Statistical techniques applied to solubility predictions and pharmaceutical formulations: an approach to problem solving using mixture response surface methodology

Mixture response surface methodology is a group of statistical methods which can generate an empirical equation that can be used to quantitatively define the relationship between some response, such as solubility, and the composition of a system, as for example, different solvent blends. The equation can be used to predict response at any proposed or desired mixture. The term response should be viewed in a very generalized sense to include any property that is affected solely by mixture composition and might include many measurable responses that are of interest to pharmacists: cost, half-life, taste, color, tablet hardness, bioavailability, extraction efficiency, chromatographic resolution, and so on. The method is in no way limited by the number of components in the mixture and thus should be viewed as being general in this sense also. The advantages of mixture response surface methodology and the mechanics involved in its use are illustrated through a prediction of the solubility of diazepam and phenobarbital in solvent blends. The approach is entirely empirical. It is based on rigorous statistical design and data analysis and can lead to excellent prediction of solubility. It also is shown how several responses can be