The Analysis of Extinction Time Data in Bioassay

T HE STATISTICAL analysis of data from bioassays depending on quantal responses has received much attention during the last twenty years and the necessary analytical principles are now well understood. In general a transformation is sought of the proportions of tests on individuals subjected to treatment, which will yield a linear relation between proportion responding, as so transformed, and the treatment as measured on some suitable scale. The regression line defining this relation is then calculated and is used to find the treatment corresponding to some standard proportion of response chosen as convenient for purposes of comparison. Where the variation in treatment is a variation in dose administered, this standard is usually the dose giving the response in 50% of subjects. It is then designated as the Effective Dose 50 (ED50), or Lethal Dose 50 (LD50) where the response observed is death. Where time of exposure is the variable in treatment we have similarly Effective Time 50 (ET50) and Lethal Time 50 (LT50). The statistical analysis also provides means of testing the linearity of the regression relation, of comparing two or more regressions for correspondence, particularly in slope, and for finding the standard errors, and hence confidence limits, of the various quantities taken as specifying the regression line or measuring the potency of the treatment. These methods have been developed particularly in relation to the type of assay where each treatment is administered to a different group of subjects, the fate of each of which can be observed individually. The experimental data then consist of proportions of individuals observed to respond to the treatment at its various levels and the analysis is undertaken by the now familiar method of probits, which has been fully described in both its derivation and its application by Finney (1947). The use of the probits in the comparison of bactericidal properties.of a range of disinfectants has been illustrated by Berry and Michaels (1947, 1948, and in the press) who counted the numbers of bacteria surviving after exposure to these disinfectants for various lengths of time of samples from an original homogeneous culture.