Parameter estimation of long-term HIV dynamic model in the COPHAR2 – ANRS 111 trial using MONOLIX
M. Lavielle (1), A. Samson (2), A.K. Fermin (3) and F. Mentré (4)
(1) INRIA Saclay, France. (2) University Paris Descartes, Paris, France. (3) University of Nanterre, France. (4) INSERM, U738 and University Paris Diderot, Paris, France.
Objectives: HIV dynamics studies, based on differential equations, have significantly improved the knowledge of HIV infection. While first studies use simplified short-term dynamic models, recent works consider more complex long-term models combined with a global analysis of whole patients data based on nonlinear mixed models. This approach increases the accuracy of the HIV dynamic analysis, however statistical issues remain given the complexity of the problem. We propose to use MONOLIX 2.4 (www.monolix.org) to simultaneously analyse the HIV viral load decrease and the CD4 increase in patients using a long-term HIV dynamic system.
Methods: In the prospective COPHAR2 – ANRS 111 trial, 115 naïve HIV patients started an HAART containing two nucleosides analogues and one protease inhibitor: nelfinavir, or indinavir (+ ritonavir), or lopinavir (+ ritonavir) [1]. Patients were followed one year with several measurements of HIV viral load and CD4 cells. We consider three previously proposed mechanistic models and implemented them using MLXTRAN [2, 3, 4]. Maximum likelihood estimation of the parameters of these models was performed using the SAEM algorithm implemented in MONOLIX 2.4 [5, 6]. which also takes into account the censoring issue due to detection limits of viral load [7]. We selected the best model using the BIC criteria and also tested the difference of efficacy of the 3 protease inhibitors.
Results: We showed that the model with latent CD4 cells was the best model. The goodness of fit of this model with 5 differential equations is very satisfactory. The 10 parameters, 7 with between patient variability, are well estimated. We showed that the efficacy of nelfinavir is reduced compared to indinavir and lopinavir.
Conclusions: We were able to use maximum likelihood estimation in order to analyze adequately, through a complex differential equation model, both viral load and CD4 count changes during treatment in HIV patients using the SAEM algorithm implemented in MONOLIX.
References:
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