Zero interaction response surfaces, interaction functions and difference response surfaces for combinations of biologically active agents.

In the field of combination experiments there is wide-spread confusion over definitions, terminology and methods for the evaluation of interaction between biologically active agents. According to our view the widely used isobole approach is the method of choice. In this contribution it is shown how the combination of the classical isobole approach with response surface modeling and computer graphics leads to powerful new methods for the assessment of interaction of biologically active agents. In particular, zero interaction response surfaces, difference response surfaces and interaction functions are proposed. Zero interaction response surfaces represent surfaces which display zero interaction in the whole dose range. Difference response surfaces display the difference between an actual response surface and the corresponding zero interaction response surface. Interaction functions are a generalization of the index of interaction, which describe the dose dependence of this quantity.