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The Quality of Life Via Semi Markov Reward Modelling

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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.

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Authors and Affiliations

  1. Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki, 54124, Greece

    Zacharias Kyritsis & Aleka Papadopoulou

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  1. Zacharias Kyritsis
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  2. Aleka Papadopoulou
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Correspondence to Zacharias Kyritsis.

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Kyritsis, Z., Papadopoulou, A. The Quality of Life Via Semi Markov Reward Modelling. Methodol Comput Appl Probab 19, 1029–1045 (2017). https://doi.org/10.1007/s11009-016-9516-5

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  • DOI: https://doi.org/10.1007/s11009-016-9516-5

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