Quantal response assays

We have found that when the whole drug is administered in suspension mice which require doses of 5 and 10 mg for quantal response assays would require doses of 15 and 30 mg when the graded response is to be used. 

The assays fall into two main groups (a) those in which an all or none effect is noted, such as the occurrence of convulsion, death, purgative effect, etc., and which are called quantal response assays and (b) those in which each response is graded in itself such as the measured fall in blood sugar level, or the coagulation time in blood systems, such assays being called continuous response assays. 

The arithmetical treatment of data from both quantal and continuous response assays are essentially the same, the difference lying in that whereas in continuous response assays the variance of a single response is established from the data itself (current or from previous experience), in quantal response assays the variance is established with infinite precision, and in some treatments (probit transformation) varies according to the level of the response. The arithmetic will be greatly reduced if the numbers in each dosage group are equal and the logarithmic interval between the dose levels the same for standard and test. 

For the purpose of example the treatment of a quantal response assay by probit transformation using two doses of standard and two of the test preparation will be considered. The data used are taken from the assay for insulin in which the number of mice displaying hypoglycaemic convulsions is taken as the response. 

The scheme shown can be used for all quantal response assays if probit transformations are to be used. When three doses of standard or test are used and the doses are equally spaced on the logarithmic scale, scores 1,... 

Reference has been made to the essential similarity in the treatment of continuous and quantal response assays. When the response groups are equal in size the treatment as described for the use of angular transformations may be applied using the mean response for the group. In such assays an estimate of variance is established from the data presented and t has the value appropriate to the degrees of freedom with which it is established. When the groups are not equal in size the more extended method used for probit transformations may be used. Each response could... 

Waud, D. (1972). Biological assays involving quantal responses. J. Pharmacol. Exp. Therap. 183 577-607. 

Gaddum, J. H. (1933). Methods of biological assay depending on the quantal response. Med Res Counc Ond Sp Rep SerNo 183, London H.M. Stationery Office. 

Miller (1950) has discussed methods of linearization which have been applied to biological assays exhibiting quantal responses. 

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