Thi Huyen Tram Nguyen (1), Thu Thuy Nguyen (1,2), France Mentré (1)
(1) IAME-UMR 1137, INSERM and University Paris Diderot, Paris, France (2) CEA, LIST, 91191, Gif-sur-Yvette, France
Objectives: In nonlinear mixed effect model (NLMEM), good estimation of individual parameters are necessary for treatment optimization, for sequential analysis in pharmacokinetic-pharmacodynamic studies, for detecting covariate effect etc. Usually, individual parameters are estimated as the maximum a posteriori (MAP), i.e., the mode of the conditional distribution given the data. Individual designs influence the estimation of individual parameters which are shrinked toward the mean of population value in case of sparse designs. We aimed to illustrate the use of Bayesian Fisher information matrix (BFIM) implemented in the package PFIM 4.0 [1] to predict standard errors (SE) and shrinkage of individual parameters, using a pharmacokinetic/viral kinetic model for various designs [2]. In this study, we also proposed a method to handle data below the quantification limit (BQL) in BFIM.
Methods: BFIM is the sum of individual Fisher information matrix (IFIM) and the inverse of random effect variance (a priori information) [3]. We studied the influence of number of samples (n), levels of inter-individual variability (w) and residual error (s) on the predicted SE and shrinkage. The contribution of BQL data in BFIM was calculated by deriving their log-likelihood, defined as the probability for the data to be under the limit of quantification.
Results: As expected, SE predicted by BFIM were lower than those predicted by IFIM. SE increased when n decreased or ω and σ increased; shrinkage increased when n decreased, ω decreased and σ increased. In absence of BQL data, RSE and shrinkage predicted by BFIM were closed to values obtained by simulation. In presence of BQL data, the new method for handling BQL data allowed for better prediction of RSE as compared to the method that ignored BQL information.
Conclusions:
BFIM can be used to predict shrinkage and SE of individual parameters estimated by MAP, either in absence or presence of BQL data. PFIM is a relevant tool to evaluate and optimize population and Bayesian design in trials analyzed by NLMEM.
References:
[1] Mentré F, Nguyen TT, Lestini G, Dumont C and the PFIM group. PFIM 4.0: new features for optimal design in nonlinear mixed effects models using R, 2014, PAGE 23 (2014) Abstr 3032 [www.page-meeting.org/?abstract=3032] [2] Guedj J, Bazzoli C, Neumann AU, Mentré F. Design evaluation and optimization for models of hepatitis C viral dynamics. Stat Med, 2011; 30:1045–1056 [3] Combes F, Retout S, Frey N, Mentré F. Prediction of shrinkage of individual parameters using the Bayesian information matrix in nonlinear mixed-effect models with application in pharmacokinetics. Pharm Res, 2013; 30:2355-2367.
Reference: PAGE 24 () Abstr 3516 [www.page-meeting.org/?abstract=3516]
Poster: Methodology - Study Design