Empirical Thyrotropin-Free Thyroxine Relationship Across the Thyrotropin Spectrum and Implications for Reference Intervals

BACKGROUND: The relationship between thyrotropin (TSH) and free thyroxine (FT4) is commonly assumed to be log-linear. However, this assumption may oversimplify hypothalamic-pituitary-thyroid axis regulation. Characterizing the empirical structure of this relationship could inform the interpretation of thyroid function tests and the validity of current TSH reference intervals. Segmented regression was used to examine the TSH-FT4 relationship to determine whether statistically derived TSH breakpoints corresponded to the current reference limits. METHODS: This study retrospectively analyzed 782 paired TSH-FT4 measurements obtained from untreated outpatients (median age, 43 years; interquartile range, 33-54 years) between July 2021 and March 2024. Patients positive for TSH receptor antibodies were excluded. Measurements obtained during treatment with levothyroxine, liothyronine, or antithyroid drugs, as well as those obtained during pregnancy, were also excluded. Segmented regression was used to model FT4 as a function of log-transformed TSH and identify the optimal breakpoints. RESULTS: Model comparison using the Akaike Information Criterion indicated that the two-breakpoint model provided the best fit. Breakpoints occurred at TSH values of 0.22 and 4.25 mIU/L, partitioning the relationship into three segments with distinct slopes. The lower breakpoint closely matched the assay-specific lower reference limit (0.27 mIU/L) but lay below the harmonized lower reference limits in Japan and the United States, whereas the upper breakpoint was close to both the assay-specific upper limit (4.20 mIU/L) and the corresponding harmonized upper limits (4.23 and 4.27 mIU/L, respectively). FT4 changed little across TSH values of 0.22-4.25 mIU/L, consistent with an approximate homeostatic plateau. CONCLUSIONS: The TSH-FT4 relationship over the entire functional TSH range is segmented rather than uniformly log-linear, and the interval over which FT4 changes little may represent physiological homeostasis. Population-based TSH reference intervals showed partial concordance with the empirically derived homeostatic range, particularly at the upper end, whereas the lower boundary was less closely aligned. Empirically derived breakpoints and population-based reference intervals may therefore offer complementary perspectives for interpreting borderline biochemical abnormalities.