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Methodology and Computing in Applied Probability

, Volume 9, Issue 3, pp 389–397 | Cite as

Parametric and Non Homogeneous Semi-Markov Process for HIV Control

  • E. MathieuEmail author
  • Y. Foucher
  • P. Dellamonica
  • J. P. Daures
Article

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 

AMS 2000 Subject Classification

60K15 62M09 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • E. Mathieu
    • 1
    Email author
  • Y. Foucher
    • 1
  • P. Dellamonica
    • 2
  • J. P. Daures
    • 1
  1. 1.Biostatistics LaboratoryClinical Research University InstituteMontpellierFrance
  2. 2.Infectious Disease DepartmentArchet HospitalNiceFrance

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