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In this issue of the EJE, we publish a critical comment (1)on a previously published study by Hoermann et al. (2).While the latter propose a complex relationship betweenthyroid hormones and TSH, Dr Leow (1) supports theclassical logarithmic–linear relationship as described inanother study also published here by Benhadi et al. (3).Assuming that the data of both studies are valid, andas both articles have been reviewed by experts in theeld, there is no reason to doubt this, it might be thatbesides the interpretation of the results, the differencesmay reside in the way the data were collected. The workof Benhadi et al. (3) is an experimental study, selecting anarrow homogeneous population that we woulddescribe as ‘hypernormal’ subjects: no thyroid disease,no thyroid antibodies, no interfering disease, nomedication and controlled administration of predeter-mined doses of thyroid hormones or placebo. Theconclusion is of a logarithmic–linear relationshipobserved in the group but not in individuals, presum-ably because of insufcient dose of thyroid hormones. Incontrast, in the study by Hoermann et al. (2) thepopulation is much larger and more heterogeneous:more than 10 000 subjects, composed of patients agedbetween 18 and 100 years, some of them are free oftreatment and some of them are on treatment witheither thyroid hormones or on anti-thyroidal drugs (2).In this aspect, this work is more related to real life.The hysteresis of TSH, mentioned by Leow (1), that isthe transient apparent deviation from the normalbehaviour because of a delayed adaptation to rapidchanges, can probably account for a part of discrepan-cies between the two studies. This may, however, also beincriminated in the study by Benhadi et al. (3) since thesubjects are not studied at equilibrium. In addition, it isnot obvious that studying patients thyroidectomized fora thyroid cancer and assessed upon thyroxine with-drawal would be the best design as they would certainlynot be studied at steady state, and hysteresis wouldoperate there, again.Certainly, the logarithmic relationship is a helpful,robust and simple way of describing the connectionbetween thyroid hormones and TSH. It is acceptablysuitable in most cases. Nevertheless, is it heretic toadmit that it is an approximation in some specicsituations, especially in non-stable conditions such asthyroid diseases whether treated or not? This discussionalso illustrates a long-lasting debate on normalreference range for TSH and thyroid hormones.A strictly ‘hypernormal’ population, at equilibrium,sampled in the morning in the fasted state, is obviouslycloser to the truth. But should we consider that themarginal outliers are sick?

Reply to: The TSH–free thyroxine relationship: logarithmic–linear or error function?