Background
A central tenet of thyroid physiology is the inverse, log-linear relationship between serum thyroid stimulating hormone (TSH) and free T4 (fT4). Studies of the TSH-fT4 relationship have however, mostly been limited to cross-sectional analysis of small datasets. The aim of this study was to evaluate the TSH-fT4 relationship by cross-sectional analysis of a large population and examine intraindividual changes in TSH and fT4. Utilizing these approaches we hope to improve understanding of the hypothalamic-pituitary-thyroid feedback loop and how this relationship may be influenced by gender, age and thyroxine therapy.

Methods
We examined records with concurrent TSH and fT4 measurements performed over a 12 year period by a single, predominantly community-based, pathology provider using the Siemens Centaur assay. After applying exclusions, 445,918 records from 152,261 patients were available for further analysis. The TSH-fT4 relationship was examined in a cross-sectional analysis of these 152,261 patients. In 29,858 subjects with three or more sets of results, we calculated individual median TSH and fT4 concentrations and examined the relationship between change in TSH for any given change in fT4 (delta TSH and delta fT4).

Results
In the cross-sectional analysis, the relationship between TSH and fT4 was not log-linear but a combination of sigmoidal curves. The rate of change of TSH with fT4 below the reference range was steep, less so with fT4 within the reference range and almost flat for elevated fT4 levels. Within the fT4 reference range the curves for patients treated or not treated with thyroxine did not significantly differ. Over the whole fT4 range the median TSH in thyroxine treated individuals was 0.3 mU/L lower than untreated individuals however, for an elevated fT4, thyroxine treated patients had a higher median TSH than untreated patients. In subjects with high-normal fT4, the relationship differed between genders such that women had lower TSH concentrations than men at any given high-normal fT4. In older people, TSH was less elevated in response to a low fT4 than in younger people. Within the reference range however, median TSH was higher for older individuals compared with younger individuals. In the intraindividual analysis, the relationship between delta TSH and delta fT4 showed distinct curves depending on whether delta fT4 was positive or negative. A gender difference was again apparent and in older patients, TSH appeared less responsive to delta fT4 than in younger patients.

Conclusion
The relationship between TSH and fT4 is not log-linear but rather a complex combination of curves which differs between genders and changes with aging. This suggests that there are gender-specific and age-related differences in hypothalamic-pituitary-thyroid function.