Comparing predicted additivity models to observed mixture data

Dose-response relationships are generally assumed to be nonlinear. Standard multiple regression models may approximate the relationship in a narrow dose range but may not adequately approximate the relationship over a wider dose range - which may have a sigmoidal shape. Further, when the number of components in a mixture is large, the required experimental design to test for interactions becomes infeasible using factorial designs. In contrast, tests for departure from additivity may be based on comparing additivity-predicted models to those of mixtures data along fixed-ratio rays of the components. As such, tests for departure from additivity in mixtures should accommodate both nonlinear relationships and efficient experimental designs. In this chapter, we illustrate the strategy using three different basic assumptions about the underlying response surface from single chemical data.