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Steroids 76 (2011) 48–55

Contents lists available at ScienceDirect

Steroids

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ccuracy of calculated free testosterone differs between equations and dependsn gender and SHBG concentration

ennifer S. Hackbartha, Jonathan B. Hoyneb, Stefan K. Grebea, Ravinder J. Singha,∗

Department of Laboratory Medicine and Pathology, Mayo Clinic, Rochester, MN, United StatesDepartment of Laboratory Medicine and Pathology, Mayo Clinic, Jacksonville, FL, United States

r t i c l e i n f o

rticle history:eceived 26 February 2010eceived in revised form 4 August 2010ccepted 25 August 2010

eywords:

a b s t r a c t

Serum free testosterone (fT) concentrations are often calculated, however different equations often yielddiscrepant results. This study explores the sources of this variability. We compared three established andtwo new equations that differed only by their testosterone association constants with isotope dilutionequilibrium dialysis in two patient groups with different gender distributions. Equation components wereexamined to determine how they impacted correlation with isotope dilution equilibrium dialysis. Associ-ation constants derived for each patient group correlated best with isotope dilution equilibrium dialysis

estosteroneree testosteroneree testosterone calculationass action equation

ex hormone binding globulinsotope dilution equilibrium dialysis

for that group and not the other set. Samples with the poorest correlation between isotope dilutionequilibrium dialysis and calculated fT results had significantly higher SHBG concentrations. Regardlessof equation, ≥25% of samples showed unacceptable deviation from isotope dilution equilibrium dialysis.Association constants and gender makeup and SHBG concentration of the patient groups used to establishan equation all significantly impact correlation with isotope dilution equilibrium dialysis. Application of

er poilibri

many fT equations to widfrom isotope dilution equ

. Introduction

Measurement of serum testosterone concentrations is a cen-ral component of the assessment of androgen status. Increasedoncentrations can be seen in women with congenital adrenalyperplasia or polycystic ovarian syndrome (PCOS), and in bothenders due to exogenous testosterone administration, adrenal-testicular-, or ovarian tumors, and in children with precociousuberty [1]. Conversely, decreased serum testosterone con-entrations are the hallmark of both primary and secondaryypogonadism in men, and, to a lesser degree, women, regardlessf the underlying etiology. Androgen deficiency in males is believedo be a particular common problem, affecting an estimated to 4.7

illion men between the ages of 30 and 79 in the United States in000, and predicted to rise to 6.5 million by 2025 [2,3]. Most of theseases represent mild to moderate deficiency, often referred to asandropause” or “late-onset hypogonadism”, a state that is blamed

Abbreviations: fT, free testosterone; SHBG, sex hormone binding globulin; PCOS,olycystic ovarian syndrome; ks , association constant for testosterone binding toHBG; ka , association constant for testosterone binding to albumin; LC–MS/MS,iquid chromatography–tandem mass spectrometry; CV, coefficient of variation.∗ Corresponding author at: Department of Laboratory Medicine and Pathology,ilton 210, Mayo Clinic, 200 First St., S.W., Rochester, MN 55905, United States.el.: +1 507 266 0481; fax: +1 507 284 9758.

E-mail address: singh.ravinder@mayo.edu (R.J. Singh).

039-128X/$ – see front matter © 2010 Elsevier Inc. All rights reserved.oi:10.1016/j.steroids.2010.08.008

pulations will therefore frequently yield results that differ substantiallyum dialysis.

© 2010 Elsevier Inc. All rights reserved.

for anergia, sexual dysfunction, declining mental ability, dimin-ished muscle strength and reduced bone density [4,5]. Decreasedtestosterone concentrations in women present with fewer and lessspecific symptoms [6,7].

Measurement of total testosterone, often combined withgonadotropin measurements, is generally sufficient to diagnosesignificant androgen excess or deficiency. However, for suspectedmild to moderate deficiency, measurement of the free, bioactive,fraction of testosterone (fT) is believed to be of superior diagnos-tic value, especially under circumstances of altered sex hormonebinding globulin (SHBG) serum concentrations or binding affinity,as may be found in hyper- or hypothyroidism, liver cirrhosis, obe-sity, or exogenous sex hormone use, especially estrogen treatments[8–11]. Serum concentrations of SHBG also increase with age, oftenaffecting fT levels disproportionately to total testosterone concen-trations [12].

Because the majority of testosterone is bound to SHBG or albu-min, fT accounts for only 1–4% of the total testosterone levels.Furthermore, the protein-bound distribution of testosterone is gen-der dependent because of differences in sex steroid distribution,with 44% of testosterone bound to SHBG in men and 66% bound

to SHBG in women [13]. These factors conspire to make measure-ments of fT challenging. The gold standard method of measurementis isotope dilution equilibrium dialysis [14–16]. While this methodis considered the most accurate, its technical and laborious naturecan result in high assay variability [17]. Analog immunoassays that

Steroids 76 (2011) 48–55 49

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Table 1Clinical characteristics of patient groups A and B.

Group A Group B

Dates collected 6/04–6/13/2003 5/22–8/14/2007n 209 191Male 171 93Female 38 98Age 55, 57 (13–88) 49, 51 (14–90)Male 58, 59 (13–88) 55.6, 57 (14–90)Female 42, 39 (16–78) 42, 43 (15–75)TT (ng/dL) 322, 335 (11–944) 238.1, 65.5 (7–1350)Male 378, 377 (13–944) 459, 420 (7–1350)Female 41.7, 33 (11–97) 26.3, 20.5 (7–115)Dialysis fT (ng/dL) 8.8, 9.0 (0.21–23.9) 5.73, 1.51 (0.07–41.8)Male 10.1, 9.79 (0.21–23.9) 11.2, 10.0 (0.19–41.8)Female 0.82, 0.63 (0.21–2.84) 0.48, 0.33 (0.07–2.82)Albumin (g/L) Not performed 43.8, 44 (24–55)Male 43.8, 44 (24–55)Female 43.8, 44 (30–51)SHBG (nmol/L) 37.7, 35.5 (2.6–112) 46.3, 37.5 (7.7–200)Male 38.3, 34.0 (2.6–98) 35, 33 (7.7–87)

J.S. Hackbarth et al. /

etect fT have been proposed as an alternative. However, they haveeen widely criticized for their lack of accuracy and variability ofesults with fluctuating SHBG concentrations [18–20], suggestinghat they do not truly measure fT.

Another alternative is to calculate fT using equations based onhe law of mass action. These equations typically incorporate theesults of serum measurements of total testosterone, albumin, andHBG. The equation originally described by Sodergard et al. [21]nd derived by Vermeulen et al. [22] also includes the testosteronessociation constants for albumin and SHBG. However, calculatedesults for fT have often been found to vary significantly fromsotope dilution equilibrium dialysis. Potential sources for this vari-tion include biological factors such inter-individual variabilityn the concentrations of competing hormones and binding pro-eins and in the affinity of testosterone for SHBG or albumin,nd laboratory factors including different SHBG and testosteroneethodologies, equations, and association constants used [23–26].

everal different constants have been published and some studiesave used empirically derived constants and equations to providehe best fit for their individual combinations of patient population,nd total testosterone-, SHBG- and albumin assays [15,27–31].

Overall, there appears to be little consensus on the best methodor calculating fT, likely because of the wide variability of perfor-

ance of these equations between studies, patient groups, andaboratories and a lack of understanding of how these factorsmpact calculated fT measurements. The purpose of this study

as to improve our understanding of how these parameters affectalculated fT results, and to determine whether satisfactory agree-ent with isotope dilution equilibrium dialysis can be achieved.

o this end we assessed the performance of three established equa-ions and two new equations, generated using two different patientroups. These equations differed only in their testosterone asso-iation constants for SHBG and albumin. Results calculated withach of these five equations in these two patient groups were com-ared with those obtained by isotope dilution equilibrium dialysiserformed on the same specimens. Demographic characteristicsf the two patient populations and equation variables includinglbumin, SHBG, and choice of association constants were exam-ned to determine how they affected the correlation with isotopeilution equilibrium dialysis results. Samples with poor correlationetween calculated and measured fT results were examined furthero find common characteristics that could explain the deviations.

. Experimental

.1. Subjects

The Mayo Clinic Institutional Review Board approved this study.on-fasting serum samples were obtained from two groups ofatients that were seen for fT testing at Mayo Clinic Rochester.roup A consisted of 209 patients (171 males/38 females) seenetween June and July, 2003. Group B consisted of 191 patients (93ales/98 females) seen between March and August, 2007. Groupconsisted of all consecutive patients, while patients for Group Bere intentionally selected to yield an equal number of males and

emales. Characteristics of patients from each group are shown inable 1.

.2. Methods

There was no change in relevant laboratory methodologies dur-ng the study. Serum was isolated by centrifugation and assayedmmediately.

Total testosterone was measured by liquid chromato-raphy–tandem mass spectrometry (LC–MS/MS, API 5000, Applied

Female 56.3, 55.3 (11–112) 57.2, 45 (11–200)

Results are given as mean, median, and full range in parentheses. ng/ml testosteroneand free testosterone can be converted to nmol/L by multiplying by 0.0347.

Biosystems-MDS Sciex, Foster City, CA; inter-assay CV 2.2.–11.6%,reportable range 7–2000 ng/dL) as previously described [32]. Theresults were used for both the calculation of fT concentration fromthe isotope dilution equilibrium dialysis-determined fT percentageand for calculating fT with the various equations (see below).

SHBG was measured using a solid phase, two-site chemilumi-nometric assay on the Immulite 2000 automated immunoassayanalyzer (Siemens, Deerfield, IL). Inter-assay CV of daily controlsaveraged over a month was 6.5 and 5.5% for 5 and 75 nmol/LSHBG, respectively, and the reportable range of the assay was2–180 nmol/L. Lot-to-lot variability over the past three years hasaveraged 3% CV. Albumin was assumed to be 43 g/L for all patientsexcept for an initial experiment comparing measured and assumedalbumin concentrations and their effect on the fT calculations inpatient group B. The albumin measurements for this subgroupwere performed using a bromocresol green dye photometric assay(Roche Diagnostic Corp., Indianapolis, IN) on the Roche ChemistryModular System. Inter-assay CV was <3% for 2.5 and 5 g/dL albuminand the reportable range of the assay was 1–7 g/dL.

As gold standard reference for fT concentrations, the percentageof fT was measured by isotope dilution equilibrium dialysis as pre-viously described [14,33]. Briefly, undiluted serum samples wereprepared in a pH 7.4 phosphate buffer using HPLC-purified 30 ng/dL[3H]-testosterone per sample (Amersham, San Francisco, CA) as thetracer. Radioactivity was measured in tubing and dialysate follow-ing a 17 h dialysis at 37 ◦C on a Taurus liquid scintillation counter(Micro-Medic, Huntsville, AL). The resulting fT percentage was thenmultiplied by the total testosterone concentration measured byLC–MS/MS (see above) to obtain the fT concentration. Total errorfor the measurement of fT concentration is therefore the sum ofthe error in fT percentage and total testosterone concentrationmeasurements. Inter-assay CV for the measurement of percent fTwas determined in 100 additional patient samples (50 M/50 F) andranged from 1 to 5%. Combining this error with the inter-assay CVfor the measurement of total testosterone described above resultedin a total inter-assay error of 19 and 10% CV for concentrations of 1and 5 �g/dL, respectively.

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fT (mol/L) =

2a

For the calculated fT, total testosterone, SHBG and albumin(assumed or measured) values were entered into the mass actionequation originally described by Sodergard et al. [21] and into the

50 J.S. Hackbarth et al. / Steroi

Table 2Testosterone association constants.

ka (L/mol) ks (L/mol) Ref.

Vermeulen 3.6 × 104 1 × 109 [21]Sodergard 4.06 × 104 5.97 × 108 [22]Emadi-Konjin 1.3 × 104 1.4 × 109 [34]cA 2.4 × 104 1.2 × 109 *

cB 1.8 × 104 1 × 109 *

Where ka is the association constant of testosterone binding to albumin and ks ist

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he association constant of testosterone binding to SHBG.* Constants cA and cB were derived from patient groups A and B in this study,

espectively. These constants were the only variables used in the mass action equa-ion described in Section 2 to generate the similarly named five equations.

ariation of this equation derived by Vermeulen et al. [22] andmadi-Konjin et al. [34]:

= ka + ks + (ka × ks) ([SHBG] + [alb] − [TT])

= 1 + ks [SHBG] + ka [alb] − (ka + ks) [TT]

here ka is the association constant of testosterone binding to albu-in (L/mol), ks is the association constant of testosterone binding to

HBG (L/mol), [SHBG] is the concentration of SHBG (nmol/L), [alb]s the concentration of albumin (converted from g/L to mol/L usinghe molecular weight of 69,000 g/mol), and [TT] is the concentra-ion of total testosterone (mol/L). Different association constantsere entered into the above mass action equation to generate five

quations. The three sets of association constants of testosteroneith SHBG and albumin that have been previously published byermeulen et al. [22], Sodergard et al. [21], and Emadi-Konjin et al.

34] were used for the calculations. In addition, new constants (cAnd cB) were empirically derived for both patient groups to yieldhe best agreement with the isotope dilution equilibrium dialysisata, defined as a regression slope as close to 1 as possible. Theseonstants used in the study are the only variable in the above massction equation and are summarized in Table 2.

.3. Data analysis

Results in Table 1 are shown as mean, median, and full range.eming regression and Bland-Altman analysis was performedsing Analyse-It version 3.0 (Analyse-It Software Ltd., Unitedingdom) to compare fT results measured by isotope dilution equi-

ibrium dialysis to results calculated by the above equation, usinghe different constants. Agreement between equations and isotopeilution equilibrium dialysis fT results was also expressed as per-ent difference:

Difference = |fTcalc − fTIDED|(fTcalc + fTIDED)/2

Calculated fT concentrations that deviated by more than 20%rom their paired isotope dilution equilibrium dialysis result werelassified as analytically unacceptable. Males and females wereivided into four groups (Q1–Q4) based on percent difference andtatistical significance between groups was determined using theann–Whitney U-test and JMP version 6 (SAS Institute, Inc., Cary,C).

. Results

There was no significant impact of albumin concentration on

alculated fT, regardless of whether the measured albumin resultsr a constant value of 43 g/L were used (y = 0.9733x + 0.0459,2 = 0.99, data not shown), indicating that albumin concentrationseen in typical ambulatory patients have a negligible impact onhe calculated fT concentration [22]. All subsequent calculations

ds 76 (2011) 48–55

of fT were therefore made using the constant value of 43 g/L foralbumin.

The agreement between calculated and isotope dilution equi-librium dialysis measured fT concentrations varied depending onpatient groups and association constants used in various equa-tions (Fig. 1). As expected, the derived constants yielded thebest fit with isotope dilution equilibrium dialysis results for therespective groups they had been derived from, surpassing thepublished constants (cA, group A: y = 1.05x − 0.41, cB, group B:y = 1.06x − 0.53). However, the derived constants yielded a worse fitwhen used on the other group (cA, group B: 0.83x − 0.25, cB, groupA: y = 1.35x − 0.69), indicating that custom-derived constants areless effective outside of their designated patient set. Bland-Altmananalysis yielded similar results (Supplementary data Fig. 1).

Since the major difference between the two groups was gen-der composition, differences between the sexes appeared to beresponsible for this variation. To examine this further, males andfemales from both groups A and B were examined separately.Agreement between calculated and isotope dilution equilibriumdialysis measured fT results was expressed as percent difference.Percent differences above 20% were deemed unacceptable. His-togram analysis was performed to determine the distribution ofpatients with acceptable and unacceptable agreement (Fig. 2). Thisdistribution varied both between genders and between equations.A significant percentage of patients displayed unacceptable agree-ment of calculated fT with isotope dilution equilibrium dialysis fTfor at least one of the equations used; depending on the equation,this percentage of patients ranged from 32–72% in males to 29–57%in females. Some patients showed unacceptable agreement of cal-culated fT with isotope dilution equilibrium dialysis fT for multiplecalculation equations, with 14.9% of males and 11.1% of femalesshowing poor fit by all five calculations (data not shown). A further13.1% of males and 28.5% of females showed poor agreement byfour equations, 28.9% of males and 6.4% of females by three equa-tions, 22.4% of males and 15.8% of females by two equations, and20.5% of males and 38% of females by a single equation. This highpercentage cannot be explained solely by variability of the isotopedilution equilibrium dialysis assay. Repeating 100 patient samples(50 M/50 F) by isotope dilution equilibrium dialysis yielded a lin-ear regression slope of y = 0.92 + 0.10, r2 = 0.95 (Supplementary dataFig. 2). Only 4% of these repeats had percent differences greater than20% (data not shown).

In order to determine other sources of the variation betweencalculated and measured fT and between the different calcula-tions, each of the components of the equations was examined. Ageand concentration of albumin, total testosterone, and fT did notsignificantly correlate with percent difference (data not shown),indicating that those factors do not contribute to the observedvariation. However, the SHBG concentration was related to thegoodness of fit between calculated and isotope dilution equilibriumdialysis fT. Linear regression of a plot of SHBG concentration ver-sus percent difference yielded a positive slope for most equations,indicating that increasing SHBG correlated with increasing percentdifferences and poorer fit (Fig. 3). The exception was the Sodergardequation, which had a neutral slope indicating a minimal impactof SHBG on the fit. Certain equations, such as the Emadi-Konjinand cA equations, were more affected by SHBG than other equa-tions, such as the cB equation, as indicated by a larger slope. Fits formales and females were similarly impacted by SHBG concentra-tions when the Sodergard, Emadi-Konjin, and cB equations wereused as indicated by their similar slopes. By contrast, the fit for

males was affected more by SHBG compared to the fit for femaleswhen the Vermeulen and cA equations were used. These resultsindicate that both SHBG and gender can significantly affect thegoodness of fit between calculated and isotope dilution equilibriumdialysis fT results.

J.S. Hackbarth et al. / Stero

Fig. 1. Deming regression of calculated fT results compared to isotope dilutionequilibrium dialysis. Regression analysis was performed on group A and B patientscomparing free testosterone results measured by isotope dilution equilibrium dial-ysis with results calculated using Vermeulen (A), Sodergard (B), Emadi-Konjin (C),cA (D), and cB (E) equations. Slope, intercept, and standard error of estimate (Syx)are shown in insets. Dashed lines represent 95% confidence intervals.

ids 76 (2011) 48–55 51

The relationship between SHBG concentration, gender, and fitwas further examined by dividing males and females into quartiles(Q1–Q4) based on percent difference (Fig. 4). Group Q1 consisting ofpatients with the best agreement between isotope dilution equilib-rium dialysis and calculated fT, with percent differences in groupQ1 ranging from 0 to 18% in males and from 0 to 11% in femalesdepending on the equation used. Group Q4 consisted of patientswith the worst agreement, with percent differences increasing to23–103% for males and 22–105% for females. Similar to the regres-sion analysis of percent difference and SHBG described above,patients in group Q4 had significantly higher concentrations ofSHBG, with average concentrations in group Q1 of 26.4–41.8 nmol/Lin males and 30.6–58.9 nmol/L in females (data not shown), whilethe corresponding values in group Q4 were 33.4–47.4 nmol/L and60.5–97.7 nmol/L, respectively (p < 0.05 or <0.001, depending onequation). The percentage of male and female patient samplestested at our institution over the past year with SHBG concentra-tions greater than 47.4 nmol/L in males and 97.7 nmol/L in femalesis 13% (n = 586) and 11% (n = 881), respectively (data not shown).This relationship between SHBG and fit was again observed for allequations except for the Sodergard equation.

4. Discussion

During the past decade, many laboratories have shifted awayfrom isotope dilution equilibrium dialysis because of the cost andlabor required and the amount of variability inherent in the assay.Measuring fT by ultrafiltration, while showing promising results inseveral studies [35–37], was found to have an unacceptable rate ofdevice failure at our institution. The problems with these methodsmake calculated fT an attractive alternative. However, several pub-lications have pointed out the variability of calculated fT resultsbetween studies, patient groups, and laboratories [23–26]. Thereis currently no consensus on which equation and constants areconsidered ideal. Instead the recommendation has been to tai-lor equations to individual laboratories and patient populationsto obtain the best results with the gold standard. This approachwould make it difficult to compare results between laboratoriesand potentially complicate any future attempts to standardize cal-culated fT assays.

In this study, we compared calculated fT results, derived byusing several variation of the mass action equation first pub-lished by Sodergard et al., in two patient groups with matchedresults obtained by the gold standard methodology of isotope dilu-tion equilibrium dialysis. Sodergard-derived equations incorporateserum concentrations of albumin, SHBG, and total testosteroneand association constants for testosterone binding to albumin andSHBG. As previously reported, albumin concentration had littleeffect on the calculated result [22]. Total and fT concentrationswere also found to minimally impact equation performance. How-ever, regardless of the equation used, there were a significantproportion of samples that had highly discrepant results betweenisotope dilution equilibrium dialysis and calculated testosterone.The high number of discrepant samples cannot be explained solelyby inherent variabilities in the isotope dilution equilibrium dialysisassay.

This study shows a significant number of patients with dis-crepant calculated and isotope dilution equilibrium dialysis fTresults. Even though the Sodergard equation was minimallyaffected by SHBG, it still displayed poor performance overall, with

29% of females and 34% of males in this study showing unacceptableagreement between that equation and isotope dilution equilib-rium dialysis. When examining all male and female patient samplestested at our institution over the past year, 11% of male and 13% offemale samples had SHBG concentrations above the average con-

52 J.S. Hackbarth et al. / Steroids 76 (2011) 48–55

Fig. 2. Histogram distribution of percent difference between calculated and isotope dilution equilibrium dialysis measured fT. Histogram plots were created for femalesand males from both groups A and B (F = 136, M = 264) based on percent difference between free testosterone results measured by isotope dilution equilibrium dialysis andcalculated using Vermeulen (A), Sodergard (B), Emadi-Konjin (C), cA (D), and cB (E) equations. Percentages of total males or females with a percent difference greater thanthe acceptability limit of 20% are indicated in insets for each equation.

J.S. Hackbarth et al. / Steroids 76 (2011) 48–55 53

Fig. 3. Linear regression of fit between calculated and isotope dilution equilibrium dialysis fT results and SHBG concentration. Female (�) and male (©) patients from bothg rcentc cA (D( cient

cl

ytcmss1a

roups A and B (F = 136, M = 264) were plotted for SHBG concentration versus peompared with calculated using Vermeulen (A), Sodergard (B), Emadi-Konjin (C),dashed line) and male (dotted line) samples. Slope, intercept, and correlation coeffi

entration in the Q4 group. These patients would therefore be moreikely to receive an inaccurate calculated fT result.

Consistent methodologies for isotope dilution equilibrium dial-sis, SHBG, and total testosterone analysis were used throughouthis study. The number of discrepant samples would undoubtedlyhange with the introduction of other methods and platforms to

easure SHBG and total testosterone. For example, recent CAP PT

urvey results for SHBG indicate that the Immulite 2000 used in thistudy had 5.8–6.8% CV between laboratories, while the Immulite000 had up to 13.4% CV (Y Ligand Special, 2009). This higher vari-bility will result in higher variability in the fT calculation and larger

difference of free testosterone measured by isotope dilution equilibrium dialysis), and cB (E) equations. Linear regression lines were determined for both femaleare indicated in insets.

numbers of samples with discrepant calculated and isotope dilutionequilibrium dialysis fT results. The use of different testosterone andSHBG assays over serial fT calculations of a patient would introduceadditional variability and potentially complicate interpretation ofthe patient’s status. Several studies have demonstrated that the useof different assays to measure SHBG yield different calculated fT

results and different correlations between measured and calculatedfT [17,38]. The wide range of SHBG values in this study, attributableto inter-individual factors including gender, age, alterations in hor-monal and metabolic factors, and polymorphisms in the SHBG gene,may also contribute to the variation between equations [39].

54 J.S. Hackbarth et al. / Steroi

Fig. 4. Effect of SHBG and gender on fit between calculated and isotope dilutionequilibrium dialysis fT results. Female and male patients from groups A and Bwere divided into four groups (Q1–Q4) based on percent difference between iso-tope dilution equilibrium dialysis results and results calculated using Vermeulen(A), Sodergard (B), Emadi-Konjin (C), cA (D), and cB (E) equations. Group Q1 sampleshad the best agreement between the two methods, while group Q4 had the worst.Female n = 33 per quartile, male n = 66 per quartile. Top, middle, and bottom of boxesrepresent 75th percentile, median, and 25th percentile, respectively. Error bars rep-resent 1.5 times the interquartile range. Outliers are indicated by circles. Significantdifferences between groups were determined using the Mann–Whitney two-tailedtest. *p < 0.05, **p < 0.001.

ds 76 (2011) 48–55

Testosterone association constants and SHBG, the remainingcomponents of the fT equation, were both found to impact equa-tion performance. Systematic and random errors varied widelydepending on the association constants used. Choice of associa-tion constants significantly affected calculated results, as constantsderived specifically for this study were found to correlate betterwith isotope dilution equilibrium dialysis results than previ-ously published constants. However, these derived constants onlyyielded a superior fit with isotope dilution equilibrium dialysisresults when used on the patient groups from which they had beenderived. These findings indicate that there is significant variabilityin the performance of the constants between groups of as smallas 200 patients. It is not fully understood why certain sets of con-stants correlated better with isotope dilution equilibrium dialysisthan others, though the performance of certain constants may beaffected by other circulating hormones including estradiol and DHT.

Males and females with the poorest fit between calculated andmeasured fT results had significantly higher serum concentrationsof SHBG. This relationship between fit and SHBG was dependent onwhich equation was used. Results calculated using the Sodergardequation were not affected by SHBG, while results calculated usingthe other equations were affected to various degrees. This char-acteristic of the Sodergard equation may be because the assumedaffinity of testosterone for SHBG used in the equation was the low-est of the five equations examined, therefore samples with highSHBG would display less discrepancy between calculated and mea-sured fT results. In addition, the large range of SHBG concentrationsin this study, a consequence of examining both males and femalesin this study as well as other inter-individual factors, may havecontributed to the variation between measured and calculated fTresults.

Gender was also a factor in variability between calculated andassayed results. Deming regression demonstrated that the equa-tions performed differently in patient groups A and B, which haddifferent compositions of males and females. Males and femalesalso had a different distribution of percent differences betweencalculated and assayed fT results. In addition, a higher SHBG con-centration was found to affect fit in males more than in femaleswhen certain equations were used. While the exact cause of thisgender variability is not known, it is possible that differencesbetween genders including the distribution of sex steroids play arole. These and similar equations may depend too much on SHBGconcentration and neglect the contribution of other binding pro-teins and steroids, such as estradiol and DHT, which vary betweenthe genders and may affect testosterone association constants.More detailed equations may show better agreement with isotopedilution equilibrium dialysis.

In conclusion, variability in performance of the family of testos-terone mass action equations examined in this study is affected byseveral factors, chiefly gender, SHBG concentration and choice ofassociation constants. Because of this variability, a large percent-age of patients show a substantial and unacceptable deviation ofcalculated fT results from those obtained by the reference method-ology, isotope dilution equilibrium dialysis. Designing differentequations specifically for patient subgroups, e.g. male or femalepatients or patients who have elevated SHBG concentrations, mayimprove performance. However, these equations that use onlytotal testosterone and SHBG measurements may be too simplis-tic to encompass the entire range of patients referred for fT testing,resulting in a percentage of patients that will be discrepant fromisotope dilution equilibrium dialysis regardless of alterations to

the equation. While additional analysis of other hormones mayyield more accurate results, this will increase overall cost, labor,and variability, reducing or eliminating the advantages of usingthe equations in the first place. Currently, isotope dilution equilib-rium dialysis appears the only valid approach for fT measurements,

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therwise accuracy of individual measurements can be severelyompromised in many patients.

ppendix A. Supplementary data

Supplementary data associated with this article can be found, inhe online version, at doi:10.1016/j.steroids.2010.08.008.

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