  During primary HIV infection, the kinetics of plasma virus concentrations and
CD4+ cell counts is very complex. Parametric and nonparametric models have been
suggested for fitting repeated measurements of these markers. Alternatively,
mechanistic approaches based on ordinary differential equations have also been
proposed. These latter models are constructed according to biological knowledge
and take into account the complex nonlinear interactions between viruses and
cells. However, estimating the parameters of these models is difficult. A main
difficulty in the context of primary HIV infection is that the date of
infection is generally unknown. For some patients, the date of last negative
HIV test is available in addition to the date of first positive HIV test
(seroconverters). In this paper we propose a likelihood-based method for
estimating the parameters of dynamical models using a population approach and
taking into account the uncertainty of the infection date. We applied this
method to a sample of 761 HIV-infected patients from the Concerted Action on
SeroConversion to AIDS and Death in Europe (CASCADE).
