Statistical manipulation for normalization of data: in vitro thyroid function tests

Interest in chemical and statistical methods chosen to define "normal" populations for the clinical significance of tests has grown recently. Because few clinical values are distributed in gaussian fashion, recommendations for smoothing of data by transforms have been prepared. In this paper we examine mathematical transformations as they are applied to in vitro tests of thyroid function and evaluate the use of multivariate regression analysis. Mathematical transforms used included square root, two parameter log, three parameter log, and inverse hyperbolic sine methods. Multivariate regression analysis was obtained by comparing test data for the T3 uptake, T4, and effective thyroxine ratio with clinical diagnoses as individual and aggregate weighting values for decision. None of the mathematical transforms resulted in complete elimination of diagnostic errors when compared with clinical diagnoses. The effective thyroxine ratio by itself had the highest correlation with patient findings. Additions of other commonly used in vitro function tests added little diagnostic accuracy.