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(16)

Regarding the comparison of the estimation methods for multiple response models, no problems of convergence were apparent with SAEM or the FO method for the 1000 simulated data files (see Section 3.3). However, it was difficult to fulfill convergence conditions with the FOCE method for which convergence was observed for only 853 of 1000 datasets. The simulation study illustrated the accuracy of the SAEM algorithm in the simultaneous approach, the parameter estimates being unbiased and with small RMSE. Similar results were observed for the FOCE method, but conclusions must be made with caution due to problems of convergence, as noted previously. Regarding FO, the large bias and RMSE already observed in the context of single response models [31] was also observed in this context of multiple response models with simultaneous estimation. The FO method produced larger RSE on all PD parameters compared to those computed with the FOCE method. This is in accordance with the recommendation to use the FOCE method instead of the FO method in this simultaneous estimation context [6, 7]. This apparent difference can be explained by considering the difference between FO and FOCE approximations. The FO method approximates the likelihood by linearizing the population model in its random effects about a value of zero whereas FOCE is defined by a linearization of the model around individual estimates of the random effects. The FOCE method uses more information than the FO method, which is an advantage for estimation in multiple response models. Although the estimation method FO performed badly, the same first order approximation in the computation of MF to predict SE performed well. The limitations of this first order

approximation around the expectation of the random effects thus differ for design evaluation where derivatives of log-likelihood are computed and for parameter estimation. Several studies have considered the single response, stressing the limitations of this linearization for design evaluation. Using a simple model with few random effects, Han [32] found that MF was quite different when computed by linearization than by an adaptative Gaussian quadrature method. Merlé et al. [33] compared the Fisher information matrix computed by linearization to one computed by stochastic simulation and showed that the linearization seems to have no impact on the population D-optimal designs obtained but only on the true efficiency of the designs. Whether via adapative Gaussian quadrature or via stochastic simulation, the evaluation of the Fisher information matrix without linearization is computationally intensive and is also limited to a matrix of small dimensions. Finally, in the context of Bayesian design where prior distributions are used, Han et al. [34] proposed an attractive solution to compute MF; however, it is also time consuming.

inserm-00371363, version 1 - 27 Mar 2009

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