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Browsing Articles by Author "Jonsson, Robert"

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    A Markov Chain Model for Analysing theProgression of Patient´sHealth States
    (2011) Jonsson, Robert
    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.
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    Tests of Markov Order and Homogeneity in a Markov Chain
    (2011) Jonsson, Robert
    A three-state non-homogeneous Markov chain (MC) of order m≥0, denoted M(m), was previously introduced by the author. The model was used to analyze work resumption among sick-listed patients. It was demonstrated that wrong assumptions about the Markov order m and about homogeneity can seriously invalidate predictions of future health states. In this paper focus is on tests (estimation) of m and of homogeneity. When testing for Markov order it is suggested to test M(m) against M(m+1) with m sequentially chosen as 0, 1, 2,…, until the null hypothesis can’t be rejected. Two test statistics are used, one based on the Maximum Likelihood ratio (MLR) and one based on a chi-square criterion. Also more formal test strategies based on Akaike’s and Baye’s information criteria are considered. Tests of homogeneity are based on MLR statistics. The performance of the tests is evaluated in simulation studies. The tests are applied to rehabilitation data where it is concluded that the rehabilitation process develops according to a non-homogeneous Markov chain of order 2, possibly changing to a homogeneous chain of order 1 towards the end of the period.