Characterization of a three-drug nonlinear mixture response model.

Our group recently developed a response-surface modeling paradigm (White et al: Curr Drug Metab 2, 399-409, 2003) and tested its application to both mixtures of anticancer agents and antifungals. This new model is a Hill-type equation, with the slope and potency parameters being functions of the normalized drug ratios, using polynomial expressions. Response surface methods allow one to model and interpret all of the information present in the full concentration-effect data set, to visualize local regions of synergy, additivity and antagonism, and even to quantify the degree of synergy or antagonism, both globally, and across local regions of the response surface. In the present article, we study the effect of changes in the different parameters of the polynomial expressions for two-drug and three-drug mixtures, on the geometrical shapes of several 2-dimensional representations of the 3-dimensional concentration-effect surface. A secondary goal of this report is to compare the mathematical characteristics of the rival White and (Minto et al: Anesthesiol 92, 1603-1616, 2000) modeling paradigms.