A useful transformation for comparing dose-response curves

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Abstract
Several mathematical equations have been tested for their ability to fit pharmacological dose-response curves over the range 5 to 95% of the maximal response. It has been shown that one such equation, which will be called the L-transformation, adequately fits sets of dose-response data obtained from a number of different tissues. The graphical application of this equation has been suggested previously by other workers but has been used only to a very limited extent. Techniques have now been developed which enable the L-transformation to be fitted to single sets of dose-response data, and to pairs of sets of data simultaneously. By itself the L-transformation cannot adequately fit all dose-response curves. However if another preliminary transformation is carried out on the measured responses then the L-transformation can usefully be applied to dose-response curves of widely different shapes and slopes. Various applications of these techniques are discussed. When the L-transformation is applied to pairs of dose-response curves obtained, for example, from a single piece of isolated tissue, it can be used to calculate potency ratios, with standard errors and fiducial limits. When combined with the occupation theory of drug action and use of the null method, the L-transformation can be applied to suitable pairs of dose-response curves to provide estimates of the affinity constants (with their standard errors) of drugs for their receptors. The techniques can be extended to other models of drug-receptor interaction. Computer programs are available which greatly facilitate the application of these curve fitting methods to the types of problem outlined above.

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