum & Petar Momčilović & Izack Cohen, 2020. "Bed Blocking in Hospitals Due to Scarce Capacity in Geriatric Institutions—Cost Minimization via Fluid Models," Manufacturing & Service Operations Management, INFORMS, vol. 22(2), pages 396-411, March.
    7. Henry Ergas, 2009. "Providing Aged Care: The Case for Reform," Agenda - A Journal of Policy Analysis and Reform, Australian National University, College of Business and Economics, School of Economics, vol. 16(2), pages 21-44.
    8. Casucci, Sabrina & Lin, Li & Nikolaev, Alexander, 2018. "Modeling the impact of care transition programs on patient outcomes and 30 day hospital readmissions," Socio-Economic Planning Sciences, Elsevier, vol. 63(C), pages 70-79.
    9. McGrory, C.A. & Pettitt, A.N. & Faddy, M.J., 2009. "A fully Bayesian approach to inference for Coxian phase-type distributions with covariate dependent mean," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4311-4321, October.
    10. Samuel Davis & Nasser Fard, 2020. "Theoretical bounds and approximation of the probability mass function of future hospital bed demand," Health Care Management Science, Springer, vol. 23(1), pages 20-33, March.
    11. Yuta Kanai & Hideaki Takagi, 2021. "Markov chain analysis for the neonatal inpatient flow in a hospital," Health Care Management Science, Springer, vol. 24(1), pages 92-116, March.
    12. C Pelletier & T J Chaussalet & H Xie, 2005. "A framework for predicting gross institutional long-term care cost arising from known commitments at local authority level," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 56(2), pages 144-152, February.
    13. Harris, Shannon L. & May, Jerrold H. & Vargas, Luis G., 2016. "Predictive analytics model for healthcare planning and scheduling," European Journal of Operational Research, Elsevier, vol. 253(1), pages 121-131.
    14. H Xie & T J Chaussalet & W A Thompson & P H Millard, 2007. "A simple graphical decision aid for the placement of elderly people in long-term care," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(4), pages 446-453, April.
    15. Manuel L. Esquível & Gracinda R. Guerreiro & Matilde C. Oliveira & Pedro Corte Real, 2021. "Calibration of Transition Intensities for a Multistate Model: Application to Long-Term Care," Risks, MDPI, vol. 9(2), pages 1-17, February.
    16. Zuoxiang, Peng & Weng, Zhichao & Nadarajah, Saralees, 2010. "Rates of convergence of extremes for mixed exponential distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 92-99.
    17. Teresa Cardoso & Mónica Oliveira & Ana Barbosa-Póvoa & Stefan Nickel, 2012. "Modeling the demand for long-term care services under uncertain information," Health Care Management Science, Springer, vol. 15(4), pages 385-412, December.
    18. K Cooper & S C Brailsford & R Davies, 2007. "Choice of modelling technique for evaluating health care interventions," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(2), pages 168-176, February.
    19. Sujee Lee & Philip A. Bain & Albert J. Musa & Jingshan Li, 2021. "A Markov chain model for analysis of physician workflow in primary care clinics," Health Care Management Science, Springer, vol. 24(1), pages 72-91, March.
    20. S McClean & P Millard, 2007. "Where to treat the older patient? Can Markov models help us better understand the relationship between hospital and community care?," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(2), pages 255-261, February.
    21. W. Hare & A. Alimadad & H. Dodd & R. Ferguson & A. Rutherford, 2009. "A deterministic model of home and community care client counts in British Columbia," Health Care Management Science, Springer, vol. 12(1), pages 80-98, March.

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