Parametric and Non Homogeneous Semi-Markov Process for HIV Control |
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Authors: | E Mathieu Y Foucher P Dellamonica J P Daures |
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Institution: | (1) Biostatistics Laboratory, Clinical Research University Institute, 641 av. D.G. Giraud, 34093 Montpellier, France;(2) Infectious Disease Department, Archet Hospital, BP 3079, 06202 Nice, France |
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Abstract: | 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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Keywords: | Non homogeneous semi-Markov process Maximum likelihood estimation Monte Carlo Markov chain algorithm Interval transition probabilities |
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