Maximum Likelihood Estimation of Long-Term HIV Dynamic Models and Antiviral Response

Abstract

HIV dynamics studies, based on differential equations, have significantly improved the knowledge on HIV infection. While first studies used simplified short-term dynamic models, recent works considered more complex long-term models combined with a global analysis of whole patient data based on nonlinear mixed models, increasing the accuracy of the HIV dynamic analysis. However statistical issues remain, given the complexity of the problem. We proposed to use the SAEM (stochastic approximation expectation-maximization) algorithm, a powerful maximum likelihood estimation algorithm, to analyze simultaneously the HIV viral load decrease and the CD4 increase in patients using a long-term HIV dynamic system. We applied the proposed methodology to the prospective COPHAR2-ANRS 111 trial. Very satisfactory results were obtained with a model with latent CD4 cells defined with five differential equations. One parameter was fixed, the 10 remaining parameters (eight with between-patient variability) of this model were well estimated. We showed that the efficacy of nelfinavir was reduced compared to indinavir and lopinavir.

Joint Population Pharmacokinetic Analysis of Zidovudine, Lamivudine, and Their Active Intracellular Metabolites in HIV Patients

“…The large difference in intracellular triphosphates between AZT and 3TC (i.e., very different MMR values) demonstrates that there are substantial differences in the extent of conversion of these antiviral agents, especially for cellular transport and metabolism. A further step will be to study relationships between intracellular concentrations and antiviral response through modeling (24) to really study the potential of intracellular concentrations as a therapeutic determinant of the efficacy or toxicity of antiretroviral therapy, as observed in previous studies (1,3,17,25,33).…”

Joint modelling of longitudinal and repeated time-to-event data using nonlinear mixed-effects models and the stochastic approximation expectation–maximization algorithm

“…In Web Appendix 1, a detailed description of the SAEM algorithm is presented. SAEM is extremely fast and has already been used to help treat a large range of real-world problems including Hepatitis C treatment outcomes, [27] longitudinal data analysis, [28] parameter estimation in HIV models, [29,30] bioequivalence crossover trials, [31] and much more. The Monolix software provides a general implementation of SAEM that can be easily extended by the user to new modelling challenges.…”

Modelling the interindividual variability of organogenesis in sugar beet populations using a hierarchical segmented model

“…Nonlinear mixed models are of particular interest for the analysis of repeated measures data, in many research elds (Ke and Wang, 2001) such as pharmacokinetics (Comets et al, 2007;Beal and Sheiner, 1982), agriculture (Hall and Bailey, 2001;Li, 2007;Makowski and Lavielle, 2006;Mutz et al, 2004;Nothdurft et al, 2006), ecology (Bolker et al, 2009), epidemiology (Lavielle et al, 2010;Morrell et al, 1995), ... Repeated-measures data can be generated by observing a number of individuals repeatedly under various conditions, assuming that the subjects constitute a random sample of the population of interest.…”