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The Quality of Life Via Semi Markov Reward Modelling

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  • Zacharias Kyritsis

    (Aristotle University of Thessaloniki)

  • Aleka Papadopoulou

    (Aristotle University of Thessaloniki)

Abstract

The quality of life is recognized as an important element which is generally treated at least as primary or secondary criterion in most clinical trials. So, its measurement and statistical analysis remain an issue. In the present, a non-homogeneous semi Markov model is defined for the description of the evolution of a patient’s health status. Also, a stochastic process where the state space elements are the quality of life states of a patient and the transition probabilities are dependent on the health status is considered. A methodology via Markov modelling in order to combine the health and the quality of life status of a patient is provided. Next, we extend the above model by attaching rewards of making transitions between the states of the two kinds for indexing through rewards the quality of life for patients of all health states. The mean, the second non central moment, the variance and the high order moments of a patients interval reward are calculated by means of the basic parameters of the semi Markov chain and the quality status process. The above results provide us with a tool which could operate as a measure for indicating the quality of life status. Finally, the theoretical results are illustrated numerically with synthesized data.

Suggested Citation

  • Zacharias Kyritsis & Aleka Papadopoulou, 2017. "The Quality of Life Via Semi Markov Reward Modelling," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1029-1045, December.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:4:d:10.1007_s11009-016-9516-5
    DOI: 10.1007/s11009-016-9516-5
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    References listed on IDEAS

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    1. L. Jianyong & Z. Xiaobo, 2004. "On Average Reward Semi-Markov Decision Processes with a General Multichain Structure," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 339-352, May.
    2. Aleka A. Papadopoulou & George Tsaklidis & Sally McClean & Lalit Garg, 2012. "On the Moments and the Distribution of the Cost of a Semi Markov Model for Healthcare Systems," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 717-737, September.
    3. Fredrik Stenberg & Raimondo Manca & Dmitrii Silvestrov, 2007. "An Algorithmic Approach to Discrete Time Non-homogeneous Backward Semi-Markov Reward Processes with an Application to Disability Insurance," Methodology and Computing in Applied Probability, Springer, vol. 9(4), pages 497-519, December.
    4. Aleka Papadopoulou & George Tsaklidis, 2007. "Some Reward Paths in Semi-Markov Models with Stochastic Selection of the Transition Probabilities," Methodology and Computing in Applied Probability, Springer, vol. 9(3), pages 399-411, September.
    5. N/A, 2004. "Index for 2004," European Union Politics, , vol. 5(4), pages 511-512, December.
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