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(15)

3.3 Comparison of three estimation methods

The relative bias and relative RMSE obtained with the three estimation methods are presented in Table 3. Convergence was not achieved for 15% of the simulated datasets using the FOCE method whereas the FO method and the SAEM algorithm converged for all datasets. Regarding the FO method, bias and RMSE were large especially for the parameters of the PD model (fixed effects, random effects and residual errors) whereas FOCE and SAEM provided reasonable bias and RMSE for all the parameters. For the fixed effects, slightly lower bias and RMSE were observed for the SAEM procedure compared to FOCE. We observed important

2

RMSE (>40%) for the parameter ωC whatever the estimation method. This is in agreement 50

inserm-00371363, version 1 - 27 Mar 2009

with the large RSE obtained for that parameter previously.

4 Discussion

We evaluated the expression of the population Fisher information matrix for multiple response models using a linearization of the model [25], as for single response models. Note that our evaluation focused on the case of multiple responses, in which some parameters are involved in several responses. For cases in which parameters differ across responses, the same information would be obtained using MF either for a single response or multiple responses. The expression of MF for multiple response models has been implemented in PFIM 3.0, an extension of the R function PFIM, dedicated to population design evaluation and optimization [21-23]. Using a PKPD model, we have shown the appropriateness of the predicted RSE obtained with MF computed by PFIM 3.0 by comparison to those computed without any linearization by the SAEM algorithm implemented in the MONOLIX software (see Section 3.1). The predicted RSE were indeed all very close except for a slight discrepancy in the RSE for C50 variability.

The simulation study on the PKPD example showed the concordance between the RSE predicted by PFIM and the empirical RSE computed from estimation results with the FOCE or the SAEM algorithm using simulated datasets (see Section 3.2). Regarding results using the FO algorithm, the empirical RSE were much larger than those predicted by PFIM or obtained with FOCE or SAEM, in particular regarding the variability of the PD parameters. The distribution of the RSE obtained with FO, FOCE and SAEM from the simulated data files are in accordance with their respective empirical ones.

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