Complex relationship between free thyroxine and TSH in the regulation of thyroid function

Objective: The present study re-evaluates the inverse log TSH-free thyroxine (fT(4)) relationship, which has generally been assumed to characterize the thyroid pituitary hypothalamic feedback regulation in thyroid function. Design and Methods: The correlation between fT(4) and TSH was analyzed in two data sets from differing time periods involving 3223 and 6605 patients referred for thyroid testing, representing the whole range of thyroid functions from hypothyroidism to hyperthyroidism. Results: We found that the data do not support a linear log TSH-fT(4) relationship; instead, the correlation's gradient varies with thyroid function. As a consequence, an alternate model, based on the error function, was introduced. When directly comparing the models by means of curve fitting, using F-test and Akaike criteria, the alternate model results in a significantly better fit. The model was verified in the independent second set of data. Subgroup analysis of untreated patients added further proof to the non-linear model. Conclusions: We propose a refined non-linear model to describe the relationship between TSH and fT(4). It implies that TSH response to a deviating fT(4) value may not be log-linear, but may be disproportionally related to the extent of the deviation from an optimum set point. A better understanding of the complex nature of the TSH-fT(4) relationship may further the development of more precise clinical models and aid in better defining subclinical states of thyroid dysfunction. Also, it may encourage other biological interrelations to be reconsidered in the wake of advanced measurement techniques and more powerful computerized statistical procedures.