The log TSH-free T4 relationship in a community-based cohort is nonlinear and is influenced by age, smoking and thyroid peroxidase antibody status

Summary Background The TSH–T4 relationship was thought to be inverse log‐linear, but recent cross‐sectional studies of selected populations report a complex, nonlinear relationship. The TSH–T4 relationship has not been evaluated in an unselected, community‐based cohort, and there are limited data regarding clinical factors which affect it. Objective To analyse the TSH–free T4 relationship in a community‐based cohort. Design, participants and methods In a cross‐sectional, retrospective study, we analysed serum TSH and free T4 concentrations from 4427 participants (55% female) in the 1994 Busselton Health Study who were not taking thyroxine. Simple linear, segmented‐linear and nonlinear regression models of log10TSH on free T4 were compared for goodness of fit. Results All 5 log TSH–free T4 models tested (separate lines, segmented conterminal line, quartic, error function, double‐sigmoid curve) fitted significantly better than a simple linear model (each P < 0·01 by Vuong test). Ranking by Akaike information criterion indicated that the segmented conterminal line and double‐sigmoid models provided best fit, followed by the error function, quartic and separate lines models. From multiple regression analysis, age tertile, current smoking and TPOAb status each significantly influenced the TSH–free T4 relationship, whereas BMI category and diabetes did not. A sex difference in the TSH–free T4 relationship was apparent only in the lower part of the free T4 reference range. Conclusion In a community‐based setting, the relationship between log TSH and free T4 is complex, nonlinear and influenced by age, smoking and TPOAb status.