A bivariate reference interval for TSH and free thyroxine

Abstract

Frequently, the serum concentrations of TSH (s-TSH) and free thyroxine (s-FT4) are interpreted together when a physician considers the patient’s thyroid status. Then, each measurement is compared with its univariate reference interval. However, a pair of s-TSH and s-FT4 may be more appropriately assessed if compared with a bivariate reference interval. We constructed a bivariate reference interval for s-TSH and s-FT4 from their measurements in 495 healthy blood donors. After Box-Cox transformation, we estimated the Mahalanobis distances from each pair of s-TSH and s-FT4 to the center of the bivariate distribution. The 95 percentile in the distribution of the Mahalanobis distances was defined as the limit of the bivariate reference interval. Univariate reference intervals comprising the central 95% (2.5–97.5 percentile) and 97.5% (1.25–98.75 percentile) of reference values were estimated from the same data. Normal thyroid function was defined as both s-TSH and s-FT4 within their respective univariate reference intervals, or as a Mahalanobis distance within the 95% bivariate reference interval. In 177,514 specimens from adult individuals in out-patient care, 76.6% were classified as bivariate normal. The corresponding figures for the 95% and 97.5% univariate reference intervals were 68.9% and 76.2%, respectively. The kappa statistics for classification agreement between the bivariate 95% reference interval and the 95% and 97.5% univariate reference intervals were 0.790 and 0.881, respectively. We thought the bivariate reference interval to be clinically most accurate but were unable to prove it.