Mixture Experimentation in Pharmaceutical Formulations: A Tutorial

Mixture experimentation is commonly seen in pharmaceutical formulation studies, where the relative proportions of the individual components are modeled for effects on product attributes. The requirement that the sum of the component proportions equals 1 has given rise to the class of designs, known as mixture designs. The first mixture designs were published by Quenouille in 1953 but it took nearly 40 years for the earliest mixture design applications to be published in the pharmaceutical sciences literature by Kettaneh-Wold in 1991 and Waaler in 1992. Since then, the advent of efficient computer algorithms to generate designs has made this class of designs easily accessible to pharmaceutical statisticians, although the use of these designs appears to be an underutilized experimental strategy even today. One goal of this tutorial is to draw the attention of experimental statisticians to this class of designs and their advantages in pursuing formulation studies such as excipient compatibility studies. We present sufficient materials to introduce the novice practitioner to this class of design, associated models, and analysis strategies. An example of a mixture-process variable design is given as a case study.