Estimation of population pharmacokinetic parameters of saquinavir in HIV patients with the MONOLIX software

Abstract

In nonlinear mixed-effects models, estimation methods based on a linearization of the likelihood are widely used although they have several methodological drawbacks. Kuhn and Lavielle (Comput. Statist. Data Anal. 49:1020-1038 (2005)) developed an estimation method which combines the SAEM (Stochastic Approximation EM) algorithm, with a MCMC (Markov Chain Monte Carlo) procedure for maximum likelihood estimation in nonlinear mixed-effects models without linearization. This method is implemented in the Matlab software MONOLIX which is available at http://www.math.u-psud.fr/~lavielle/monolix/logiciels. In this paper we apply MONOLIX to the analysis of the pharmacokinetics of saquinavir, a protease inhibitor, from concentrations measured after single dose administration in 100 HIV patients, some with advance disease. We also illustrate how to use MONOLIX to build the covariate model using the Bayesian Information Criterion. Saquinavir oral clearance (CL/F) was estimated to be 1.26 L/h and to increase with body mass index, the inter-patient variability for CL/F being 120%. Several methodological developments are ongoing to extend SAEM which is a very promising estimation method for population pharmacockinetic/pharmacodynamic analyses.

Figure 1

Observed individual concentrations (in ng/ml) of saquinavir

Figure 2

Distribution of BMI conditionally to diarrhea

Figure 3

For model 1 fitted without any covariate, relationships between individual log(CL/F) and BMI (top left), individual random effects for log(CL/F) and BMI (top right), individual log(CL/F) and diarrhea (bottom left), individual random effects for log(CL/F) and diarrhea (bottom right).

Figure 4

For model 4 fitted with the covariate BMI on log(CL/F), relationships between individual log(CL/F) and BMI (top left), individual random effects for log(CL/F) and BMI (top right), individual log(CL/F) and diarrhea (bottom left), individual random effects for log(CL/F) and diarrhea (bottom right).

Figure 5

For model 6 fitted with the covariate diarrhea on log(CL/F), relationships between individual log(CL/F) and BMI (top left), individual random effects for log(CL/F) and BMI (top right), individual log(CL/F) and diarrhea (bottom left), individual random effects for log(CL/F) and diarrhea (bottom right).

Figure 6

Goodness of fit plots for model 4 (BMI on CL/F). Top: observations versus predictions (in ng/ml), with on left population prediction and on right individual predictions; bottom: residuals versus time, with on left population residuals and on right individual residuals

Figure 7

Example of convergence of SAEM with model 4 from poor initial estimates

Figure 8

Four different Information criteria for selecting between 0 and 6 covariates: BIC using the total number of observations in the penalization term (BIC_N), BIC using the number of individuals in the penalization term (BIC_ntot), AIC and corrected AIC (AIC_c).