A Comparison of Two Approaches to the Construction of Models for Quantal Responses to Mixtures of Drugs

The authors amplify certain aspects of their past work on the construction of models for quantal responses to mixtures of drugs, introduce some new material, and compare their approach with that adopted by Ashford and Smith. The authors point out that their attitude towards classification of joint drug actions has changed since 1952, although they disagree with Ashford and Smith's suggestion that the authors' classification of 1952 is subject to anomalies. The authors' later work has emphasized a general method for development of mathematical models to correspond with specific biological situations, and questions of classification of biological or mathematical models appear to them less important than formerly. Perhaps the most important difference between the two approaches lies in the concept of dose as a variable. The authors have used the word 'dose' in its usual sense, to mean a quantity of drug measured in ordinary scientific units, whereas Ashford and Smith use it to mean any monotonic transformation of the dose as ordinarily conceived. This drastic generalization of the dose variable inevitably leads to mathematical models that are in general almost devoid of predictive properties. However, such generalization seems to be unnecessary for most pharmacological and toxicological situations. Concerning more specialized terms, it is stressed that Ashford and Smith use several of the same terms as the authors do, but with different meanings. The significance of Ashford and Smith's concepts is discussed.