Fisher信息矩阵用于非线性混合效应的多重效应模型：用于的药代动

Author manuscript, published in "Statistics in Medicine 2009;28(14):1940-56"

DOI : 10.1002/sim.3573

Fisher information matrix for nonlinear mixed effects multiple response models: evaluation of the appropriateness of the first order linearization

using a pharmacokinetic/pharmacodynamic model

Caroline Bazzoli*, Sylvie Retout, France Mentré

INSERM, U738, Paris, France; Université Paris Diderot, UFR de Médecine, Paris, France

*

corresponding author: Caroline Bazzoli,

9

002Inserm U738, raM16, rue Henri Huchard 72 - 75018 Paris, France 1 noiFax: 33 1 44 85 62 83

sre v,Email: caroline.bazzoli@inserm.fr

363

1 73

00-mresni

SUMMARY

We focus on the Fisher information matrix used for design evaluation and optimization in nonlinear mixed effects multiple response models. We evaluate the appropriateness of its expression computed by linearization as proposed for a single response model. Using a pharmacokinetic–pharmacodynamic (PKPD) example, we first compare the computation of the Fisher information matrix by approximation to one derived from the observed matrix on a large simulation using the stochastic approximation expectation–maximization algorithm (SAEM). The expression of the Fisher information matrix for multiple responses is also evaluated by comparison to empirical information obtained through a replicated simulation study using the first order linearization estimation methods implemented in the NONMEM

inserm-00371363, version 1 - 27 Mar 2009

software (FO, FOCE) and the SAEM algorithm in the MONOLIX software. The predicted errors given by the approximated information matrix are close to those given by the information matrix obtained without linearization using SAEM and to the empirical ones obtained with FOCE and SAEM. The simulation study also illustrates the accuracy of both FOCE and SAEM estimation algorithms when jointly modelling multiple responses and the major limitations of the FO method. This study highlights the appropriateness of the approximated Fisher information matrix for multiple responses, which is implemented in PFIM 3.0, an extension of the R function PFIM dedicated to design evaluation and optimization. It also emphasizes the use of this computing tool for designing population multiple response studies, as for instance in PKPD studies or in PK studies including the modelling of the PK of a drug and its active metabolite.

KEYWORDS: nonlinear mixed effects models; multiple responses; Fisher information matrix; population design; first order approximation; PFIM

1 Introduction

Nonlinear mixed effects models (NLMEM) are widely used to analyze various biological processes described by longitudinal data. Since the primary models developed by Sheiner et al. [1] in pharmacokinetic (PK) and pharmacodynamic (PD), NLMEM are become widely used for modelling of biological processes. NLMEM, also called the population approach, allow estimation of the mean value of the parameters in the studied population and their interindividual variability, or population characteristics. NLMEM are also now commonly used for the joint modelling of several biological responses such as the PK of parent drugs and of their active metabolite. NLMEM allow a sparse sampling design with few data points per individual in a large set of individuals. This can be particularly useful in studies in specific populations such as children or patients with serious diseases, where classical studies with a large number of samples are often limited for ethical or physiological reasons.

Estimation of the parameters in NLMEM is commonly performed by maximum likelihood. However, due to the nonlinearity of the regression function, an analytical expression of the log-likelihood in nonlinear mixed effects models cannot be provided. To solve this issue several methods for estimating the parameters have been proposed, based on an approximation of the log-likelihood such as the First Order method (FO) or the First Order Conditional Estimate (FOCE) method proposed by Linsdstrom and Bayes [2]. Both methods use a linearization of the structural model either around the expectation of the random effects parameter (FO) or around individual estimates of the random effects (FOCE). These methods have been implemented in the NONMEM software [3, 4] but also in the nlme function of Splus and R software [5]. Compared to FO, the FOCE method provides less biased estimates and, in the context of joint modelling of multiple responses, is more appropriate with fewer problems of convergence or of inter-individual variance estimation [6, 7]. Alternative methods have also been proposed to maximize the likelihood using a stochastic approximation of the integrals, such as the Gaussian quadrature [8] or the Adaptative Gaussian quadrature methods implemented in the NLMIXED procedure of SAS. Recently, the Stochastic Approximation Expectation–Maximization algorithm (SAEM) has been developed and implemented in the MONOLIX software [9, 10]. It uses a stochastic approximation version of the standard expectation–maximization (EM) algorithm [11, 12]. The convergence and the consistence of the estimates have been proved by the authors. In this algorithm, the EM algorithm is used for finding maximum likelihood estimates of parameters

inserm-00371363, version 1 - 27 Mar 2009

in models, where the model depends on unobserved variables corresponding to the random effects in the NLMEM.

An appropriate choice of experimental design for estimating parameters in NLMEM is required. Called a population design in this framework, a design is defined as a group of elementary designs; each elementary design is composed of a set of sampling times to be performed in several individuals. Determining a population design involves identifying both the allocation of the …… 此处隐藏：6238字，全部文档内容请下载后查看。喜欢就下载吧 ……