Discrepancies in Four Algorithms for the Calculation of Free and Bioavailable Testosterone

To the Editor:

Testosterone (T) binds to sex hormone-binding globulin (SHBG) and albumin (Alb) to form SHBG-T and Alb-T (1). If total testosterone (TT) is low or SHBG concentration is altered, free testosterone (FT) is recommended (1). Bioavailable testosterone (BioT) including FT and Alb-T correlates with FT (1, 2). FT and BioT can be measured by equilibrium dialysis and ammonium sulfate [(NH₄)₂SO₄] precipitation, respectively (1). FT and BioT can also be calculated using algorithms (1) described by Vermeulen (2), Sodergard (3), and Emadi-Konjin (4), or using the empirical equation by Morris (5). We aimed to determine which equation, based on our own TT and SHBG assays, generates results that are closer to our reference laboratory values before bringing the FT and BioT tests in house.

Forty-nine sera with known FT (0.05 to 19.22 ng/dL, or 1.7 to 666.2 pmol/L) and BioT (1.2 to 542.0 ng/dL, or 0.04 to 18.80 nmol/L) were obtained from the reference laboratory, where FT and BioT were calculated using a proprietary algorithm and TT and SHBG were measured by a LC-MS/MS assay and an immunoassay, respectively. In our laboratory, TT was measured by an LC-MS/MS assay with an analytical measurement range of 2.0 to 2330.4 ng/dL or 0.07 to 80.80 nmol/L, and interassay coefficient of variation of 4.7%, 2.6% and 2.4% at 3.2, 868.0, 1851.4 ng/dL, respectively. SHBG was measured by an immunoassay (Roche Diagnostics) with an analytical measurement range of 2 to 200 nmol/L, and interassay coefficients of variation of 1.8%, 2.1%, and 4.0% at 14.9, 45.7, and 219 nmol/L, respectively.

The in-house TT assay demonstrated a negative bias of −11.5% ± 7.5% (mean ± SD) relative to the reference laboratory assay, although both were certified by the CDC Hormone Standardization Program. There was no significant bias between the 2 SHBG assays (Table 1).

Table 1.

Comparison of TT, SHBG, FT, and BioT results by different methods^a.

Method x	Method y	Deming regression equation	Standard error of the estimate (SEE)	Correlation coefficient (R)	Bias% (mean ± SD)	Samples with result difference ≤25%
Reference lab TT	In-house TT	y = 0.939x − 8.1	22.4 ng/dL	0.9978	−11.5% ± 7.5%	48 of 49
Reference lab SHBG	In-house SHBG	y = 1.019x − 0.6	3.0 nmol/L	0.9966	3.3% ± 4.5%	0 of 49
Reference lab FT	Vermeulen FT	y = 0.984x − 0.139	0.435 ng/dL	0.9970	−9.3% ± 7.8%	47 of 49
	Sodergard FT	y = 1.131x − 0.012	0.532 ng/dL	0.9966	15.6% ± 11.1%	38 of 49
	Emadi-Konjin FT	y = 1.339x − 0.834	1.838 ng/dL	0.9704	−6.6% ± 23.4%	35 of 49
Reference lab FT%	Vermeulen FT%	y = 1.075x − 0.063	0.090%	0.9863	2.6% ± 4.8%	49 of 49
	Sodergard FT%	y = 1.017x + 0.365	0.085%	0.9864	30.9% ± 11.0%	15 of 49
	Emadi-Konjin FT%	y = 1.799x − 0.966	0.303%	0.9430	5.3% ± 23.5%	41 of 49
Reference lab BioT	Vermeulen BioT	y = 0.835x − 3.454	9.628 ng/dL	0.9973	−21.1% ± 9.1%	29 of 49
	Sodergard BioT	y = 1.078x − 0.605	15.47 ng/dL	0.9958	13.0% ± 14.4%	41 of 49
	Emadi-Konjin BioT	y = 0.430x − 6.287	15.71 ng/dL	0.9733	−68.5% ± 8.0%	0 of 49
	Morris BioT	y = 0.540x + 4.011	21.18 ng/dL	0.9692	−23.3% ± 28.8%	19 of 49
	(NH4)2SO4 BioT	y = 0.883x − 10.93	21.85 ng/dL	0.9875	−28.9% ± 12.6%	16 of 49
(NH4)2SO4 BioT%	Reference lab BioT%	y = 0.937x + 9.252	4.49%	0.9442	27.1% ± 18.0%	20 of 49
	Vermeulen BioT%	y = 0.874x + 7.033	4.10%	0.9464	12.9% ± 15.1%	39 of 49
	Sodergard BioT%	y = 0.900x + 19.54	5.40%	0.9166	62.4% ± 28.0%	7 of 49
	Emadi-Konjin BioT%	y = 0.568x − 3.249	1.80%	0.9745	−55.6% ± 7.5%	0 of 49
	Morris BioT%	y = 0.146x + 25.15	3.43%	0.5044	10.2% ± 38.1%	18 of 49

^aTo convert testosterone or FT from ng/dL to nmol/L, multiply the value in 1 ng/dL by 0.0347.

Using in-house TT and SHBG results and a fixed albumin concentration of 4.3 g/dL or 43 g/L, FT was calculated with the Vermeulen, Sodergard, and Emadi-Konjin algorithms. Vermeulen FT showed the best correlation with the reference laboratory FT by Deming regression analysis: y = 0.984x − 0.139 (R = 0.9970) (Table 1). In comparison with the reference laboratory FT results, 47, 38, and 35 out of 49 samples had FT results within a difference of 25% by Vermeulen, Sodergard, and Emadi-Kongjin algorithms, respectively. These samples demonstrated percentage biases of −9.3% ± 7.8% (mean ± SD) for Vermeulen FT, 15.6% ± 11.1% for Sodergard FT, and −6.6% ± 23.4% for Emadi-Konjin FT. As calculated FT was affected by the bias between TT and SHBG assays, even when the same algorithm was used, calculated FT% and the following BioT% were also compared (Table 1). In comparison with the reference laboratory results, 49, 15, and 41 out of 49 samples had FT% results within a difference of 25% by Vermeulen, Sodergard, and Emadi-Kongjin algorithms, respectively. The Vermeulen FT% showed the smallest percentage bias of 2.6% ± 4.8%. Therefore, the Vermeulen algorithm demonstrated the best agreement with the reference laboratory in calculated FT or FT%.

BioT and BioT% were calculated with the Vermeulen, Sodergard, Emadi-Konjin, and Morris algorithms, and measured with (NH₄)₂SO₄ precipitation (4, 5). Compared to the reference laboratory BioT results, 29, 41, 0, 19, and 16 out of 49 samples had BioT concentrations within a difference of 25% by Vermeulen, Sodergard, Emadi-Kongjin, Morris, and (NH₄)₂SO₄ precipitation, respectively; the percentage biases were −21.1% ± 9.1% for Vermeulen BioT, 13.0% ± 14.4% for Sodergard BioT, and −28.9% ± 12.6% for (NH₄)₂SO₄ BioT (Table 1). The Sodergard algorithm showed the best agreement with the reference laboratory BioT, followed by the Vermeulen algorithm. When compared with measured (NH4)₂SO4 BioT%, 20, 39, 7, 0, and 18 out of 49 samples had BioT% results within a bias of 25% by reference laboratory, Vermeulen, Sodergard, Emadi-Kongjin, and Morris algorithms, respectively; the percentage biases were 12.9% ± 15.1% and 62.4% ± 28.0% for Vermeulen and Sodergard BioT%, respectively (Table 1). Sodergard BioT% also showed a large positive bias compared to the reference laboratory (data not shown).

In summary, the results for the Vermeulen algorithm based on the data of the in-house TT and SHBG assays show favorable agreement with the reference laboratory results. Significant discrepancies exist among 4 algorithms for the calculation of FT or BioT, stressing the importance of revalidating calculation algorithms locally. Clinicians and laboratorians should be aware that FT and BioT calculated using different algorithms and TT and SHBG assays may not be exchangeable. This study provides a template for other laboratories to compare different algorithms with their own reference laboratories to select the best algorithm with calculated FT and BioT results that align most closely with their reference laboratory results, so that they can report comparable results after bringing the test in house.

Nonstandard Abbreviations

T, testosterone; SHBG, sex hormone-binding globulin; Alb, albumin; TT, total testosterone; FT, free testosterone; BioT, bioavailable testosterone.

Author Contributions

The corresponding author takes full responsibility that all authors on this publication have met the following required criteria of eligibility for authorship: (a) significant contributions to the conception and design, acquisition of data, or analysis and interpretation of data; (b) drafting or revising the article for intellectual content; (c) final approval of the published article; and (d) agreement to be accountable for all aspects of the article thus ensuring that questions related to the accuracy or integrity of any part of the article are appropriately investigated and resolved. Nobody who qualifies for authorship has been omitted from the list.

Jianbo Yang (Conceptualization-Equal, Data curation-Equal, Formal analysis-Equal, Investigation-Equal, Methodology-Equal, Validation-Equal, Visualization-Equal, Writing—original draft-Equal), Christopher Hamilton (Conceptualization-Equal, Data curation-Equal, Formal analysis-Equal, Investigation-Equal, Methodology-Equal, Validation-Equal, Writing—review & editing-Equal), Kimberly Robyak (Conceptualization-Equal, Data curation-Equal, Formal analysis-Equal, Investigation-Equal, Methodology-Equal, Validation-Equal, Writing—review & editing-Equal), and Yusheng Zhu (Conceptualization-Equal, Data curation-Equal, Formal analysis-Equal, Investigation-Equal, Methodology-Equal, Project administration-Equal, Resources-Equal, Supervision-Equal, Validation-Equal, Writing—review & editing-Equal)

Authors’ Disclosures or Potential Conflicts of Interest

Upon manuscript submission, all authors completed the author disclosure form.

Research Funding

Y. Zhu is supported by the National Institute of Diabetes and Digestive and Kidney Diseases (1 U01 DK135126-01), Abbott Laboratories, Supelco, Inc., and Chan Zuckerberg Initiative.

Disclosures

Y. Zhu, AACC Board of Directors; President of AACC Academy, Chair of AACC Academy Council; President of Association of Clinical Scientists.