Parametric and Non Homogeneous Semi-Markov Process for HIV Control

E. Mathieu (), Y. Foucher, P. Dellamonica and J. P. Daures
Additional contact information
E. Mathieu: Clinical Research University Institute
Y. Foucher: Clinical Research University Institute
P. Dellamonica: Archet Hospital
J. P. Daures: Clinical Research University Institute

Methodology and Computing in Applied Probability, 2007, vol. 9, issue 3, 389-397

Abstract: 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.

Keywords: Non homogeneous semi-Markov process; Maximum likelihood estimation; Monte Carlo Markov chain algorithm; Interval transition probabilities; 60K15; 62M09 (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11009-007-9033-7

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