Marc Lavielle (1) and France Mentré (2)
(1) University Paris-Sud, Bat. 425, Orsay; (2) INSERM U738, Bichat hospital, Paris , France
Context: We developed the software MONOLIX which implements an algorithm for maximum likelihood estimation in nonlinear mixed effects models without linearization. The algorithm combined the SAEM (stochastic approximation version of EM) algorithm [1], with a Markov Chain Monte Carlo procedure [2]. This Matlab software is available at http://www.math.u-psud.fr/~lavielle/monolix/logiciels.
Objectives: Our objectives were 1) to apply and illustrate MONOLIX on a real data set; 2) to estimate the population pharmacokinetic parameter of saquinavir in HIV patients; 3) to test the effects of several covariates on saquinavir pharmacokinetics.
Methods: Concentration data were obtained after single administration of 600 mg of saquinavir alone in 100 HIV patients who never received protease inhibitor before [3]. In order to evaluate the influence of several covariates, three groups of patient were enrolled in this prospective trial: asymptomatic patients (N = 30), AIDS symptomatic subjects without diarrhea (N = 37) or with diarrhea (N = 33). Each patient had three samples collected in 3 periods: 0 to 1.5 h, 2 to 4 h, and 5 to 12 h. There was a total of 240 concentrations, i.e. it was a rather sparse design. A one compartment model with first order absorption after a time-lag was used, with exponential random effects for each PK parameter (V/F, CL/F, ka and Tlag). We defined the best error model and then construct the covariate model using a systematic ascending procedure based on BIC. Eleven covariates were tested: gender, age, BMI, creatinine clearance, diarrhea, mean weight of stools per 24 h, plasma albumine, xylose, lactulose/mannitol ratio, alkaline phosphate level, CD4 count.
Results: The best error model was an homoscedastic error model. Although several covariates were significantly related to CL/F in the univariate LRT or Wald tests (BMI, darrhea, CD4 count, creatinine clearance, xylose), the best model from BIC had only a BMI effect on CL/F and no further covariate effect on none of the parameters. The final population parameters were CL/F = 1210 L/h (SE=169), V = 738 L (SE= 192), ka = 0.55 h-1 (SE =0.04) and Tlag= 1.12 h (SE = 0.10). The variances (and their SE) of all the random effects were estimated and were 1.34 (0.26) for CL/F, 2.78 (0.68) for V/F, 0.20 (0.05) for ka and 0.48 (0.11) for Tlag. The variance of the residual error was 85.9 (ng/ml)2 (SE=11.8). CL/F increases with BMI (fixed effects of 0.11 with SE of 0.03) which confirms the enhancement of saquinavir exposure in patients with low BMI [3].
Conclusions: MONOLIX is a fast and efficient algorithm as illustrated in this real example with a sparse design and large inter-patient variability. We will show, on the saquinavir example, the estimation capabilities of this software from several initial parameters values and display the graphs produced.
Acknowledgements: We thank Dr Trout and Pr Bergmann, Lariboisière Hospital, Paris, for the access to the data of the PK trial on saquinavir.
References:
[1] Kuhn E and Lavielle M. Maximum likelihood estimation in nonlinear mixed effects model, Computational Statistics and Data Analysis. (2005) to appear
 [2] Delyon B, Lavielle M and Moulines E. Convergence of a stochastic approximation version of the EM algorithm. Annals of Statistics. 27 (1999), 94-128.
 [3] Trout E, Mentré F, Panhard X, Kodjo A, Escaut L, Pernet P, Gobert JG, Vittecoq D, Knellwolf AL, Caulin C and Bergmann JF. Enhanced saquinavir exposure in HIV1-infected patients with diarrhea and/or wasting syndrome. Antimicrobial Agents and Chemiotherapy, 48 (2004) 538-545.
Reference: PAGE 14 (2005) Abstr 813 [www.page-meeting.org/?abstract=813]
Poster: poster