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A Markov Chain Model for Analysing the Progression of Patient’s Health States

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  • Jonsson, Robert

    (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University)

Abstract

Markov chains (MCs) have been used to study how the health states of patients are progressing in time. With few exceptions the studies have been based on the questionable assumptions that the MC has order m=1 and is homogeneous in time. In this paper a three-state non-homogeneous MC model is introduced that allows m to vary. It is demonstrated how wrong assumptions about homogeneity and about the value of m can invalidate predictions of future health states. This can in turn seriously bias a cost-benefit analysis when costs are attached to the predicted outcomes. The present paper only considers problems connected with model construction and estimation. Problems of testing for a proper value of m and of homogeneity is treated in a subsequent paper. Data of work resumption among sick-listed women and men are used to illustrate the theory. A nonhomogeneous MC with m = 2 was well fitted to data for both sexes. The essential difference between the rehabilitation processes for the two sexes was that men had a higher chance to move from the intermediate health state to the state ‘healthy’, while women tended to remain in the intermediate state for a longer time.

Suggested Citation

  • Jonsson, Robert, 2011. "A Markov Chain Model for Analysing the Progression of Patient’s Health States," Research Reports 2011:6, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    • Handle: RePEc:hhs:gunsru:2011_006
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    File URL: http://gupea.ub.gu.se/handle/2077/27932
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    References listed on IDEAS

    as
    1. Jonsson, Robert, 2011. "Tests of Markov Order and Homogeneity in a Markov Chain," Research Reports 2011:7, University of Gothenburg, Statistical Research Unit, School of Business, Economics and Law.
    2. Sally McClean & Peter Millard, 1998. "A three compartment model of the patient flows in a geriatric department: a decision support approach," Health Care Management Science, Springer, vol. 1(2), pages 159-163, October.
    3. P. J. Avery & D. A. Henderson, 1999. "Fitting Markov chain models to discrete state series such as DNA sequences," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(1), pages 53-61.
    4. Adrian Raftery & Simon Tavaré, 1994. "Estimation and Modelling Repeated Patterns in High Order Markov Chains with the Mixture Transition Distribution Model," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 179-199, March.
    5. J. P. Hughes & P Guttorp & S. P. Charles, 1999. "A non‐homogeneous hidden Markov model for precipitation occurrence," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 48(1), pages 15-30.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Rehabilitation; transition probability; prediction; Maximum Likelihood;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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