Sylvie Retout, Emmanuelle Comets and France Mentré
INSERM - University Paris 7
Context We have recently developed PFIMOPT 1.0 for population designs optimisation . This generic Splus or R function is based on the optimisation of the D-optimal criterion, that is the maximisation of the determinant of the Fisher information matrix. This function can determine the best sampling times of the population design as well as its best structure, that is the number of groups, and for each group, the number of subjects, the number of sampling times and the allocation of the times. PFIMOPT uses the Simplex algorithm to maximise the D-optimal criterion. It is a general algorithm which optimises the sampling times in some given continuous intervals of times. A more specific algorithm has been proposed for designs optimisation, the Fedorov-Wynn algorithm, already used in . It optimises also both the group structure and the sampling times but in a given finite set of times.
Objectives To compare the performance of the Simplex algorithm to the Fedorov-Wynn algorithm for population designs optimisation. In particular, to evaluate the amount of information provided by the designs optimised with those two algorithms.
Methods We use the example of the simple biexponential model of HIV viral decay. This model involves 4 fixed effects. An additive error with an homoscedastic variance characterised by σ2 is assumed. The vector of the population parameters is then composed of the four fixed effects, plus the variance of their additive random effects and σ2. A priori values are given to those parameters from HIV literature. Based on those values, several designs with different groups structures are optimised with both the Fedorov-Wynn and the Simplex algorithms: designs with 8, 5, or 4 samples per subject are optimised. The allowed sampling times for the Fedorov-Wynn is the set of 12 sampling times from 0 to 56 days used in . The optimisation with the Simplex algorithm allows sampling times from 0 to 56 days in a continuous interval. To be clinically feasible, the sampling times are rounded to the nearest day. Moreover, a minimum delay of 1 hour between two successive sampling times is imposed. Some optimised designs are then selected to be simulated by replication of 1000 data sets analysed with the nlme function of Splus.
Results Designs optimised with the Simplex and the Fedorov-Wynn algorithm may be different but lead to a quite similar group structure and a same efficiency. Whatever the algorithm, the optimised designs provide precise parameter estimates, both on the fixed effects (CV < 4%) and on the variance of the random effects (CV < 43%). Preliminary simulations on designs with 5 samples per subject have already confirmed those results.
References
[1] Retout S. and Mentré F. Optimisation of individual and population designs using Splus. J Pharmacokin Pharmacodyn. 30 (2003), 417-443.
[2] Mentré F., Mallet A. and Baccar D. Optimal design in random-effects regression models. Biometrika. 84 (1997), 429-442.
[3] Retout S., Mentré F. and Bruno R. Fisher information matrix for non-linear mixed-effects models: evaluation and application for optimal design of enoxaparin population pharmacokinetics. Stat Med. 21 (2002), 2623-2639.
[4] Wu H., Ding A.A. and De Gruttola V. Estimation of HIV dynamic parameters. Stat Med. 17 (1998), 2463-2485.
[5] Wu H. and Ding A.A. Design of viral dynamics studies for efficiently assessing potency of anti-hiv therapies in AIDS clinical trials. Biometrical J. 44 (2002), 175-196.
Reference: PAGE 13 (2004) Abstr 527 [www.page-meeting.org/?abstract=527]
Poster: poster