Inference in HIV dynamics models via hierarchical likelihood

Authors:
D. Commenges;D. Jolly;J. Drylewicz;H. Putter;R. Thiébaut
Affiliations:
INSERM, Epidemiology and Biostatistics Research Center, Bordeaux, France and University of Bordeaux 2, ISPED, France;INSERM, Epidemiology and Biostatistics Research Center, Bordeaux, France and University of Bordeaux, IMB, France;INSERM, Epidemiology and Biostatistics Research Center, Bordeaux, France and University Medical Center Utrecht, Department of Immunology, The Netherlands;University of Leiden, Department of Medical Statistics and Bioinformatics, The Netherlands;INSERM, Epidemiology and Biostatistics Research Center, Bordeaux, France and University of Bordeaux 2, ISPED, France
Venue:
Computational Statistics & Data Analysis
Year:
2011

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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.