Methods of estimating the LD 50 in quantal response data

Abstract

A quantal response is one in which a certain event either happens or does not happen. If, in an animal experiment, we record merely whether or not the animal dies, we are measuring a quantal response. The type of data with which we are concerned here is familiar to all workers in biological assay, and occurs constantly in bacteriological and immunological experiments. A number of animals is divided randomly into several groups, and all the animals in each group are treated with the same dose of a certain substance. The doses differ from group to group, and are frequently arranged so that successive doses differ by a common dilution factor. At each dose the numbers of animals which respond positively and negatively are recorded. The potency of the substance may be measured by that dose which would in the long run produce a positive response in exactly 50 % of the animals, and the main statistical problem is how to estimate this dose (the LD 50) from the available data. It is assumed that any inaccuracies in measuring the doses are negligible in comparison with the sampling errors due to the inevitable differences between experimental animals.