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

Abstract

In 1952 we considered how the quantal responses in groups of organisms can be expressed as functions of the doses of two poisons administered together, and what we wrote applies to drugs in general. Our aim was a general theory for the interpretation of data of this kind, a theory properly related to the underlying mechanisms of joint drug action. So far as we know, advance in this field has since been confined to Ashford's [1958] alternative method of deriving an equation for simple similar action. Sampford [1952] made progress in the allied field of response-time distributions for drug mixtures. Despite criticisms (see discussion) we maintain that our approach to the problem was sound, though now think that it was not sustained adequately because, as explained below, the results lacked unity. This paper is the first of a series in which a unified theory is presented. Many of the equations obtained before remain, but as special cases of new ones; the latter clear away difficulties, and should enable a wider variety of data to be interpreted. The biological mechanism of joilnt action can vary according to the pair of drugs, and the relation between the quantal response and the jointly applied doses differs according to this mechanism. Thus in our previous paper (Plackett and Hewlett [1952]) we set up biological models of joint action, and deduced the relations, i.e. mathematical models, from them. The s;et of biological models sprang from a twoway classification. The joint action was defined as similar or dissimilar according as the sites of primary action in the organism were the same