Data came from the Dietary Intervention Study in Children (DISC). DISC was a multicenter randomized controlled clinical trial sponsored by the National Heart, Lung, and Blood Institute (NHLBI) to test safety and efficacy of a dietary intervention to reduce serum low-density lipoprotein cholesterol (LDL-C) in children with elevated LDL-C. Design and results of DISC have been described.^{7}^{, }^{8}^{, }^{9} Briefly, between 1988 and 1990, 663 eight to ten year olds with elevated LDL-C were randomly assigned to a dietary intervention to reduce fat intake or to usual care at one of six DISC clinical centers. The initial DISC protocol was designed for 3 years and was subsequently extended with planned intervention and follow-up of all participants until 18 years of age. The timing of the last blood draw relative to study initiation was variable due to early termination of the study in 1997 for lack of a treatment effect.

DISC recruited 362 boys and 301 girls through schools, health maintenance organizations, and pediatric practices. Boys were eligible if they were 8.6–10.8 years old and girls were eligible if they were 7.8–10.1 years old. Eligibility requirements stipulated that children have serum LDL-C level in the 80th to 98th percentiles, had no major illness, were not taking medications that affect lipid levels or growth, were at least in the 5th percentile for height and in the 5th–90th percentiles for weight for height, were Tanner stage 1 for genital and pubic hair development, and had normal psychosocial and cognitive development.

Assent was obtained from DISC participants and written informed consent was obtained from their parents or guardians prior to randomization and again when the study was extended. The DISC protocol and Hormone Ancillary Study were approved by Institutional Review Boards at all participating centers, and a National Heart, Lung, and Blood Institute-appointed independent data and safety monitoring committee provided oversight.

Hormone Assays

Blood was collected at a visit through a single blood sample by venipuncture in the morning after an overnight fast. Serum was separated by centrifugation after the blood sample was kept at room temperature for at least 45 minutes to allow complete clotting. Serum was then aliquoted and stored in glass vials at −80° C.

Dorgan and colleagues^{10}^{,}^{11} provide extensive details of the assays used for this study. We summarize some of their characteristics here. Hormone assays were performed by Esoterix Endocrinology, Inc. (Calabasas Hills, CA) using standard procedures. Estradiol (E_{2}) was measured using a modification of the procedure developed by Wu and Lundy.^{12} Serum samples were extracted with hexane: ethyl acetate, 80:20 (vol/vol). The extract was then washed with dilute base, concentrated and chromatographed on Sephadex LH20 micro columns (Sigma, St. Louis, MO). E_{2} was specifically eluted using benzene: methanol, 85:15 (vol/vol). E_{2} was quantified by RIA in duplicate using antiserum raised to an Estradiol-6-oxime-BSA conjugate.

Testosterone (T) was measured using a modification of the procedure developed by Furuyama et al.^{13} Samples were extracted with hexane: ethyl acetate, 90:10 (vol/vol), and the extracts were applied to aluminum oxide micro columns. The columns were washed with hexane containing 0.55% ethanol, and T was specifically eluted using hexane containing 1.4% ethanol. T in eluates was quantified in duplicate by RIA using antiserum raised to a testosterone-3-oxime-BSA conjugate.

To measure DHT, serum samples were first extracted with seven volumes of hexane: ethyl acetate. Extracts were then evaporated to dryness and redissolved in potassium permanganate to oxidize steroids containing conjugated ketones. DHT was then selectively re-extracted. Duplicate aliquots of each purified sample were measured by RIA using antiserum raised to a DHT-3-oxime-BSA conjugate.

SHBG was measured by a radioimmunometric assay. The serum sample and an SHBG monoclonal antibody labeled with ^{125}I were incubated with plastic beads coated with a different SHBG monoclonal antibody. The beads were washed to remove unbound label and the bound radioactivity was measured.

The percent non-SHBG bound estradiol and the percent non-SHBG bound testosterone were determined by ammonium sulfate precipitation as described by Mayes and Nugent.^{14} The concentration of non-SHBG bound steroid was then calculated as the product of its total concentration and the percent that was non-SHBG bound. In the paper, we refer to these as assay measured values. Assay measured non-SHBG bound T was collected for boys only, while assay measured non-SHBG bound E_{2} was collected for girls only.

Serum albumin was not measured in all subjects at all visits; however the subjects were healthy, allowing for its approximation when missing using the average measured albumin level.

For external quality assurance, three sex-specific external quality controls indistinguishable from participant samples were included in each hormone batch. Lab personnel were blinded to which samples were participant samples and which were quality control samples. As reported by Dorgan,^{10}^{,}^{11} coefficients of variation (CV) of these assays, as estimated from the external quality control samples, were 6%–30% for E_{2} for girls, 6%–26% for T for both sexes, 13%–24% for DHT for boys, and 15% for SHBG for girls. Higher CVs were generally related to lower mean hormone levels. The limits of detection for T, E_{2}, and DHT, were 3.0 ng/dL, 0.5 ng/dL, and 2.0 ng/dL, respectively.

RIA and mass spectometry estimates of E_{2}, DHT, and T at levels commonly seen in children showed good agreement as described by Dorgan and colleagues.^{11} This was similar to unpublished adult data from Esoterix Endocrinology that found a regression slope of MS on RIA of 1.14 for E_{2} (coefficient of determination, R^{2}=0.98) and a slope of RIA on MS of 1.09 for T (R^{2}= 0.99), indicating some bias.

Calculating non-SHBG bound E_{2} and T

Assay measures of total estradiol (E_{2}), testosterone (T), sex hormone-binding globulin concentration (C_{SHBG}), and albumin concentration (C_{a}) used to calculate the bioavailable fractions of estradiol including free and non-SHBG bound levels of estradiol in girls were collected at years 1, 3, 5, 7 and the last follow-up visit of the study. Assay measures of total E_{2}, T, C_{SHBG}, C_{a} and dihydrotestosterone (DHT) used to calculate free and non-SHBG bound levels of testosterone in boys were collected at years 3, 5, 7 and the last follow-up visit of the study. Because few children completed both a 7 year follow-up and a last visit due to early study termination, we do not present the 7-year follow-up data from children with both visits in tables. However, these values were used in plots described below.

We used the methods detailed in Rinaldi et al.^{3} to first estimate the amount of free testosterone (fT) and free estradiol (fE_{2}) for boys and girls using this data. We then used these results to estimate the amount of non-SHBG bound T and non-SHBG bound E_{2} for comparison with assay measured values. As cited in Rinaldi et al.^{3}, we used the single equation models^{4}, and the multi-equation models (3 equations for boys, 2 equations for girls)^{5} to estimate fT and fE_{2}. We could not use the three-equation model in girls since DHT data were not collected for them. However, girls’ DHT concentrations remain low throughout puberty.

The equations are based on the mass action law. T, DHT and E_{2} circulate in serum free or are bound to albumin or SHBG. The equations use the following affinity constants in liters/mol for albumin as cited in Rinaldi and colleagues^{3}: K_{a}T=4.06×10^{4} (testosterone), K_{a}E_{2} =4.21×10^{4} (estradiol), K_{a}DHT=3.5×10^{4} (DHT), and the following respective constants in liters/mol for C_{SHBG}: K_{s}T=1×10^{9}, K_{s}E_{2}=3.14×10^{8}, K_{s}DHT=3×10^{9}. Specifically, we calculated fT and fE_{2} in girls by solving for fT and fE_{2} using the following set of equations adapted from Rinaldi.^{3} In the equations, fT and fE_{2} are the only two unknowns.

We compared this to results from the single equation method reproduced from Rinaldi

^{3} that does not use testosterone data:

Similarly, we calculated fT, fE_{2}, and fDHT in boys using the following set of equations also reproduced from Rinaldi.^{3} In the equations, fT, fE_{2}, and fDHT are the only unknown quantities.

We compared this to results from the single equation method reproduced from Rinaldi

^{3} that does not use estradiol or DHT data:

The single equation methods can be calculated analytically using the quadratic formula. We solved for unknown values in the two and three equation methods using the optimization package “optim” macro in R (The R Foundation for Statistical Computing, Vienna, Austria).

To validate our findings, we compared calculated serum non-SHBG bound E_{2} and T with assay measured results. We used calculated fT, calculated fE_{2}, and assay measured C_{a} to estimate the amount of serum non-SHBG bound E_{2} and the amount of non-SHBG bound T with the following set of equations: non-SHBG bound E_{2} in moles/liter is K_{a}E_{2} × C_{a} × fE_{2} + fE_{2}, and non-SHBG bound T in moles/liter is K_{a}T × C_{a} × fT + fT. For ease of interpretation, we report these as ng/dL. We provide S.I. conversion factors in the tables.

We substituted the observed mean value of C_{a}, 4.5 g/dL, for individuals with missing assay measured albumin levels. The observed mean was the same for boys and girls.

We examined Bland-Altman

^{15} plots to investigate agreement between calculated and observed values. For the y-axis of the Bland-Altman plots, we plotted the proportion of the difference with respect to the average of the two values. Negative proportions indicate that calculated values were larger than assay measured values. For example, for the Bland-Altman plots of non-SHBG bound hormones, the y-axis consists of the points created by the following formula:

. We report the quartiles of these proportional differences in the tables.

We used simple linear regressions fit on the data used to generate the Bland-Altman plots to estimate the relationship of the calculated with assay measured values. To more evenly spread the data, we depict the x-axis on the log scale in the Bland-Altman plots. However, we did not use log transformations for the regression analyses. We examined multiple linear regressions in which we included the average of calculated and assay measured hormone values, age, and the interaction between age and average values to investigate if the relationship between assay measured and calculated values differed by age. We also examined regressions in which we included average and average squared to test for nonlinear trends. We estimated all regressions using generalized estimating equations (GEE) assuming unstructured correlation matrices and robust standard errors to account for the correlation of multiple measurements within the same child.^{16}

As a sensitivity analysis to the robustness of our results, we compared the GEE estimated simple linear regressions with Deming^{17} regressions of the observed regressed on the calculated values. The Deming regressions consider both model response and covariate to be measured with error, but do not account for the correlation of measurements over time. We assumed equal measurement error variances for the Deming regressions since we did not have duplicate measurements to estimate the variances. We estimated all regressions using the “xtgee” and “deming” commands in STATA version 10 (StataCorp, College Station, Texas).

To convert E_{2} from ng/dL to pmol/L, multiply by 36.76. To convert T in ng/dL to pmol/L, multiply by 34.72.