Influence of curvature of response lines in antibiotic agar diffusion assays

Abstract

In the agar plate diffusion assay of antibiotics it is common practice to base calculation procedures on the assumption of a straight line relationship between logarithm of dose and zone diameter. In fact the line is slightly curved, although this may not be apparent unless precision of the assay is high and the dose range sufficiently wide. Substitution of a function of zone diameter may lead to a line which is straight over a wide range of doses. However, use of the approximation based on zone diameters is a well established routine that works well in practice. The purpose of the work reported now was to estimate the bias resulting from the assumption of a linear relationship when zone diameters are used directly. It is shown mathematically that in symmetrical assays the quadratic component of curvature does not contribute at all to bias in the estimated potency. Practical evidence is then given as to how bias is dependent on true ratio of unknown to standard preparation and on experimental design in the assay of four antibiotics. It is concluded that bias is probably small compared with the estimated confidence limits in most routine assays. A 2 + 2 design with a 2:1 dose ratio seems ideal in that it minimises bias arising from curvature. However for work of highest accuracy a transformation of response designed to eliminate curvature is desirable.