Maximum a Posteriori Estimation in Dynamical Models of Primary HIV Infection

Dynamical models based on ordinary differential equations (ODE) are increasingly used to model viral infections such as HIV. This kind of model is based on biological knowledge and takes into account complex non-linear interactions between markers. The estimation of such models is made difficult by the lack of analytical solutions and several methods based on Bayesian or frequentist approaches have been proposed. However, because of identifiability issues, in a frequentist approach some parameters have to be fixed to values taken from the literature. In this paper we propose a Maximum A Posteriori (MAP) approach to estimate all the parameters of ODE models, allowing prior knowledge on biological parameters to be taken into account. The MAP approach has two main advantages: the computation time can be fast (relative to the full Bayesian approach) and it is straightforward to incorporate complex prior information. We applied this method to an original model of primary HIV infection taking into account several biological hypotheses for the HIV-immune system interaction. Parameters were estimated using HIV RNA load and CD4 count measurements of 710 patients from the Concerted Action on SeroConversion to AIDS and Death in Europe (CASCADE) Collaboration.