Application of the isobologram technique for the analysis of combined effects with respect to additivity as well as independence.

Combined actions of two substances with similar effects are frequently expressed by pairs of doses that produce a fixed response, usually 50%, in so-called isobolograms (ED50 isobolograms). In addition to the dose scales in such graphs we propose the addition of effect scales, where possible, to indicate the effect at certain doses, e.g., the ED30. We further propose to construct isoboles for expected independent interaction, in addition to the additivity line, for which purpose a simple procedure is delineated. In practice, an independent isobole for 50% effect passes through the point formed by the ED30s of A and of B in ED50 isobolograms. Thus, the ED30s constitute the "zenith" of an independent isobole in ED50 isobolograms. It is shown that theoretical independent isoboles can either represent additive, overadditive, or underadditive interactions, depending on the steepness of the dose-response curves of the components. Hence, drugs with shallow dose-response curves exhibit overadditive independent effects, compounds with exponentially steep curves show additive independent interactions. Substances with very steep dose-response curves, producing lethal effects, exhibited marked underadditive effects which could be ascribed largely to an independent mechanism of action of the components. Hence, the inclusion of independent isoboles into conventional isobolograms provides new insights into the mechanisms of interactions and into the actions of the components. Interactions can thus be characterized better and more completely, and misinterpretations appear less likely than with conventional isoboles.