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

Abstract

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.

Introduction

Thyrotropin (TSH) and free thyroxine (FT4) are key indicators of thyroid function, and their relationship is regulated mainly by FT4-mediated negative feedback in the hypothalamic–pituitary–thyroid (HPT) axis, with additional contribution from triiodothyronine. ¹ This system underpins the clinical assessment of thyroid disorders.^2,3 The TSH–FT4 relationship has traditionally been described as an inverse log-linear association. ¹

Accumulating evidence indicates that the TSH–FT4 relationship is not fully captured by a simple log-linear model.^4–10

Despite these insights, the structure of the nonlinear TSH–FT4 relationship remains incompletely defined. Breakpoints in this relationship have not been well characterized in clinical cohorts. Here, I used segmented regression to assess whether TSH–FT4 breakpoints align with established reference intervals. Although prior studies have commonly modeled log-transformed TSH as an outcome in relation to FT4,^4–10 an approach that primarily reflects pituitary feedback sensitivity, FT4 was instead modeled as a function of base-10 log-transformed TSH (logTSH). This approach delineated the TSH range over which FT4 remained relatively stable, consistent with homeostatic regulation.

By identifying empirically derived TSH breakpoints that define this homeostatic zone, I aimed to provide a physiological context for interpreting current TSH reference intervals.

Methods

Study design and population

This retrospective observational study included outpatients who underwent TSH and FT4 testing at Kasahara Clinic (Osaka, Japan), an endocrine clinic located in an iodine-sufficient region, between July 2021 and March 2024. After applying the exclusion criteria, 782 paired TSH–FT4 measurements were included in the analysis. Patients who tested positive for thyrotropin receptor antibodies (TRAb) were excluded at the patient level. Among TRAb-negative patients, TSH–FT4 pairs obtained during treatment with methimazole, propylthiouracil, potassium iodide, levothyroxine, or liothyronine, or during pregnancy, were excluded at the measurement level. When multiple eligible TSH–FT4 pairs were available for the same patient during the study period, only the first measurement was included in the analysis.

Individuals positive for thyroglobulin antibody (TgAb) or thyroid peroxidase antibody (TPOAb) were not excluded from the primary analysis. Sensitivity analyses excluding TgAb-positive cases, TPOAb-positive cases, and cases positive for either antibody were performed to assess the influence of thyroid autoimmunity on breakpoint estimation.

The study protocol was approved by the Kasahara Clinic Institutional Review Board (Approval No. 20240401-2). Data were extracted from the clinic’s electronic medical record database. The requirement for written informed consent was waived because of the retrospective nature of the study. Instead, information about the study was publicly disclosed, and patients were given the opportunity to opt out. All data were anonymized in accordance with the principles of the Declaration of Helsinki.

Laboratory measurements

Serum concentrations of TSH, FT4, TgAb, and TPOAb were measured using Elecsys electrochemiluminescence immunoassays (Roche Diagnostics, Basel, Switzerland) on a Cobas e411 analyzer (Roche Diagnostics GmbH, Mannheim, Germany) in a single laboratory. For Elecsys TSH on this analyzer, harmonized interpretation was based on the same values as those used in routine practice because the assay-specific conversion factor is 1.0. ¹¹ The harmonized reference interval for TSH was 0.61–4.23 mIU/L. The reference interval for FT4 adopted at my facility was 12–22 pmol/L. For thyroid autoantibodies, antibody positivity was defined as TgAb ≥30 IU/mL and TPOAb ≥30 IU/mL. The TRAb positivity cutoff for exclusion was 2.0 IU/L. The limit of quantitation for the TSH assay was 0.005 mIU/L.

Statistical analyses

All analyses were conducted in R version 4.4.2 (R Foundation for Statistical Computing, Vienna, Austria). ¹²

Segmented regression and model selection

Segmented regression was performed using the segmented package version 2.2-1. ¹³ TSH values were transformed using the base-10 logarithm. TSH values reported as <0.005 mIU/L were set to 0.005 mIU/L before transformation. LogTSH was specified as the independent variable and FT4 as the dependent variable to evaluate changes in FT4 levels across the observed TSH range.

A standard linear regression model (zero breakpoints) was compared with segmented models containing increasing numbers of candidate breakpoints. Models were evaluated using the Akaike Information Criterion (AIC). ¹⁴ When ΔAIC was greater than 10, the lower-AIC model was considered to have substantially better support; when ΔAIC was between 2 and 10, support for the lower-AIC model was interpreted more cautiously; and when ΔAIC was less than 2, competing models were considered to have similar support, with preference given to the simpler model. ¹⁵

Results

Patient characteristics

A total of 782 paired TSH and FT4 measurements were analyzed. Patient characteristics are summarized in Supplementary Table S1.

Segmented regression analysis and breakpoint estimation

Model comparisons supported a nonlinear relationship between logTSH and FT4. Fit improved as breakpoints were added, with AIC decreasing from 3,833.6 (0 breakpoints) to 3,817.1 (1 breakpoint) and 3,801.5 (2 breakpoints) (Table 1). A third breakpoint did not improve fit (AIC = 3,802.9). The two-breakpoint model yielded the lowest AIC and was selected.

Table 1.

Model Comparison of Segmented Regression Analyses in the Primary Analysis Population

Model	AIC a	Estimated breakpoints (logTSH b )	Estimated breakpoints (TSH c , mIU/L)	Breakpoint SE d (logTSH)	Segment slopes
Linear	3,833.6	NAe	NA	NA	−3.27
1-breakpoint	3,817.1	0.77	5.85	0.109	−2.95, −8.13
2-breakpoint	3,801.5	−0.65, 0.63	0.22, 4.25	0.238, 0.068	−4.94, −1.61, −7.82
3-breakpoint	3,802.9	−0.63, −0.20, 0.71	0.23, 0.63, 5.07	0.210, 0.191, 0.080	−5.49, 0.88, −2.23, −8.20

^aAIC, Akaike information criterion.

^blogTSH, base-10 logarithm of TSH.

^cTSH, thyrotropin.

^dSE, standard error.

^eNA, not applicable.

Segmented regression identified breakpoints at logTSH = −0.65 (standard error [SE], 0.24) and 0.63 (SE, 0.07), corresponding to TSH values of 0.22 and 4.25 mIU/L, respectively (Fig. 1). The slopes differ across segments (β₁ = −4.94, β₂ = −1.61, and β₃ = −7.82), where β_i denotes the within-segment slope.

FIG. 1.

Segmented regression analysis of the TSH–FT4 relationship. FT4 was modeled as a function of logTSH in the primary analysis population. Points represent individual paired measurements from 782 patients. The solid line indicates the fitted two-breakpoint segmented regression model, and the dashed vertical lines indicate the estimated breakpoints at TSH 0.22 and 4.25 mIU/L. TSH values < 0.005 mIU/L were set to 0.005 before log transformation. FT4, free thyroxine; TSH, thyrotropin.

Subgroup analysis

Sensitivity analyses showed that model selection depended mainly on how TSH values below the assay sensitivity were handled (Supplementary Table S2). When TSH values <0.005 mIU/L were set to 0.005 mIU/L, two-breakpoint models were selected in the primary analysis and in analyses excluding TgAb-positive or TPOAb-positive cases, whereas the exclusion of cases positive for either antibody favored a simpler one-breakpoint model. When TSH values <0.005 mIU/L were excluded, one-breakpoint models were selected for most analyses, and a linear model was selected when cases positive for either antibody were excluded.

Discussion

This study examined whether the widely assumed log-linear TSH–FT4 relationship adequately reflects the physiological regulation of the HPT axis across the full TSH spectrum. By modeling FT4 as a function of logTSH, I aimed to delineate the TSH range over which FT4 remains relatively stable and to consider how this range relates to population-based TSH reference intervals.

The lower breakpoint (0.22 mIU/L) closely approximated the assay-specific lower limit (0.27 mIU/L). ¹⁶ This breakpoint lies below the harmonized reference intervals in Japan and the United States,^17,18 suggesting that some individuals with mildly suppressed TSH may nonetheless maintain biochemical homeostasis; however, this lower breakpoint should be interpreted cautiously, because its identification was sensitive to the availability of data in the suppressed TSH range. The upper breakpoint (4.25 mIU/L) fell within the upper limits commonly used in clinical practice and in harmonized reference intervals (approximately 4.2–4.3 mIU/L).^16–18

These findings also underscore the limitations of conventional log-linear models in characterizing the TSH–FT4 relationship. Segmented regression revealed nonuniform slopes across the TSH range, consistent with complex nonlinear patterns described in empirical studies of TSH–FT4 feedback.^4–7,9 This nonlinearity has important diagnostic implications, suggesting that the HPT axis can maintain FT4 within a relatively narrow range while permitting substantial variation in TSH (0.22–4.25 mIU/L), consistent with robust homeostatic control rather than a simple log-linear response. Identifying such physiological transition points may help contextualize borderline thyroid function test abnormalities.

Although prior community-based data indicated that the logTSH–FT4 relationship is influenced by TPOAb status, ⁹ the exclusion of TPOAb-positive cases did not materially change the overall pattern in sensitivity analyses.

This study had several limitations. It was a single-center retrospective analysis of a predominantly female cohort, which may limit generalizability and may not fully account for unmeasured confounders. Additionally, alternative nonlinear models such as sigmoid functions were not evaluated. Although TgAb and TPOAb are markers of chronic autoimmune thyroiditis, many antibody-positive individuals have normal thyroid function tests. In the primary analysis, antibody-positive individuals were therefore not excluded to reflect real-world outpatient heterogeneity. TRAb levels were measured when hyperthyroidism or atrophic thyroiditis was suspected, and individuals with positive results were excluded. However, because TRAb levels were not measured in all patients, undetected TSH receptor antibodies cannot be ruled out. Despite these limitations, the overall pattern remained broadly consistent across the primary and sensitivity analyses, with recurrent identification of a breakpoint near 4 mIU/L and persistence of a lower breakpoint in selected analyses.

These findings suggest that population-based TSH reference intervals broadly approximate the empirically derived homeostatic range, particularly at the upper end, but may not fully capture its lower boundary. Because such intervals depend on the selection of reference individuals, sample size, analytical methods, and exclusion criteria, they should be viewed as clinically useful frameworks rather than absolute physiological boundaries.^19,20

Future research should examine whether these breakpoints vary with age, iodine intake, and assay platforms. The lower breakpoint warrants prospective validation.

Conclusion

This study indicates that the TSH–FT4 relationship is well described by a segmented model with two physiologically plausible breakpoints at 0.22 and 4.25 mIU/L. This interval defines a range over which FT4 changes little, suggesting an effective zone of homeostatic regulation. Population-based TSH reference intervals showed partial concordance with this empirically derived homeostatic range, particularly at the upper end, whereas the lower boundary was less closely aligned. These findings suggest that empirically derived breakpoints and population-based reference intervals may offer complementary perspectives for interpreting borderline biochemical abnormalities.

Data Access Statement

The data used in this study were obtained from patient records at Kasahara Clinic and contained sensitive patient information. Owing to privacy and confidentiality agreements, raw data are not publicly available. The aggregated data are available from the author upon request.