Quality by Design Studies on Multi-response Pharmaceutical Formulation Modeling and Optimization

Formulation optimization, one of the most crucial components in quality by design, is performed to determine optimal settings of ingredients so that the desirable performance of critical pharmaceutical quality characteristics is achieved early in the design phase. Formulation optimization can be implemented by the use of a combination of scientific approaches; in particular, response surface methodology combined with design of experiments is typically utilized to fit linear or quadratic functions when estimating response surfaces. This approach may not always be suitable, though, since estimation accuracy heavily impacts the quality of the solutions. In addition, when a formulation with multiple quality characteristics is being considered, the desirability function (DF) approach is frequently incorporated into the optimization procedure. In this case, a weight-based overall DF is usually treated as an objective function to be maximized. However, this approach has several potential shortcomings. Therefore, in order to overcome the limitations of this traditional formulation optimization procedure, we propose a priority-based goal programming scheme that utilizes higher-order polynomial response surface functions and incorporates modified DF approaches to account for additional characteristics, such as the response variance and covariance. Finally, a numerical example is presented to illustrate the effectiveness of the proposed model.