Abstract : The study of the dynamical models of the HIV, based on non-linear systems of ordinary differential equations (ODE) has considerably improved the knowledge on its pathogenicity.
This modelling leads to complex issues for identifiability and parameter estimation. To overcome these difficulties, the first models used simplified ODE systems and analyzed each patient separately. Nevertheless, these simplified models prevent from considering the course of the infection as a whole. Recent works deal with inference in non-simplified models, using a Bayesian approach for the parameter estimation. Moreover, these approaches borrow strength from the whole sample, by using a population approach.
We propose here an alternative way based on a full likelihood inference. The complexity of these models make classical software unusable or instable, and we develop an original approach, using the particular structure of these models. We show the robustness of this approach and we apply it to the ANRS ALBI 070 clinical trial data, taking into account left-censored data of virus load. We provide an $in~vivo$ estimation of the differential treatment efficacy and illustrate thus the interest of this approach to provide an alternative tool for analyzing clinical trials. Last, we propose a method for studying the practical identifiability of HIV dynamics models. We study the impact of new quantifications in the handling of these models. By contrast, we discuss the limits of the results based on data usually available.