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The adjustment of biological assay results for variation in concomitant observations

Published online by Cambridge University Press:  15 May 2009

D. J. Finney
D. J. Finney
Affiliation:
Lecturer in the Design and Analysis of Scientific Experiment, University of Oxford
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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.

Type
Research Article
Information
Journal of Hygiene , Volume 45 , Issue 4 , December 1947 , pp. 397 - 406
Copyright
Copyright © Cambridge University Press 1947

References

REFERENCES

Bliss, C. I. (1940). Factorial design and covariance in the biological assay of vitamin D. J. Amer. Statist. Ass. 35, 498–506.Google Scholar
Bliss, C. I. (1946). An experimental design for slope-ratio assays. Ann. Math. Statist. 17, 232–7.Google Scholar
Bliss, C. I. & Marks, H. P. (1939 a). The biological assay of insulin. I. Some general considerations directed to increasing the precision of the curve relating dosage and graded response. Quart. J. Pharm. 12, 82–110.Google Scholar
Bliss, C. I. & Marks, H. P. (1939 b). The biological assay of insulin. II. The estimation of drug potency from a graded response. Quart. J Pharm. 12, 182–205.Google Scholar
Bliss, C. I. & Rose, C. L. (1940). The assay of parathyroid extract from the serum calcium of dogs. Amer. J. Hyg. 31 A, 79–98.Google Scholar
Fieller, E. C. (1940). The biological standardization of insulin. J. Roy. Statist. Soc. Suppl. 7, 1–64.CrossRefGoogle Scholar
Fieller, E. C. (1944). A fundamental formula in the statistics of biological assay, and some applications. Quart. J. Pharm. 17, 117–23.Google Scholar
Finney, D. J. (1945). The microbiological assay of vitamins: The estimate and its precision. Quart. J. Pharm. 18, 77–82.Google Scholar
Finney, D. J. (1948). The principles of biological assay. J. Roy. Statist. Soc. Suppl. 9, 46–91.Google Scholar
Fisher, R. A. (1946). Statistical Methods for Research Workers, 10th ed. Edinburgh: Oliver and Boyd.Google Scholar
Fisher, R. A. & Yates, F. (1947). Statistical Tables for Biological, Agricultural and Medical Research, 3rd ed. Edinburgh: Oliver and Boyd.Google Scholar
Irwin, J. O. (1943). On the calculation of the error of biological assays. J. Hyg., Camb., 43, 121–8.Google Scholar
Snedecor, G. W. (1946). Statistical Methods. Ames, Iowa: The Collegiate Press, Inc.Google Scholar
Wood, E. C. & Finney, D. J. (1946). The design and statistical analysis of micro-biological assays. Quart. J. Pharm. 19, 112–27.Google Scholar