SIMULATION PRACTICE = THEORY ELSEVIER Simulation Practice and Theory 2 (1995) 159-177 On three Markov models for the clinical evolvement: a simulation study M. Dumitrescu *, I. Popescu Faculty qf Mathematics, University of Bucharest, Academiei St. 14. RO-7OlOY Bucharest, Romania Received 28 July 1994; revised 27 September 1994 Abstract This is a comparison study of three Markov models for the changes in the level of glycemia when the patient suffers of diabetes. A Markov chain, a Markov pure-jump process and a Markov renewal process are considered. The sample distributions of two random characteris- tics (the number of jumps up to absorption and the time to absorption) are discussed in order to compare the three models and to offer a recommendation for the most adequate one. Key words: Markov chain; Process; Renewal process; Clinical evolvement; Diabetes 1. Introduction Stochastic processes have been widely applied in modeling medical phenomena. This paper deals with the Markov modeling of a specified clinical evolvement: the changes in the level of glycemia when the patient suffers of diabetes. The goal of our study is to give a convincing recommendation for one of the following models: a homogenous absorbant Markov chain, a homogenous Markov pure-jump process and a homogenous Markov renewal process. The analysis and the recommendations are based on a simulation study of these processes. For each case, the number of jumps up to absorption and the time to absorption are investigated. The main conclusions are the following: l The Markov chain is to be considered only in a first approximation. l The Markov pure-jump process is recommended in the case of an untreated disease, for high-risk patients. l The Markov renewal process is an appropriate model mainly for the evolution of the patients under treatment. * Corresponding author. Fax: (40-l) 614-85-07. 0928-4869/95/$09.50 0 1995 - Elsevier Science B.V. All rights reserved SSDI 0928-4869(94)00014-X