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Parametric and Non Homogeneous Semi-Markov Process for HIV Control

Author

Listed:
  • E. Mathieu

    (Clinical Research University Institute)

  • Y. Foucher

    (Clinical Research University Institute)

  • P. Dellamonica

    (Archet Hospital)

  • J. P. Daures

    (Clinical Research University Institute)

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.

Suggested Citation

  • E. Mathieu & Y. Foucher & P. Dellamonica & J. P. Daures, 2007. "Parametric and Non Homogeneous Semi-Markov Process for HIV Control," Methodology and Computing in Applied Probability, Springer, vol. 9(3), pages 389-397, September.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:3:d:10.1007_s11009-007-9033-7
    DOI: 10.1007/s11009-007-9033-7
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    References listed on IDEAS

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    1. Glen A. Satten & Maya R. Sternberg, 1999. "Fitting Semi-Markov Models to Interval-Censored Data with Unknown Initiation Times," Biometrics, The International Biometric Society, vol. 55(2), pages 507-513, June.
    2. Jacques Janssen & Raimondo Manca, 2001. "Numerical Solution of non-Homogeneous Semi-Markov Processes in Transient Case," Methodology and Computing in Applied Probability, Springer, vol. 3(3), pages 271-293, September.
    3. Ori Davidov, 1999. "The steady‐state probabilities for regenerative semi‐Markov processes with application to prevention and screening," Applied Stochastic Models and Data Analysis, John Wiley & Sons, vol. 15(1), pages 55-63, March.
    4. Pierre Joly & Daniel Commenges, 1999. "A Penalized Likelihood Approach for a Progressive Three-State Model with Censored and Truncated Data: Application to AIDS," Biometrics, The International Biometric Society, vol. 55(3), pages 887-890, September.
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    Cited by:

    1. Vlad Stefan Barbu & Nicolas Vergne, 2019. "Reliability and Survival Analysis for Drifting Markov Models: Modeling and Estimation," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1407-1429, December.

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