Arai Hiroaki, Suzuki Tatsuya, Kaseda Chosei, Takayama Kozo
Formulation Technology Research Laboratories, Daiichi Sankyo Co., Ltd, 1-12-1 Shinomiya, Hiratsuka, Kanagawa 254-0014, Japan.
Chem Pharm Bull (Tokyo). 2009 Jun;57(6):572-9. doi: 10.1248/cpb.57.572.
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 (RSM(S)). 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.
基于4种实验设计（Box-Behnken设计、中心复合设计、D-最优设计和全因子设计）数据集的茶碱片剂配方最优解，采用结合多元样条插值的响应面法（RSM(S)）进行计算。这些解的可靠性通过自助法（BS）重采样技术进行评估。从Box-Behnken设计、D-最优设计和全因子设计数据集中得出的最优解相似。为这些数据集计算的BS最优解分布是对称的。因此，最优解的准确性和可重复性使得能够基于这些分布的偏差进行定量评估。然而，为中心复合设计数据集计算的BS最优解分布几乎不对称，并且无法对这些分布进行基本统计。认为该问题的原因是全局最优和局部最优的混合。因此，应用自组织映射（SOM）聚类来识别全局最优解。通过SOM聚类将BS最优解分为4个簇，对每个簇中最优解的准确性和可重复性进行定量评估，并识别包含全局最优的簇。因此，无论数据集风格如何，SOM聚类被认为可以加强BS重采样方法对最优解可靠性的评估。
