Relative potency in nonsimilar dose-response curves

This article discusses the concept of relative potency of herbicides in bioassays where individual dose-response curves can be similar or nonsimilar, often denoted parallel and nonparallel curves, and have different upper and lower limits. The relative potency is constant for similar dose-response curves and measures the relative horizontal displacement of curves of a similar shape along the dose axis on a logarithmic scale. The concept of similar dose-response curves has been used extensively to assess results from herbicide experiments, for example, with the purpose of adjusting herbicide doses to environmental conditions, formulations, and adjuvants. However, deeming dose-response curves similar when they are not may greatly affect the calculation of the relative potency at response levels such as effective dosage (ED)(90), which is relevant for effective weed control, or ED10, which is used in crop tolerance studies. We present a method for calculating relative potencies between nonsimiliar dose-response curves at any response level. It also is demonstrated that if the upper, lower, or both limits among response curves are substantially different, then the ED50 or any other ED level cannot be used indiscriminately to compute the relative potency. Rather, the relative potency should be viewed as a function of the response level.