Canonical Correlation Analysis of Formulation Optimization Experiments

Formulation optimization experiments are primarily composed of two groups of variables, a set of independent variables and a set of dependent variables. Simultaneous consideration of all the variables in a single analysis is desirable since it provides an opportunity to study the interrelationships of all variables, independent as well as dependent at the same time and imparts an in-depth insight into the entire system as a whole. A multivariate statistical analysis, known as canonical correlation analysis, has indeed this capability. In addition, the analysis has the capacity of extracting the maximum possible correlation, called canonical correlation, between the variables of the two sets. The larger the value of the canonical correlation (0.90 or above), the higher is the predictability of one set from the other set. The analysis produces two composite canonical functions, one for each set. They can be used to streamline the subsequent search process associated with the full-fledged optimization analysis. The analysis also has the cardinal property to rank-order the variables in each set according to their relative contributions to the canonical prediction function, and to delineate the most important variable in each set. This information can be useful in monitoring the future performance of the formulation in a time-and-cost effective manner and in selecting variables for future experiments. All the relevant features of the analysis have been depicted in this paper in the context of a mobile phase composition optimization experiment.