Inference in HIV dynamics models via hierarchical likelihood

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.