Comparison of Ratio and Covariance Analysis of TSH Assays

Abstract

Sakiz and Guillemin (1) examined the calculation of the results of the McKenzie(2) assay for TSH activity. They recommended: a) transformation of both the initial and the response radioactivity counts to logarithms; b) analysis of the log response counts using the log initial count as a covariate. They demonstrated that the transformation removes the heterogeneity of variance inherent in the original (untransformed) counts. Levy et al (3) analyzed the logarithm of the ratio of the response count to the initial count, remarking that they used this procedure because in prior work they had found only minor gains in precision by using covariance analysis. It is the purpose of this paper to examine the consequences of using as the response metameter the logarithm of the ratio of the response count to the initial count as compared with the technique of covariance analysis.

The mathematical model underlying the covariance analysis may be written y = a + b log dose + c z + e where y is the logarithm of the response count, z is the logarithm of the initial count a,b,c are (unknown) constants and e is a normally distributed random variable with mean zero and variance s² The mathematical model for the “ratio analysis” is similar to the above, with the a priori assumption that c = 1. We may then write y′ = a′ + b′ log dose + e′ where y′ = log (response count/initial count) = y — z a′, b′ are constants, and e′ is a random variable.

From a strictly statistical point of view, the question at issue is the appropriateness of either of these models to the biological system; the only ‘proper’ analysis is the one based on the ‘right’ model.