Reliability assessment for the optimal formulations of pharmaceutical products predicted by a nonlinear response surface method

A novel method of evaluating the reliability of the optimal formulations of pharmaceutical products was developed based on statistical techniques. Hydrogel ointments, PEGylated emulsions, and solid dispersions were chosen as the model data for the pharmaceutical products, and the formulations of these models were optimized using a nonlinear response surface method incorporating multivariate spline interpolation. A bootstrap resampling method combined with a Kohonen's self-organizing map, was used to estimate the confidence intervals of the optimal formulations. To understand the factors significantly affecting the optimal formulations, a leave-one-factor-out (LOFO) method and a random number technique were introduced as sensitivity analyses. Our results suggest that the random number technique is a better approach than the LOFO method. To determine the design space and control space based on a scientific rationale that can satisfy a number of specifications of the pharmaceutical responses, a novel approach that takes advantage of the random number technique was investigated. The control space was successfully defined as a super-cubic area inscribed in a super-spherical area in the design space of the factors.