Bootstrap re-sampling technique to evaluate the optimal formulation of theophylline tablets predicted by non-linear response surface method incorporating multivariiate spline interpolation

Optimal solutions of theophylline tablet formulations were derived from three types of experimental datasets, composed of different numbers of data-points using the response surface method incorporating multivariate spline interpolation (RSMs). The reliability of these optimal solutions was evaluated by a bootstrap resampling technique. Different levels of three causal factors were used as factors of response surface analysis: the lactose/cornstarch ratio (X-1), the amount of carmellose calcium (X-2), and the amount of hydroxypropylcellulose (X-3). The target responses were the dissolution ratio of theophylline for the first 15 min (Y-1) and the hardness (Y-2) of each of the prepared tablets. Similar optimal solutions were estimated in three different sizes of datasets. A bootstrap re-sampling with replacements from the original dataset was applied, and optimal solutions for each bootstrap dataset were estimated. The frequency of the distribution of the optimal solution generated by the bootstrap re-sampling technique demonstrated almost normal distribution. The average and standard deviation of the optimal solution distribution were calculated as evaluation indices reflecting the accuracy and reproducibility of the optimal solution. It was confirmed that the accuracy was sufficiently high, irrespective of the dataset size; however, the reproducibility worsened with a decrease in the number of the experimental datasets. Consequently, it was considered that the novel evaluation method based on the bootstrap re-sampling technique was suitable for evaluating the reliability of the optimal solution.