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(11)

and Samson et al. [29] to show the appropriateness of this approximation in a single response model. This SAEM algorithm allows the observed population Fisher information matrix to be computed according to two approaches. The first approach was developed by Samson et al. [29] and has been used to evaluate an “exact” population Fisher information matrix using the Louis’s principle [30]. It does not require any linearization and can thus be considered as the “true” population Fisher information matrix. The second approach evaluates the Fisher information matrix using a linearization of the model around the conditional expectation of the individual parameters previously estimated by SAEM without any linearization. To perform this comparison, we first computed the predicted MF for the population design associated with the PKPD example using PFIM 3.0, based on the linearization. We then simulated a dataset of PK and PD observations for 10 000 individuals in order to achieve asymptotic properties using the software R 2.4.1. To do that, we used the parameter values given in Table 1 and the sampling times shown in Figure 1, defining the PKPD example (section 2.3). For each individual i, we simulated a vector of random effects bi in N(0, ), where the diagonal elements of are the variance of the random effects, and we calculated the individual parameters usingθi=βexp(bi). We then calculated the individual PK concentrations fPK(θPK,tPK) predicted by the model at each time tPKof ξPK. We also computed the individual PK concentrations at each time tPD of ξPD to derive the concentration fPK(θPK,tPD) for the PD response using Equation (13). PD observations

inserm-00371363, version 1 - 27 Mar 2009

fPD(θPK,θPD,tPD) were then generated. Finally, for each response, we simulated the random

errors εPKand εPD from a normal distribution with zero mean and variance derived from Equation (6) using the parameters σslopePK andσinterPD, respectively. Those errors were added to the previously generated PK and PD data to form the simulated observations for the PK and the PD response respectively.

Using MONOLIX (Version 2.1) with SAEM as the estimation algorithm, we estimated the parameters using this simulated dataset and we then derived the observed population Fisher information matrix with the Louis’s principle procedure and the linearization method of SAEM. For these two Fisher information matrices, we then transformed the observed SE for each component of the population vector Ψ obtained with a simulation of Nsim=10000 individuals into predicted SE of a population of N=100 individuals to be adapted to the

design of the example using SEN(Ψi)=SENsim(Ψi, for the ithcomponent of Ψ.

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