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(12)

For estimation with the SAEM algorithm, we used an initial set of parameters with the values

(0.2,0.05,1.2,5,1.5) for the fixed effects, (1,1,1,1,0.5) for the variance of the random effects

and (0.5,0.5) for the residual errors. The default values for the algorithm were used except for the number of Markov chains, which was set to 4, and the number of iterations with two different steps sizes, which was set to 1000 and 1000 to ensure good convergence. The predicted SE obtained by linearization with PFIM 3.0 were designated PFIM. The notations SAEM_LO and SAEM_LI denote the predicted SE obtained with the SAEM algorithm using the Louis’s principle and the linearization method, respectively.

2.4.2 Comparison of MF to empirical information through replicated simulation

inserm-00371363, version 1 - 27 Mar 2009

Another objective was to compare the predicted SE of MF computed from PFIM 3.0 to the empirical SE obtained by the FO method, the FOCE method and the SAEM algorithm on simulated datasets. To do that, we simulated 1000 datasets of 100 individuals with the software R 2.4.1 using the same PKPD model and population design described previously. Datasets were simulated using a similar method as in section 2.4.1, using the same parameter values and the same sampling times.

For each simulated data file, we estimated the population parameters for the PKPD model using first the FO method and the FOCE with interaction method implemented in NONMEM software version V and then, using the SAEM algorithm in MONOLIX (Version 2.1). For the estimations using the FO and FOCE methods, two sets of initial parameters were defined. The first corresponded to the value of the parameters used for the simulation (Table 1). The second one was used only in the case of lack of convergence with the first set. The values of the second set of initial parameters were for the fixed effects: (0.08,0.1,1.5,3,0.8); the values of the variance of the random effects and the variance of the residual errors were the same as for the first set of initial parameters. The initial values of the parameters and the different elements required to use the SAEM algorithm were identical to those described in section 2.4.1.

For each parameter of the PKPD model, we compared the predicted SE using the three evaluations of MF with PFIM, SAEM_LO and SAEM_LI, to the empirical SE obtained with the FO method, the FOCE method and the SAEM algorithm, denoted FO, FOCE, and SAEM, respectively. These empirical SE are defined as the sample estimate of the standard deviation

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