An Alternative System for the Classification of Mathematical Models for Quantal Responses to Mixtures of Drugs in Biological Assay

Abstract

SUMMARY This paper is concerned with the classification of models for the joint action of mixtures of drugs in terms of their mathematical properties. It is emphasized that a given biological situation may be represented by a variety of alternative mathematical models and that any acceptable system of classification must be based on properties common to all such representations. The concept of interaction is discussed and a mathematical criterion for classifying models in terms of interactive and non-interactive joint action is derived. It is shown that amongst the class of non-interactive models there is a sub-set which satisfies a more stringent set of conditions, such that the probability of non-response can be expressed as the product of functions of each of the separate doses. Models of this type are termed 'independent'. The concept of 'similar action' is considered and it is shown that no valid distinction between similar and dissimilar action can be made on the basis of quantal response data alone. If, however, information about a semi-quantal response is available, a meaningful criterion for similar action may be applied.