Journal
METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY
Volume 9, Issue 3, Pages 389-397Publisher
SPRINGER
DOI: 10.1007/s11009-007-9033-7
Keywords
non homogeneous semi-Markov process; maximum likelihood estimation; Monte Carlo Markov chain algorithm; interval transition probabilities
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In AIDS control, physicians have a growing need to use pragmatically useful and interpretable tools in their daily medical taking care of patients. Semi-Markov process seems to be well adapted to model the evolution of HIV-1 infected patients. In this study, we introduce and define a non homogeneous semi-Markov (NHSM) model in continuous time. Then the problem of finding the equations that describe the biological evolution of patient is studied and the interval transition probabilities are computed. A parametric approach is used and the maximum likelihood estimators of the process are given. A Monte Carlo algorithm is presented for realizing non homogeneous semi-Markov trajectories. As results, interval transition probabilities are computed for distinct times and follow-up has an impact on the evolution of patients.
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