Context: The TSH-T4 relationship is central to thyroid pathophysiology and diagnosis of thyroid disease. Previously the relationship was thought to be inverse log-linear, but recent cross-sectional studies from our group and others report a complex, non-linear relationship (1-3). There have been no large, intraindividual studies of the TSH-T4 relationship.
Objective: To analyze the TSH-free T4 relationship within individuals.
Methods: We analyzed data from 13 379 individuals, each with 6 or more TSH/free T4 measurements and at least a 5-fold difference between individual median TSH and minimum or maximum TSH. Linear and non-linear regression models of log TSH on free T4 were fitted to data from individuals, and goodness of fit compared by likelihood ratio testing.
Results: On comparing all models, the linear model achieved best fit in 31% of individuals, followed by the quartic (27%), cubic (15%), null (12%) and quadratic (11%) models. After elimination of least favoured models (with reassignment of individuals to the best fitting, available models), the linear model fitted best in 43% of individuals, quartic in 42%, and the null model in 15%. As the number of records per individual increased, so did the proportion of individuals in whom the linear model achieved best fit, increasing to 62% of individuals with 20 or more records. When the linear model was applied to all individuals and plotted according to individual median free T4 values, differences in slope and intercept described a non-linear relationship between log TSH and free T4.
Conclusions: The log TSH-free T4 relationship appears linear in some individuals and non-linear in others, but is predominantly linear in the most informative individuals with the largest number of results. An inverse log-linear relationship within individuals can be reconciled with a non-linear relationship across a population.