Mixture Modelling for the Detection of Subpopulations in a Pharmacokinetic/Pharmacodynamic analysis
A. Lemenuel-Diot (1,2), C. Laveille( 2), N.Frey (2), R. Jochemsen (2), A. Mallet (1)
(1) INSERM U436, Dept Biomathematics, CHU Pitie Salpetriere, 91 bd de líHŰpital, 75013 Paris, France (2) Institut de Recherches Internationales Servier, 6 place des Plťiades, 92415 Courbevoie Cedex, France
Introduction and Objectives: To be able to estimate accurately parameters entering a nonlinear mixed effect model using the hypothesis that one or more subpopulations can exist rather than assuming that the entire population is best described by unimodal distributions for the random effects, we developed a methodological approach based on the likelihood approximation using the Gauss-Hermite quadrature. The idea is to combine the estimation of the model parameters and the detection of homogeneous groups of patients in the population using a mixture for the distribution of the random effects. This work presents an application of this methodology on a PKPD population analysis and we compared the results with those obtained by Frey et al (2002) who used NONMEM.
Methods: Accuracy of the likelihood approximation is likely to govern the quality of the estimation of the different parameters entering the nonlinear mixed effect model ; we propose to base this approximation on the use of the Gauss-Hermite quadrature. This work presents improvements of this quadrature that render it accurate and computational efficient for likelihood approximation. Moreover, a strategy allowing the detection and explanation of heterogeneity including the Kullback-Leibler test used to estimate the number of components in the mixture is proposed. In order to evaluate the capability of the method to take into account heterogeneity, this methodology was applied in a PKPD analysis using the same database as Frey et al and the structural model they selected. This analysis is based on data collected during the clinical development of a once-a-day modified release formulation of gliclazide, a second-generation sulphonylurea used in the treatment of Type 2 diabetes. Frey et al looked for non-responders and thus looked for a subpopulation of patients in whom therapeutic effect would be null. Here we look for subpopulations of patients whatever their specificity with respect to such and such parameter entering the effect description. For this reason the distributions of the random parameters are specified as mixture of Gaussian distributions. Each component of the mixture will be identified a subpopulation exhibiting specific characteristics.
Results: Looking at the heterogeneity in the population, same results in term of heterogeneity explanation were found on the parameter corresponding to the baseline of glycaemia. According to the other parameters, heterogeneity was pointed out in the distribution of two parameters entering the effect description. Part of this heterogeneity was explained specifying the relationships between the different subpopulations and covariates and a discussion about the resultant subpopulations was proposed. Looking at the parameters estimation, similar results were found using NONMEM and the proposed methodology with slight differences discussed in this work as partly due to the way non-responders were accounted for in the different methods.
N. Frey, C. Laveille, M. Paraire, M. Francillard, N. H. G. Holford and R. Jochemsen. Population PKPD modelling of the long-term hypoglycaemic effect of gliclazide given as a once-a-day modified release (MR) formulation. J. Clin. Pharmacol. 55:147-157 (2002)