Andrew Hooker, Michael G. Dodds, Paolo Vicini
Resource Facility for Population Kinetics, Department of Bioengineering, University of Washington, Seattle, Washington, USA
Objectives: In previous work, we evaluated computed population optimal designs via simulation studies [1].   Others have evaluated optimal designs without simulation by looking directly at the Fisher information matrix (FIM) and the predicted parameter variances (the diagonal elements of the FIM) [2]. However, the FIM is only an asymptotic lower bound on the covariance matrix of the model parameter values and it is not clear how well the FIM predicts experimentally measured variances in studies where the number of samples and number of individuals are not close to the asymptotic limit. In this work, we compare population D-optimal pharmacokinetic (PK) designs using both the asymptotic Fisher information matrix (FIM) predicted model parameter variances and model parameter variances derived from simulation studies. Previous work has looked at this problem for one specific model [3], here we expand this comparison and look at three separate models.
Methods: Taking three models from the literature, we compute various optimal designs for each. Then, for each optimal design strategy we calculate the predicted asymptotic percent coefficients of variation (CVs) for all model parameters from the FIMs for each design. Next, using NONMEM, we simulate numerous replicate experiments and compute the simulated parameter CVs for each optimal design. Finally, we compare the two designs by looking at their percent difference.
Results: The results of this study indicate that the asymptotic FIM CVs can, in general, be a good predictor of the trends seen in the CVs of simulation/estimation experiments. However, the CV values predicted by the asymptotic FIM do not seem to reliably predict the CV values seen in simulation/estimation experiments. In general, the CV values seen using the asymptotic FIM will tend to underestimate the actual CV values of simulation/estimation experiments. These results are similar to those found by Retout and Mentre [3]. However, in their work, no differences were found between the FIM CVs and the simulation/estimation CVs for the fixed effects of their model. We expect the difference, when present, to be model and design dependent.
Conclusions: Our results imply that using the FIM to compare different designs is possible, but using the FIM to predict actual values (not the trends) of estimated parameter variances may not be reliable. In practical terms, it appears that we can use asymptotic variance values as a guide to investigate designs, but conclusions should be drawn from a combination of asymptotic variance values and simulation studies. It should also be noted that the asymptotic FIM variance values can give us no information about the likely bias in the parameter estimates; simulation studies must be done to examine bias.
References:
[1] A. Hooker, M. Foracchia, M. G. Dodds, and P. Vicini. An evaluation of populaiton d-optimal designs via pharmacokinetic simulations. Ann. Biomed. Eng., 31:98–111, 2003.
[2] F. Mentre, C. Dubruc, and J. P. Thenot. Population pharmacokinetic analysis and optimization of the experimental design for mizolastine solution in children. J. Pharmacokinet. Pharmacodyn., 28:299–319, 2001.
[3] S. Retout, F. Mentre, and R. Bruno. Fisher information matrix for non-linear mixed-effects models: evaluation and application for optimal design of enoxaparin population pharmacokinetics. Stat. Med., 21:2623–2639, 2002.
Reference: PAGE 13 () Abstr 526 [www.page-meeting.org/?abstract=526]
Poster: poster