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(4)

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 sampling times and the whole group structure, that is to say the number of elementary designs, the number of samples per elementary design and the proportion or the number of individuals in each elementary design according to a fixed total number of samples. Simulation studies have shown that the precision of estimation of the parameters depends on the choice of the design [13, 14] and that an appropriate choice can thus substantially improve the efficiency of studies. In the context of NLMEM with sparse designs, the challenge is then to determine the trade-off between few sampling times and informative data to obtain correct parameter estimates.

To evaluate population designs, the theory of optimum experimental design described for instance by Atkinson and Donev [15] or by Walter and Pronzato [16] in classical nonlinear models, has been extended to NLMEM. This theory uses criteria based on the Fisher information matrix (MF). It comes from the Cramer-Rao inequality; indeed, the inverse of MF is the lower bound of the variance covariance matrix of any unbiased estimators of the parameters. As the likelihood has no closed form in our framework, a linearization of the model around the expectation of the random effects has been proposed by Mentré et al. [17] and extended by Retout et al. [18] to derive an approximate expression of MF. Accuracy of this approximation was first shown by simulation of an example based on a real PK study [18, 19], and was confirmed by comparison of the predicted SE computed from this approximate MF to those given by an evaluation of MF without linearization obtained by stochastic approximation using the SAEM algorithm of MONOLIX [20]. The approximated expression of MF has been implemented in R functions PFIM and PFIMOPT for population design evaluation and optimization, respectively [21-23]. Recently, PFIM Interface 2.1, a graphical user interface version, has been developed, allowing both evaluation and optimization in the same tool [21]. However, currently, these tools only allow evaluation and optimization of population designs of single response models. For multiple response models, the same linearization method around the expectation of the random effects as for single response models has been proposed to approximate the population MF [24-27]. In those papers, illustrations of this development were provided using either a PKPD model or a joint PK inserm-00371363, version 1 - 27 Mar 2009

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