Quantitative estimation of overadditive and underadditive drug effects by means of theoretical, additive dose-response curves

Abstract

A graphical method is described that permits simple and adequate quantitative and statistical evaluation of combinations of synergistically acting drugs. Thereby, the dose-response (DR) of a drug A can be determined in the presence as well as in the absence of a certain concentration of a drug B. The effects of A + B combined are expressed as combined (total) effects related to the control value before addition of B. The DR curve obtained in this manner is compared with a theoretical DR curve of additive synergism, which can be constructed simply. This procedure allows differentiation of overadditive or underadditive from additive interactions of A + B and the quantitation of nonadditive drug effects. DR curves of additive interaction coincide with the respective theoretical additive DR curve. Overadditive DR curves are characterized by a left shift from the theoretical additive DR curve that can be expressed by a dose factor. Increased maximum effects of A + B over A can be treated statistically (t-test). Underadditive DR curves show a shift to the right from the theoretical additive DR curve that can likewise be expressed by a dose factor. Decreased effects of A + B below the maximum of A can likewise be treated by t-test. The quantitative expression of overadditive drug interactions further allows differentiation between sequential and functional synergism, the DR curve of the latter can also be constructed simply. The application of this method to experiments with isolated coronary arteries had yielded examples of additive, overadditive, and underadditive drug interactions. The method appears to be a superior alternative to the isoboles method of Loewe and Muischnek (1926).