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.
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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.