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The relationship between serum TSH and free T4 in older people
  1. Penny M Clark1,
  2. Roger L Holder2,
  3. Sayeed M Haque2,
  4. F D Richard Hobbs2,
  5. Lesley M Roberts2,
  6. Jayne A Franklyn3
  1. 1The Regional Endocrine Laboratories, University Hospital Birmingham NHS Foundation Trust, Birmingham, UK
  2. 2Primary Care Clinical Sciences, University of Birmingham, Birmingham, UK
  3. 3School of Clinical and Experimental Medicine, University of Birmingham, Birmingham, UK
  1. Correspondence to Dr Penny M Clark, University Hospital Birmingham NHS Foundation Trust, The Regional Endocrine Laboratory, Birmingham B29 6JD, UK; penelope.clark{at}


The frequency distribution of serum thyroid stimulating hormone (TSH) shows a skewed pattern that may change with age. The set point of the hypothalamic-pituitary-thyroid axis for an individual is thought to be genetically determined and has been described as a log-linear relationship of serum TSH to free thyroxine (T4); however, the validity of this hypothesis has yet to be established in older people. The aim of the study was to describe the relationship between serum TSH and free T4 in older people and define factors influencing this relationship. We conducted a cross-sectional, observational study of thyroid function in a community population of older subjects over 65 years of age. The relationship between serum TSH and free T4 was not linear as previously described, but is best described as a fourth-order polynomial. Both gender and smoking status affected the relationship. This suggests that more complex modelling is required when investigating the hypothalamic-pituitary-thyroid axis.

  • Thyroid endocrinology
  • thyroid
  • adrenal gland

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Measures of thyroid function such as serum thyroid-stimulating hormone (TSH) and free thyroxine (T4) concentrations have been shown to have narrower within-individual limits of variability than inter-individual limits.1 Although environmental factors such as iodine intake, cigarette smoking, early life factors and ethnicity may influence these parameters individually, there is evidence from twin studies that heritability accounts for approximately 64% of the individual variability in serum TSH.2–4 This narrow within-individual range is thought to reflect the individual's hypothalamic-pituitary-thyroid (HPT) set point. Two experimental approaches have been used to investigate the nature of this set point, either large cross-sectional population studies of the relationship between serum free T4 and TSH under stable conditions or smaller studies involving the administration of T4. Both approaches have described the relationship between serum T4 and TSH concentrations as inverse log-linear.5–7 It has, however, been found that using the latter in vivo approach the log-linear relationship was not significant in all individuals.7

The aim of this study was to determine the relationship between serum TSH and free T4 in an ambulant older population as an indicator of the pituitary set point and to establish some of the factors that influence that relationship.

Patients and methods

The population studied comprised a large group of community dwelling subjects aged 65 years or older.8 Applicants were excluded if they were currently receiving T4 or medications known to affect the HPT axis (T4, antithyroid therapy, amiodarone, glucocorticoids) or if during the previous 12 months they had had thyroid surgery, radioiodine therapy or suffered an endocrine disorder. The study group comprised 2510 males, 2607 females (total n=5117). Serum TSH and free T4 were measured by chemiluminescent immunoassay (Advia Centaur, Siemens Healthcare Diagnostics). The reference range for serum TSH was 0.4–5.5 mU/l, inter-assay coefficient of variation of 4.4%–10.9% over the range of 0.41–24.5 mU/l. The laboratory reference range for free T4 was 9.0–20.0 pmol/l, inter-assay coefficient of variation of 4.2–6.9% over the range 4.0–16.0 pmol/l.

Informed consent was obtained from all participants. The Multi Centre Research Ethics Committee provided ethical approval.

Statistical methods

The relationship between free T4 and loge TSH was investigated using a general linear model (GLM) using SPSS V.17.00 (SPSS Inc.). The possibility of a non-linear relationship between loge TSH and free T4 was investigated by including powers of free T4 up to (free T4)4 as further independent variables in the GLM thus creating a possible quartic or fourth-order polynomial relationship between loge TSH and free T4. Further analysis of the effects of smoking, age and gender on this relationship was performed by suitably expanding the GLM to include components which reflect such effects. The effect of a non-Gaussian distribution on the GLM residuals was addressed by computing non-parametric bootstrap p values corresponding to each quoted p value and denoted (pb).


The relationship between serum loge TSH and free T4 was non-linear for the total population and subgroups for gender with powers of free T4 up to (free T4)4 being significant in the GLM (a fourth-order polynomial). There was a significant effect of gender and smoking on the relationship of serum loge TSH to free T4 ((p<0.0001, pb<0.001) and (p<0.0001, pb<0.001), respectively), but no effect of age ((p=NS, pb=NS); figure 1). The effect of gender was found to differ at low free T4/high TSH concentrations compared with high free T4/low TSH concentrations as illustrated by crossover of the two fourth-order polynomial lines shown for the two genders (figure 1). Thus, for example, at free T4 concentrations below the lower limit of normal, female subjects had a higher serum TSH than male subjects. There was a significant effect of smoking on the loge TSH–free T4 relationship, with smokers having lower serum TSH concentrations for a given serum free T4. Within the reference range for free T4 (9.0–20.0 pmol/l), the quadratic term (ie, non-linearity) remained significant (p=0.002, pb=0.004) as did the effects of gender and smoking (p=0.000, pb<0.001 and p=0.001, pb<0.001, respectively). The mean difference in TSH between smokers and non-smokers was −0.26 (CI −0.42 to 0.10) mIU/l.

Figure 1

Relationship between serum loge thyroid stimulating hormone (TSH) and free T4 (FT4) according to gender. The best-fit line is described as a fourth-order polynomial according to gender. The grey (shown as green in the online colour version) straight line illustrates the log-linear relationship previously reported. TSH is given in units of mU/l and FT4 in pmol/l (n=5117). This figure is produced in colour in the online journal—please visit the website to view the colour figure.


In this study, the relationship between serum loge TSH and free T4 was best described by a fourth-order polynomial equation, rather than a first-order linear relationship. This suggests that the sensitivity of the HPT axis differs with thyroid status as small changes in the concentration of free T4 outside of the reference range are associated with a larger increase (or decrease) in serum TSH compared with the smaller variability within the reference ranges. The possibility of such a non-linear relationship was discussed by Hansen and colleagues2 in their study of the genetic influences on the regulation of the pituitary-thyroid axis. They concluded that they had not been able to demonstrate non-linearity because of the limited concentration range of serum TSH and free T4 in their study population.

Comparison with earlier studies reporting a linear relationship can only be limited because of differences in population age, medication usage and lack of exclusions for non-thyroidal illness.5 The influence of analytical methodology should also be considered. The bias of different TSH assays is significant9 and estimates of free T4 whether from a derived index (T4/T3 uptake) or measured by immunoassay or Liquid chromatography-tandem mass spectrometry (LC-MS/MS) may also affect this relationship.5 10 11 Jonklaas and colleagues12 studying an adult population and using a log-linear model found a stronger correlation of serum TSH to free T4 when ultrafiltration LC-MS/MS was used to measure free T4 compared with immunoassay, though higher-order models for this relationship were not investigated.

The alternative approach to investigating the HPT set point is to determine the changes in serum TSH on administration of T4 and this has been used, for example, to study patients with thyroid hormone resistance with the control group showing an inverse log-linear relationship.6 In a recent study of 21 healthy subjects given T4 (mean age 60 years),7 a log-linear relationship between serum TSH and free T4 was demonstrated for the group as a whole, but not for all subjects when considered individually. The subjects had been given placebo, 125 μg and then 250 μg of T4 with a consequent small number of data points for any given individual and covering a limited concentration range of serum TSH and free T4.

Our findings in a large cross-sectional study of ambulant older subjects clearly suggest that more sophisticated modelling of the relationship between serum loge TSH and free T4 may be required and could usefully be explored in a younger age group with consideration of the potential effects of ethnicity, body mass index and indices of thyroid autoimmunity. In addition, we have demonstrated that the relationship between serum loge TSH and free T4 was also influenced by smoking status and gender but not by age and that for a given serum free T4 concentration smokers of either gender have a lower serum TSH though the relationship is non-linear for all groups.

Take-home messages

  • The relationship between serum loge TSH and free T4 was best described by a fourth-order polynomial equation, rather than a first-order linear relationship which has been widely reported.

  • The relationship is affected by gender and by smoking status, with smokers having a lower serum TSH.

  • Within the age range studied, age had no effect on the relationship between serum TSH and free T4.


We thank Professor J V Parle, University of Birmingham and all the participants, nursing staff and healthcare providers who participated in and supported the study.



  • Funding This work was supported by the Healthcare Foundation UK, the Primary Care Research and Clinical Trials Unit and MidRec (Midlands GP Research Consortium). This work was also supported by Queen Elizabeth Hospital Birmingham Charity. The funding organisations have not directly influenced the design and conduct of the study; collection, management, analysis and interpretation of the data; and preparation, review or approval of the manuscript.

  • Competing interests None.

  • Ethics approval Ethics approval was obtained from the Multi Centre Research Ethics Committee.

  • Provenance and peer review Not commissioned; externally peer reviewed.