The adjustment of biological assay results for variation in concomitant observations

Abstract

When individual responses in a biological assay show considerable variation associated with the values of a concomitant variate, covariance analysis may be used in order to adjust the mean responses and to improve the precision of the assay. Usually this is preferable to the choice of an adjustment which involves an arbitrary assumption about the effect of variations in the concomitant variate on the measured response. Published accounts of the process are open to certain theoretical objections, though they may be sufficiently exact for most practical purposes.The present paper describes a method of calculating the relative potency, and its precision, which may be a little more laborious, but which is in full accord with standard statistical practice. The computations are illustrated on data from a prolactin assay by the pigeon crop-gland technique, in which the final crop-gland weight showed a positive correlation with the body weight at the start of the assay. The results are compared with those obtained either from the unadjusted crop-gland weights or from these weights expressed as proportions of body weights. The covariance method leads to a more precise estimate of the potency of the test preparation than do either of the others; there is evidence, however, that the increase in precision will not necessarily be large unless the correlation between the response and the concomitant variate is very close.In a final section, the full statistical tests of assay validity in the covariance analysis are described; these are lengthy, and fortunately are required only when the validity is in considerable doubt.The methods of adjustment have been described in this paper with respect to an assay depending upon parallel regression lines of responses on the logarithms of doses. They may be adapted for use with ‘slope-ratio’ assays (Bliss, 1946; Finney, 1945; 1948; Wood & Finney, 1946), in which the regression of response on dose itself is linear. So far the need for adjusting for concomitant variation in these assays seems not to have arisen, and discussion of computational details may be postponed until the need is felt.