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BY 4.0 license Open Access Published by De Gruyter September 5, 2022

Thyroid stimulating hormone: biased estimate of allowable bias

  • Arne Åsberg EMAIL logo , Ingrid Alsos Lian and Gustav Mikkelsen

To the Editor,

We read with interest the article on biological variation for serum thyroid biomarkers recently published in CCLM by Bottani et al. [1]. For thyroid stimulating hormone (TSH) the authors estimated an allowable bias of 10.0%. We believe this value may be downwardly biased. It was calculated as 0.25 times the total biological coefficient of variation. This way of estimating allowable bias stems from a paper of Gowans et al. [2]. The idea was that laboratories serving the same population and wanting to use the same reference limits should aim to keep the analytical bias less than one quarter of the standard deviation (SD) of Gaussian distributed reference values. If the reference values are log-Gaussian distributed, as in the case of TSH [1], the allowable bias depends on the ratio between the upper (u) and lower (l) reference limits [3]. This is so because on the log scale the total biological variation SD is [ln(u) − ln(l)]/(2 · 1.96)=ln(u/l)/3.92 and the allowable bias is ±0.25 · ln(u/l)/3.92=±ln(u/l)/15.68. On the measurement scale this transforms to a factor (f), where f=e[ln(u/l)/15.68]. As addition on the log scale corresponds to multiplication on the measurement scale, the allowable positive bias is c · f − c, i.e.100 · (c · f − c)/c%=100 · (f − 1)%, where c is the analyte concentration. Likewise, as subtraction on the log scale corresponds to division on the measurement scale, the allowable negative bias is c/f − c, i.e. 100 · (c/f − c)/c%=100 · (1/f − 1)%. For instance, if f = 1.10, the allowable positive bias is 100 · (1.10 − 1)%=10.0% and the allowable negative bias is 100 · (1/1.10 − 1)%=−9.1%. However, the different numerical values of allowable positive and negative bias were not emphasized in Ref. [3].

So in accordance with tradition, but not with theory, only one value (10.0%) of allowable bias was given in the article of Bottani et al. [1]. In contrast, using the reference limits of TSH in our laboratory, which are 0.5 and 4.0 mIU/L with a u/l-ratio of 8, we calculated f of 1.142 (see above), allowable positive bias of 14.2%, and allowable negative bias of − 12.4%. The numerical values of these bias estimates are considerably larger than 10.0%.

Admittedly, we used reference limits estimated from reference values that included analytical variation, while Bottani et al. estimated allowable bias from “pure” total biological variation, excluding analytical variation [1].

To test whether this could explain the difference, we performed data simulations: From a log-Gaussian distribution of 10,000 randomly drawn values with 2.5 percentile of 0.5 and 97.5 percentile of 4.0, the u/l-ratio was calculated. This was repeated 10,000 times for an analytical coefficient of variation (CVa) of 0–5%, in steps of 1%, a range that should include the CVa for most TSH analytical methods. For a CVa of 0% the mean u/l-ratio was 7.98. For a CVa of 1 and 5% the mean u/l-ratio was 7.98 (SD 0.03) and 8.03 (SD 0.06), respectively. In terms of allowable bias, the results were hardly discernible.

Thus, the reason why the allowable bias for TSH given by Bottani et al. [1] was lower than our estimates was not related to analytical variation. Instead the reason may be differences in the reference populations. If the allowable bias of 10.0% [1] could be interpreted as an f of 1.10, the corresponding u/l-ratio is 4.5. Given an upper reference limit of 4.8 mIU/L [1], this u/l-ratio indicates a lower reference limit of 4.8/4.5 mIU/L=1.1 mIU/L, which is an improbable value. One could speculate that the reference population of 91 individuals, 85 of whom contributed to the TSH data [1], was too small to be representative of the TSH distribution in the general, healthy population. Another reason may be that Bottani et al. calculated the total biological variation from within-subject biological variation in all 85 individuals and between-subject biological variation in 38 men [1], because the between-subject biological variation in men was less than that in women. This decision was in accordance with EuBIVAS policy [4]. Using the women’s value of between-subject biological variation [1], the allowable bias would be 12.4%, which is more like our estimates.

In conclusion, if allowable bias is to be derived from reference values [2], we believe it is important to use data from a representative reference population of sufficient size. When the reference values of the analyte have an approximate log-Gaussian distribution, as in the case of TSH and several other analytes [5], more accurate estimates are achieved using the calculations given above.


Corresponding author: Arne Åsberg, Department of Clinical Chemistry, St. Olav’s Hospital, POB 3250 Torgarden, 7006 Trondheim, Norway, E-mail:

  1. Research funding: None declared.

  2. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  3. Competing interests: Authors state no conflict of interest.

  4. Informed consent: Not applicable.

  5. Ethical approval: Not applicable.

References

1. Bottani, M, Aarsand, AK, Banfi, G, Locatelli, M, Coşkun, A, Díaz-Garzón, J, et al.. European biological variation study (EuBIVAS): within- and between-subject biological variation estimates for serum thyroid biomarkers based on weekly samplings from 91 healthy participants. Clin Chem Lab Med 2022;60:523–32. https://doi.org/10.1515/cclm-2020-1885.Search in Google Scholar PubMed

2. Gowans, EM, Hyltoft Petersen, P, Blaabjerg, O, Hørder, M. Analytical goals for the acceptance of common reference intervals for laboratories throughout a geographical area. Scand J Clin Lab Invest 1988;48:757–64. https://doi.org/10.3109/00365518809088757.Search in Google Scholar PubMed

3. Hyltoft Petersen, P, Gowans, EM, Blaabjerg, O, Hørder, M. Analytical goals for the estimation of non-Gaussian reference intervals. Scand J Clin Lab Invest 1989;49:727–37. https://doi.org/10.3109/00365518909091551.Search in Google Scholar PubMed

4. Carobene, A, Aarsand, AK, Bartlett, WA, Coskun, A, Diaz-Garzon, J, Fernandez-Calle, P, et al.. The European biological variation study (EuBIVAS): a summary report. Clin Chem Lab Med 2021;60:505–17. https://doi.org/10.1515/cclm-2021-0370.Search in Google Scholar PubMed

5. Haeckel, R, Wosniok, W. Observed, unknown distributions of clinical chemical quantities should be considered to be log-normal: a proposal. Clin Chem Lab Med 2010;48:1393–6. https://doi.org/10.1515/CCLM.2010.273.Search in Google Scholar PubMed

Received: 2022-08-11
Accepted: 2022-08-26
Published Online: 2022-09-05
Published in Print: 2022-10-26

© 2022 the author(s), published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.

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