A Unified Theory for Quantal Responses to Mixtures of Drugs: Non-Interactive Action

Abstract

The joint action of drugs is classified into interactive and non-interactive types according to whether one drug does or does not modify the biological action of another. Simple similar action and independent action (Biol. Abstr. 23(3): 8966 (1949); J. R. Stat. Soc. B 14(2): 141 (1952) are regarded as the extreme forms of non-interactive action. Basic equations for these extremes, expressing the conditions of non-response in the individual organism, are given; these place no restriction on the correlation of tolerances, nor on the relative slopes of the N.E.D. -log-dose lines for the separate drugs. Introduction of a parameter measuring the degree of similarity between the modes of action of the 2 drugs enables basic general equations for non-interactive joint action to be derived. When a basic general equation for non-interactive action is combined with an assumption of a bivariate-normal distribution of log-tolerances, the response to a mixture of drugs can be calculated. In general the calculation requires integration of the bivariatenormal function over a particular non-rectangular region, which is feasible with an electronic computer; however, certain useful special cases require only a desk calculating machine. Exemplary sets of theoretical dose-response curves for mixtures are given.