Effect of an Experimental Design for Evaluating the Nonlinear Optimal Formulation of Theophylline Tablets Using a Bootstrap Resampling Technique

The optimal solutions of theophylline tablet formulations based on datasets from 4 experimental designs (Box and Behnken design, central composite design, D-optimal design, and full factorial design) were calculated by the response surface method incorporating multivariate spline interpolation (RSMS). Reliability of these solutions was evaluated by a bootstrap (BS) resampling technique. The optimal solutions derived from the Box and Behnken design, D-optimal design, and full factorial design dataset were similar. The distributions of the BS optimal solutions calculated for these datasets were symmetrical. Thus, the accuracy and the reproducibility of the optimal solutions enabled quantitative evaluation based on the deviations of these distributions. However, the distribution of the BS optimal solutions calculated for the central composite design dataset were almost unsymmetrical, and the basic statistic of these distributions could not be conducted. The reason for this problem was considered to be the mixing of the global and local optima. Therefore, self-organizing map (SOM) clustering was applied to identify the global optimal solutions. The BS optimal solutions were divided into 4 clusters by SOM clustering, the accuracy and reproducibility of the optimal solutions in each cluster were quantitatively evaluated, and the cluster containing the global optima was identified. Therefore, SOM clustering was considered to reinforce the BS resampling method for the evaluation of the reliability of optimal solutions irrespective of the dataset style.