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Inference in HIV dynamics models via hierarchical likelihood

Author

Listed:
  • Commenges, D.
  • Jolly, D.
  • Drylewicz, J.
  • Putter, H.
  • Thiébaut, R.

Abstract

HIV dynamical models are often based on non-linear systems of ordinary differential equations (ODE), which do not have an analytical solution. Introducing random effects in such models leads to very challenging non-linear mixed-effects models. To avoid the numerical computation of multiple integrals involved in the likelihood, a hierarchical likelihood (h-likelihood) approach, treated in the spirit of a penalized likelihood is proposed. The asymptotic distribution of the maximum h-likelihood estimators (MHLE) for fixed effects is given. The MHLE are slightly biased but the bias can be made negligible by using a parametric bootstrap procedure. An efficient algorithm for maximizing the h-likelihood is proposed. A simulation study, based on a classical HIV dynamical model, confirms the good properties of the MHLE. The method is applied to the analysis of a clinical trial.

Suggested Citation

  • Commenges, D. & Jolly, D. & Drylewicz, J. & Putter, H. & Thiébaut, R., 2011. "Inference in HIV dynamics models via hierarchical likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 446-456, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:446-456
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    References listed on IDEAS

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