Adrenal and Gonadal Hormone Replacement in Anorexia Nervosa: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Adrenal and Gonadal Hormone Replacement in Anorexia Nervosa (NCT00310791), a randomized phase 2, phase 3 study. The primary outcome is Areal Bone Density by DXA.

2. Clinical Question

The registry record describes a trial designed to examine whether combined adrenal and gonadal hormone replacement was associated with differences in bone-related measures compared with placebo. The reported primary result concerns areal bone density; it does not directly report every biological measure or structural analysis described in the study summary. The central statistical question is therefore narrower than the broader study rationale: what difference in mean areal bone density was observed between the randomized groups at the stated follow-up, and how precisely was that difference estimated?

3. Trial Design

The registry record describes a randomized, parallel-group trial with triple masking. It lists phase 2 and phase 3 and an enrollment of 80. The study status is completed. The study start is listed as 2004-04, and primary completion as 2009-10. The sponsor is Boston Children's Hospital. The condition listed is anorexia nervosa.

The two groups were placebo and active treatment. The active arm is described as combined DHEA and hormone replacement therapy with estrogen/progestin; the comparator was a sugar pill described as identical to the treatment medication capsule. The study summary describes an 18-month treatment course. The primary endpoint is reported at 18 months. The registry's arm description gives some treatment information, but the complete protocol and full treatment details are not reported in the registry record.

The planned enrollment and the sample sizes attached to the primary endpoint should not be treated as interchangeable. The registry lists enrollment of 80, while the endpoint summary reports 30 participants in the placebo arm and 31 in the active arm. The reasons for the difference between the enrollment figure and the endpoint sample sizes are not reported in the registry record. The adverse-event display separately reports 40 participants at risk in each group; the relationship between those safety denominators and the endpoint denominators is not explained.

The design labels identify random assignment, masking, and parallel groups, but do not describe how allocation was generated or concealed, how masking was implemented, or whether masking was assessed. The original statistical analysis plan, the trial's own sample-size justification, and any interim analyses are not reported in the registry record. These omissions limit what can be inferred about the planned analysis and its conduct beyond the design features explicitly recorded.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Areal Bone Density by DXA, measured over 18-Months.

The primary endpoint is areal bone density measured by dual-energy X-ray absorptiometry (DXA), with the result reported in g/cm2 as a mean and standard deviation for each arm. Areal bone density is an estimate of bone mineral content relative to projected bone area. DXA provides a quantitative measure that can be summarized across participants and compared between randomized groups.

Bone density was relevant to the study's stated rationale: the registry summary describes concern about early bone loss and osteoporosis among young women with anorexia nervosa. The study also describes interest in bone turnover markers, serum IGF-I, and bone structure, but the only posted outcome result is areal bone density. The endpoint therefore addresses one part of the broader biological question and should not be treated as a direct report of every bone-related process mentioned in the study summary.

The posted endpoint is a group mean at 18 months. The registry record does not report baseline bone density or a change-from-baseline estimate, so the reported comparison should be read as the endpoint means and their difference, not as a reported within-person change. Nor does the endpoint summary identify the anatomical measurement site or provide additional detail on DXA procedures. These details are not reported in the registry record.

7. Results Posted in the Registry

• Active: mean 0.89 versus 0.88 on control; difference 0.01 (95% CI -0.04 to 0.06), standardized effect d = 0.10; z-test p = 0.696.

8. Statistical Interpretation

9. Statistical Methods Explained

What does a mean difference express?

A mean difference is the average outcome in one group minus the average outcome in the comparison group. Here, the contrast is active treatment minus placebo for areal bone density. A positive value means the reported active-group mean is higher; a negative value means it is lower. The estimated mean difference is 0.01 g/cm2. This is a difference between group averages, not a statement about how every participant's measurement changed or about the experience of an individual participant.

The mean is a useful summary for a continuous measure because it expresses the central level of the outcome in the group using the outcome's original units. It can be informative when the mean is an appropriate summary of the distribution. The registry reports standard deviations but does not provide distributions, individual observations, or diagnostic checks, so the shape of the outcome data cannot be assessed from the posted summaries.

What does the standard deviation describe?

The standard deviation describes how spread out individual measurements are around a group mean. It is not the uncertainty in the mean itself, and it is not the same as a confidence interval for a treatment contrast. The registry reports a standard deviation of 0.1 g/cm2 in each arm. A standard deviation helps characterize variation among participants, while the confidence interval for the mean difference describes uncertainty in the estimated contrast between groups.

In general, the standard error of an estimate reflects how much an estimate would vary across repeated samples under the statistical model. Larger participant samples tend to reduce standard errors when other features are similar, but the precise uncertainty also depends on variability and the analysis. The endpoint record reports arm sample sizes and standard deviations alongside the confidence interval; it does not report a full analysis description explaining exactly how that interval and test were calculated.

How should the confidence interval be read?

A confidence interval is a range produced by a statistical procedure intended to have a stated coverage rate over repeated applications under its assumptions. It represents uncertainty around an estimate, rather than a range containing a specified proportion of individual participants. The interval for the mean difference runs from -0.040 to 0.060 g/cm2. Its inclusion of zero means the reported interval does not rule out a zero group difference at the corresponding confidence level. Its inclusion of values on both sides of zero also leaves the direction uncertain.

The interval does not establish that all values in its range are equally plausible, and it does not measure the probability that the true difference lies within this particular realized interval. Interpretation also depends on design and analysis assumptions. The registry record does not give enough detail to assess all such assumptions or the handling of missing endpoint observations.

What does the p-value add?

The unadjusted p-value is 0.696. In general, a p-value measures how unusual data at least as inconsistent with a specified null model would be if that model and the test assumptions held. It does not quantify the size of the effect, and it is not a measure of clinical importance. It should be interpreted alongside the estimated mean difference and its confidence interval, which communicate direction, scale, and precision more directly.

The label unadjusted indicates that this p-value is not presented as adjusted for multiple comparisons. The registry record does not describe a multiplicity plan, the full set of planned tests, or a detailed analysis plan. Consequently, the posted p-value should not be assumed to account for any other outcomes or analyses that may have been considered.

Why does variation matter?

Participant measurements vary even when all participants are assigned to the same group. Statistical methods use the observed variability and sample sizes to quantify uncertainty in group summaries and contrasts. If variability is large relative to the difference being estimated, a study may produce an imprecise estimate. The posted standard deviations and confidence interval show that the estimated difference should be read with its uncertainty rather than as an exact separation between groups.

General statistical methods may need to account for features such as skewed distributions, repeated measurements, clustering, or over-dispersion when those features apply. Over-dispersion means that observed variability is greater than a model's assumed variability, which can make ordinary uncertainty estimates too small if not handled appropriately. The registry record does not report whether these features were assessed or what modeling methods were used. They should not be presumed to have been present or absent.

For a continuous outcome, the reported mean-based comparison is one way to summarize a randomized-group contrast. Other estimands, such as adjusted endpoint values or change from baseline, could answer related but distinct questions. The registry record does not report those estimates. Without the protocol and analysis plan, it is not possible to establish whether the posted comparison was the prespecified analysis or how it relates to any analyses not shown in the registry.

10. Confidence Intervals and Precision

The estimated active-minus-placebo mean difference in areal bone density was 0.01 g/cm2, with a 95% confidence interval from -0.040 to 0.060 g/cm2. This interval is wide enough to include a negative difference, zero, and a positive difference. It therefore does not pin down the direction of the contrast or support a highly precise estimate of its magnitude.

The interval should be read in the original outcome units. It describes uncertainty about the difference in group means, not the spread of individual participants' bone-density values. The group standard deviations were 0.1 g/cm2 in both arms. The standard deviation and the confidence interval answer different questions: one describes participant-to-participant variation, while the other expresses uncertainty in the estimated group contrast.

Precision is distinct from whether a result crosses a conventional statistical threshold. The unadjusted p-value was 0.696, but the confidence interval gives more information about the range of effect estimates compatible with the data. Because the registry record does not report a clinically important difference threshold, it is not possible to classify the range in the interval as clinically negligible or important based only on these results.

The confidence interval's interpretation relies on the analysis and sampling assumptions used to construct it. Full details of the interval method, missing-data handling, and analysis population are not reported in the registry record. Those omissions limit independent assessment of the precision calculation and of how representative the endpoint sample is of all enrolled participants.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The sample-size figures are planning illustrations based on the observed effect, not the trial's original design justification. They assume a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each scenario considers detecting a stated fraction of the observed effect. The figures are participants per arm, not total participants or total events; the total-events convention applies to time-to-event planning displays, not to this continuous endpoint.

For 100% of the observed effect, the illustration gives 1,570 participants per arm for 80% power and 2,102 participants per arm for 90% power. For 75% of the observed effect, it gives 2,791 participants per arm for 80% power and 3,736 participants per arm for 90% power. For 50% of the observed effect, it gives 6,280 participants per arm for 80% power and 8,406 participants per arm for 90% power.

In plain terms, the 80% power column is the planned number per arm under the stated assumptions for a design with an 80% chance of detecting the specified effect if that effect were the true effect and the model assumptions held. The 90% column uses a higher target chance of detection and therefore gives larger planning figures. Smaller effects require more participants to distinguish them from random variation with the same planned power.

These figures are not observed power. The trial's own original sample-size assumptions and justification are not reported in the registry record, and these illustrations should not be read as evidence that the completed trial was designed around these numbers.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 0.010; pooled standard deviation σ = 0.100.
2. n = 2 × (1.96 + 0.842)² × 0.100² / 0.010² = 1,569.8, rounded up to 1,570 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- 0.01                      # observed difference in means
sigma <- 0.1                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(310791)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 1,570 (80% power), 2,102 (90% power)
 75% of observed effect: n per arm = 2,791 (80% power), 3,736 (90% power)
 50% of observed effect: n per arm = 6,280 (80% power), 8,406 (90% power)
power.t.test: 1570.7 
Simulated power at n = 1,570 per arm: 0.802 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Multiplicity, Missing Data and Analysis Populations

The registry record posts one primary outcome measure, areal bone density by DXA, and no secondary outcome results. The study summary describes additional interests, including bone turnover markers, serum IGF-I, and bone structure, but results for those measures are not reported in the registry record. The number and order of all outcomes planned in the protocol are also not reported.

The posted p-value is unadjusted. In general, testing multiple outcomes, time points, or analysis variants can increase the chance of at least one nominally unusual result if no multiplicity strategy is used. Whether that issue applies, and how it was addressed in the trial's planned analysis, cannot be determined because the multiplicity plan and full statistical analysis plan are not reported in the registry record. The single posted primary result should therefore be interpreted as that result, not as a complete account of every test that may have been planned or conducted.

The registry record reports endpoint sample sizes of 30 in the placebo arm and 31 in the active arm, while planned enrollment is 80. It does not explain the difference. Missing outcome data, withdrawals, exclusions, and the reasons participants may not appear in the endpoint summary are not reported. The record also does not describe imputation or other missing-data methods.

The analysis population is not reported in the registry record. It is not specified whether the endpoint comparison followed an intention-to-treat principle, included only participants with observed measurements, or used another definition. The methods of randomization, allocation concealment, model adjustment, and handling of protocol deviations are also not reported. These details matter for judging how closely the posted estimate reflects the randomized comparison and how robust it is to missing data or departures from the intended analysis.

14. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

The adverse-event figures report zero serious adverse events among 40 participants at risk in the placebo group and zero among 40 participants at risk in the active group. The registry also reports zero other adverse events among 40 participants at risk in each group. No serious-event terms are listed.

These are counts from the registry's adverse-event display. A zero count means that no event in that category was recorded for the stated group and denominator in the posted figures; it does not establish that no such event could occur or that the groups have identical safety profiles. The display does not provide event descriptions, timing, severity beyond the serious/other categories, or participant-level follow-up details.

Deaths are listed as null for both groups. Death counts are therefore not reported in the registry record; null should not be interpreted as a confirmed count of zero. The safety denominators are 40 per group, whereas the primary endpoint summaries report 30 participants in placebo and 31 in active treatment. The registry does not explain the difference between these denominators. The adverse-event figures should be read independently from the endpoint analysis counts.

15. What the Result Does, and Does Not, Mean

The posted result describes a randomized comparison of mean areal bone density at 18 months. The placebo mean was 0.88 g/cm2 among 30 participants, and the active-treatment mean was 0.89 g/cm2 among 31 participants. The estimated mean difference was 0.01 g/cm2, with a 95% confidence interval from -0.040 to 0.060 g/cm2. The estimate is uncertain in both direction and magnitude.

This result does not by itself establish equivalence between the groups. A confidence interval that includes zero does not prove that the true difference is zero; it indicates that the posted data and interval procedure do not exclude zero. Nor does the result establish that one treatment is better or worse. It reports an estimated group contrast and its uncertainty, not a clinical recommendation or a conclusion about an individual's outcome.

The endpoint is one measure of bone status. The study summary also describes questions about bone turnover, IGF-I, and bone structure, but results for those outcomes are not reported in the registry record. Accordingly, this primary result cannot answer those separate questions. It is also not reported as a baseline-adjusted or change-from-baseline comparison, and the registry record does not provide the details needed to infer changes over time from the endpoint means alone.

The safety display reports no serious or other adverse events in either group's posted counts, with 40 participants at risk per group. Death counts are not reported in the registry record. Those figures do not resolve all questions about safety, because the registry does not provide event-level information or explain the denominators' relationship to the endpoint samples.

Interpretation is further bounded by unreported analysis details, including missing-data handling, the analysis population, and the original statistical plan. The posted data are informative about the registered primary endpoint but should not be extended to unreported outcomes, unreported analyses, or conclusions beyond the measured comparison.

16. Why This Trial Matters Statistically

This trial is statistically informative because it illustrates the distinction between an estimated effect and the precision of that estimate. The mean difference is 0.01 g/cm2, but the confidence interval extends from -0.040 to 0.060 g/cm2. Reading the point estimate alone would conceal the range of uncertainty; reading the interval alongside it makes clear that the data do not determine the direction of the contrast precisely.

The record also makes an important distinction between enrollment and the sample sizes used for the endpoint summary. Enrollment is listed as 80, while the primary result reports 30 participants in placebo and 31 in active treatment. The registry record does not explain this difference. That gap highlights why clear reporting of participant flow, analysis populations, and missing outcome data is necessary for readers to assess how the analysis relates to the randomized cohort.

The study summary describes a broad set of biological questions, but the registry posts only the primary bone-density result and no secondary outcome results. This emphasizes the need to separate a study's rationale and intended measures from outcomes available for statistical interpretation. Claims about outcomes without posted results cannot be supported by the primary endpoint estimate.

Finally, planning calculations based on an observed effect are not substitutes for an original design justification. The sample-size illustrations show how assumptions about the effect size and desired power influence planning, while the trial's own design assumptions are not reported in the registry record. Keeping observed results, uncertainty, planning illustrations, and unreported protocol details distinct leads to a more careful reading of the evidence.

17. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The main limitation of the posted evidence is that the endpoint comparison is reported without a detailed account of who was included and how missing measurements were handled. The registry lists enrollment of 80, but the primary endpoint has 30 participants in the placebo arm and 31 in the active arm. The record does not explain those numbers or report participant flow, withdrawals, exclusions, or missingness. It also does not identify the analysis population.

The outcome is reported as an 18-month group mean, with no baseline values or change-from-baseline estimate. The measurement site, DXA procedures, and any adjustment variables are not reported in the registry record. The available summary therefore does not support assessment of baseline balance, within-participant change, or the influence of adjustment choices.

Although the study summary describes bone turnover, IGF-I, and bone structure, no secondary outcome results are posted. The scope of conclusions is consequently limited to the reported areal bone-density comparison. The registry record does not report the full statistical analysis plan, multiplicity strategy, original sample-size justification, or interim analyses. It also does not provide enough detail to assess the randomization and masking procedures beyond their design labels.

Safety reporting has a separate limitation: the adverse-event display gives 40 participants at risk per group, while the endpoint summaries use smaller arm counts, and the record does not explain the difference. Death counts are null rather than numerical. These reporting gaps make it important not to treat the posted safety figures as a complete characterization of all possible harms or follow-up.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Adrenal and Gonadal Hormone Replacement in Anorexia Nervosa — NCT00310791.
• Registry record last updated 2018-04-11; status last verified 2018-03.
• Results first posted 2013-02-01.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

NCT00310791, titled “Adrenal and Gonadal Hormone Replacement in Anorexia Nervosa,” is listed as a completed randomized, triple-masked, parallel-group phase 2/phase 3 trial sponsored by Boston Children's Hospital. The registry lists enrollment of 80 and a study population of young women with anorexia nervosa.

The active intervention was combined DHEA and estrogen/progestin hormone replacement therapy, compared with placebo. The primary outcome was areal bone density by DXA at 18 months. The reported means were 0.89 g/cm2 in the active arm and 0.88 g/cm2 in the placebo arm; the mean difference was 0.01 g/cm2, with a 95% confidence interval from -0.040 to 0.060 g/cm2 and an unadjusted p-value of 0.696.

The registry posts no secondary outcome results. It reports zero serious and zero other adverse events in each group's posted safety counts; death counts are not reported. Details of the original statistical plan, analysis population, and missing-data handling are not reported in the registry record.