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)

from the parameter estimates for each method, considering only the subset of datasets fulfilling all convergence conditions.

We were also interested in comparing the distribution of the observed SE provided by each of the estimation methods to the empirical SE and to the predicted SE. In this case, we considered only the subset of datasets for which both the convergence and the variance–covariance matrix of estimation were obtained. For the distribution of the SE provided by the SAEM algorithm, we considered both methods of computation of the SE, the Louis’s principle and the linearization.

2.5 Comparison of results for estimation methods with and without linearization

Using the previous simulations, we also compared the three methods of estimation: FO, FOCE and the SAEM algorithm. For each parameter, the relative bias as well as the relative RMSE were computed for the S datasets fulfilling convergence conditions(S≤1000), which, forΨl, the lth parameter of the population vectorΨ, are given by: Bias(Ψl)

1=S

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∑

s=1

S

s Ψ0 Ψll 0 Ψ

l

(14)

RMSE(

Ψl)=

(15)

s the estimated value of Ψ for the sthsimulated datasets and Ψ0 the true value. with Ψlll

3 Results

3.1 Comparison of MF with and without linearization

The SE predicted through the use of the SAEM algorithm on a large dataset (SAEM_LI and SAEM_LO) and those predicted by PFIM 3.0 are reported in Table 2 as relative SE, i.e. SE divided by the true value of the parameter, noted RSE and expressed in %. Overall, whatever the method, the RSE of the population parameters were very close for the fixed effects with a difference of at most 1.3% for βC50 between the SE predicted by PFIM and the one given by

2

for SAEM_LO. Regarding the variance parameters, RSE were also very close, except for ωC50

which PFIM seemed to slightly overestimate the parameter estimate precision with a difference of about 10% compared to the SAEM approaches.

This evaluation shows the appropriateness of the extension of the population Fisher Information matrix for multiple response models using the first order approximation.

3.2 Comparison of MF to empirical information through replicated simulation

Convergence was achieved for all datasets and the variance–covariance estimates were obtained for 997 datasets among the 1000 simulated datasets with the FO method. Convergence with the FOCE method of NONMEM was obtained for only 853 sets. Among those 853 sets, the variance–covariance matrix of estimation was obtained for only 798 sets. Finally, with the SAEM procedure, no problem of convergence or covariance–variance matrix

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was noted for any of the 1000 datasets.

For each parameter the empirical RSE obtained with the three estimation methods and the predicted RSE of SAEM_LI, SAEM_LO and PFIM are displayed in Figure 2. Concerning the FO method, the empirical RSE were much larger than the RSE of PFIM, SAEM_LI and SAEM_LO except for the PK parameters. This difference is above all important for the PD

2 with a RSE close to 200%. In contrast, the empirical RSE for FOCE and parameter ωC

50

SAEM were very close to the RSE predicted with SAEM_LI, SAEM_LO and PFIM. The distribution of observed RSE from the three estimation methods, including both methods of computation of MF with the SAEM algorithm, are reported as boxplots in Figure 3, part (A) and part (B), for the mean and the variance parameters, respectively. For the FO method, the range of the observed RSE was much larger than for those obtained with the FOCE method or both SAEM procedures. However, the observed RSE of FO were concordant with the empirical ones. For all the parameters, the RSE predicted with PFIM were consistent with the distribution of the RSE observed with FOCE and the two SAEM procedures but not for FO. The range of the observed RSE for FOCE, SAEM and the corresponding empirical RSE were also concordant. However, for most parameters, the RSE computed using the Louis’s principle of SAEM had a broader distribution than by using linearization, with values for several datasets being outliers (Figure 3). This problem occurred in particular for the RSE on

2

ωC parameter.

50

In this example, the RSE predicted by PFIM, computed by the first order linearization, were thus concordant with the empirical ones and the observed RSE obtained from the simulation study.

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

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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 …… 此处隐藏：6575字，全部文档内容请下载后查看。喜欢就下载吧 ……