This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for Somatropin Treatment to Final Height in Turner Syndrome (NCT00191113), a randomized phase 3 study. The primary outcome is Height Standard Deviation Score (SDS) (National Center for Health Statistics [NCHS]), Change From Baseline to Last Measurement, As Randomized Population.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00191113 |
| Phase | Phase 3 |
| Condition | Turner Syndrome |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 154 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Eli Lilly and Company |
| Results posted | Yes |
2. Clinical Question
Population
Girls with Turner syndrome who entered the study at least 7 years old and younger than 13. The primary analysis included all randomized patients, analyzed according to their randomized group, using the most mature height measurement available.
Intervention
Humatrope, or somatropin, given by subcutaneous injection at 0.05 mg/kg/dose 6 times per week. The arm description also specifies ethinyl estradiol after age 13 and medroxyprogesterone acetate after age 15.
Comparator
The control arm did not receive Humatrope. Its description also specifies ethinyl estradiol after age 13 and medroxyprogesterone acetate after age 15, as in the Humatrope arm.
Primary question
How did change from baseline in height standard deviation score differ between the randomized groups, using the most mature height measurement available? The score is referenced to National Center for Health Statistics standards; a positive change indicates increased height, and a greater score indicates greater height.
The primary outcome compares the treatment strategies as randomized, rather than selecting participants according to treatment received. This distinction matters because preserving randomized groups is intended to retain the comparability created by random allocation. The clinical question is about the average difference between groups on a standardized measure of height change, not about an individual participant’s eventual height or a guarantee of a particular response.
3. Trial Design
The registry identifies this as a randomized, controlled, phase 3 trial with a parallel-group model and no masking. Enrollment was 154. The study is marked completed; the recorded start was 1989-02 and primary completion was 2007-12. The registry describes eligible participants as girls with Turner syndrome who were at least 7 years old and younger than 13 at entry.
Participants were assigned to a control group or a Humatrope group. The control group did not receive Humatrope. The Humatrope arm used subcutaneous somatropin at 0.05 mg/kg/dose 6 times per week. Both arm descriptions include ethinyl estradiol, with escalating doses to 20 mcg daily after age 13, and medroxyprogesterone acetate, 10 mg tablets ten days monthly after age 15. The stated continuation criterion refers to protocol final height. Additional detail beyond the posted arm description is not reported in the registry record.
The primary outcome analysis used the as-randomized population: all randomized patients were analyzed in their assigned groups, with the most mature measurement available. The primary outcome timeframe is baseline and the end of a 4-year addendum. The registry also lists height and several hearing and fasting-glucose outcomes among the secondary outcomes. Some secondary analyses use as-treated groups, which classify participants by treatment received rather than assignment.
The registry record does not report masking beyond identifying the study as unmasked, or give the method used to generate or conceal the random allocation sequence. Its original sample-size justification, detailed protocol, and complete statistical analysis plan are not reported in the registry record.
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.
Before assignment: Addendum 1: provided option of Humatrope treatment to patients who had been randomized to control in Core Study. Addendum 2: extended period of follow-up for 5 years after discontinuation from Core Study. Addendum 3: evaluated possible genomic imprinting effects (published: Hamelin et al. 2006).
Core Study
| Stage | As-Randomized Control | As-Randomized Humatrope |
|---|---|---|
| STARTED | 78 | 76 |
| COMPLETED | 43 | 61 |
| NOT COMPLETED | 35 | 15 |
Reasons for not completing this period:
| Reason | As-Randomized Control | As-Randomized Humatrope |
|---|---|---|
| Withdrawal by Subject | 25 | 9 |
| Protocol Violation | 6 | 2 |
| Lost to Follow-up | 3 | 0 |
| Adverse Event | 0 | 2 |
| Lack of Efficacy | 0 | 2 |
| Death | 1 | 0 |
Addendum 1
| Stage | As-Randomized Control | As-Randomized Humatrope |
|---|---|---|
| STARTED | 2 | 0 |
| COMPLETED | 2 | 0 |
| NOT COMPLETED | 0 | 0 |
Addendum 2
| Stage | As-Randomized Control | As-Randomized Humatrope |
|---|---|---|
| STARTED | 28 | 48 |
| COMPLETED | 18 | 31 |
| NOT COMPLETED | 10 | 17 |
Addendum 3
| Stage | As-Randomized Control | As-Randomized Humatrope |
|---|---|---|
| STARTED | 20 | 37 |
| COMPLETED | 20 | 37 |
| NOT COMPLETED | 0 | 0 |
Analysis population for the primary outcome, as defined in the registry: Population of all randomized patients. Intent to treat analysis with as-randomized treatment groups, at most mature measurement available.
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.
| Characteristic | Unit | As-Randomized Control | As-Randomized Humatrope | Total |
|---|---|---|---|---|
| Participants analysed | 78 | 76 | 154 | |
| Age Continuous | years | 10.46 (SD 1.77) | 10.36 (SD 1.80) | 10.41 (SD 1.78) |
| Sex: Female, Male: Female | Participants | 78 | 76 | 154 |
| Sex: Female, Male: Male | Participants | 0 | 0 | 0 |
| Region of Enrollment: Canada | participants | 78 | 76 | 154 |
| Karyotype: 45,X | participants | 48 | 45 | 93 |
| Karyotype: 45,X/46,XXqi | participants | 6 | 2 | 8 |
| Karyotype: 45,X/46,XXr | participants | 1 | 2 | 3 |
| Karyotype: 45,X/46,XX | participants | 3 | 3 | 6 |
| Karyotype: 46,XXqi | participants | 2 | 6 | 8 |
| Karyotype: 45,X/47,XXX | participants | 1 | 2 | 3 |
| Karyotype: 46,XXp | participants | 1 | 0 | 1 |
| Karyotype: 45,X/46,XXp | participants | 1 | 1 | 2 |
| Karyotype: 45,X/46,XX/47,XXX | participants | 0 | 0 | 0 |
| Karyotype: 46,XXr | participants | 0 | 0 | 0 |
| Race/Ethnicity: American Indian or Alaska Native | participants | 1 | 1 | 2 |
| Race/Ethnicity: Asian | participants | 7 | 6 | 13 |
| Race/Ethnicity: Native Hawaiian or Other Pacific Islander | participants | 0 | 0 | 0 |
| Race/Ethnicity: Black or African American | participants | 1 | 0 | 1 |
| Race/Ethnicity: White | participants | 54 | 66 | 120 |
| Race/Ethnicity: Hispanic | participants | 0 | 2 | 2 |
| Race/Ethnicity: Other | participants | 4 | 0 | 4 |
| Race/Ethnicity: Unknown | participants | 11 | 1 | 12 |
| Bone Age | years | 8.57 (SD 1.51) | 8.79 (SD 1.42) | 8.69 (SD 1.46) |
| Height | centimeters | 120.06 (SD 8.26) | 119.84 (SD 8.45) | 119.96 (SD 8.33) |
| Height Standard Deviation Score (SDS) [Lyon] | Standard Deviation Score (SDS) | -0.13 (SD 0.86) | -0.10 (SD 0.88) | -0.11 (SD 0.87) |
| Height Standard Deviation Score (SDS) [National Center for Health Statistics (NCHS)] | Standard Deviation Score (SDS) | -3.25 (SD 0.82) | -3.21 (SD 0.82) | -3.23 (SD 0.82) |
6. Primary Endpoint
The registry lists the primary outcome as Height Standard Deviation Score (SDS) (National Center for Health Statistics [NCHS]), Change From Baseline to Last Measurement, As Randomized Population, measured over Baseline, and end of 4-year addendum.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | Standard Deviation Score (SDS) [NCHS] |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is change from baseline in height standard deviation score (SDS), referenced to National Center for Health Statistics (NCHS) standards. A standardized score expresses height relative to a reference distribution, allowing height to be considered in relation to that standard rather than only in centimeters. The registry states that greater height SDS values indicate greater height, and positive change from baseline indicates increased height.
The endpoint uses the change between baseline and the most mature height measurement available. The primary analysis is as randomized and uses the most mature measurement available for each randomized patient. This focuses the comparison on growth relative to baseline while retaining participants in their assigned groups. The registry describes the timeframe as baseline and the end of the 4-year addendum.
A standardized height outcome can be useful when the clinical question concerns growth relative to a reference standard. It does not itself describe all aspects of growth, development, or health, and it is not interchangeable with a measurement in centimeters. The registry also lists height in centimeters as a secondary outcome, alongside outcomes relating to hearing and fasting glucose. The registry record does not provide a fuller rationale for selecting this primary endpoint or additional details on its measurement beyond the description above.
7. Results Posted in the Registry
- As-Randomized Humatrope: mean 0.97 versus 0.09 on control; difference 0.88 (95% CI 0.69 to 1.07), standardized effect d = 1.43; z-test p = <0.001.
Mean difference: As-Randomized Humatrope
95% CI: 0.69 to 1.07
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Height Standard Deviation Score (SDS) (National Center for Health Statistics [NCHS]), Change From Baseline, As-Treated Population | Continuous Endpoint | Mean difference | 1.08 (0.88 to 1.28) | 5 per arm |
| Height (Centimeters [cm]) | Continuous Endpoint | Mean difference | 6.89 (5.73 to 8.05) | 4 per arm |
| Number of Participants With an Abnormal Pure Tone Audiometry, Audiologist Assessment | Binary Endpoint | Risk difference | +2.1 pts (-24.1 to 28.2) | 8,975 per arm |
Height Standard Deviation Score (SDS) (National Center for Health Statistics [NCHS]), Change From Baseline, As-Treated Population
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- As-Treated Growth Humatrope: mean 0.99 versus -0.09 on control; difference 1.08 (95% CI 0.88 to 1.28), standardized effect d = 1.97; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for As-Treated Growth Humatrope than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Height (Centimeters [cm])
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- As-Treated Growth Humatrope: mean 148.52 versus 141.63 on control; difference 6.89 (95% CI 5.73 to 8.05), standardized effect d = 2.11; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for As-Treated Growth Humatrope than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Number of Participants With an Abnormal Pure Tone Audiometry, Audiologist Assessment
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- As-Treated Growth Hormone: 54.7% (29/53) versus 52.6% (10/19) on control; risk difference 2.1 percentage points (95% CI -24.1 to 28.2), risk ratio 1.04 (0.64–1.70); unadjusted two-proportion z-test p = 0.876.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between As-Treated Growth Hormone and the control. The interval gives the range of effects that remain compatible with the data.
The secondary outcomes span additional measures of growth, hearing assessments, and fasting glucose. The posted growth analyses point in the same direction as the primary result: the as-treated Humatrope group has higher estimated height SDS change and height in centimeters than the as-treated group without growth hormone. This directional consistency supports the interpretation that the posted growth measures are aligned, while they remain distinct outcomes and populations from the primary as-randomized analysis.
The hearing outcomes include audiometry and related assessments. The posted pure-tone comparison has a small estimated risk difference relative to its uncertainty, with a confidence interval that includes both negative and positive values and a reported Fisher exact p-value greater than 0.999. This result is imprecise and does not establish a clear group difference. Results for other secondary outcomes are not detailed in the analyses, so a complete endpoint-by-endpoint pattern cannot be assessed. The registry lists fasting-glucose outcomes, but their estimates are not reported in the results.
Secondary findings have less evidential weight than the prespecified primary question because several outcomes and analyses create multiple opportunities for chance findings. The registry record does not report whether a multiplicity adjustment was used or how outcomes were grouped for such adjustment. Unadjusted secondary p-values should therefore be treated as exploratory evidence rather than as a set of confirmatory tests. The as-treated growth analyses also differ from the randomized primary analysis: grouping by treatment received can lose the protection of random assignment. Secondary outcomes can add context, but they do not replace the primary randomized comparison.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Height Standard Deviation Score (SDS) (National Center for Health Statistics [NCHS]), Change From Baseline, As-Treated Population
- Height (Centimeters [cm])
- Number of Participants With an Abnormal Pure Tone Audiometry, Audiologist Assessment
- Number of Participants With Abnormal Speech Audiometry, Audiologist Assessment
- Number of Participants With Abnormal Impedance Tympanometry, Audiologist Assessment
- Number of Participants With Hearing Loss, Audiologist Assessment
- Fasting Glucose, Change From Baseline
- Maximum Fasting Glucose Value
9. Statistical Interpretation
In the as-randomized analysis, the control group had a least-squares mean change in height SDS of 0.09, with a standard error of 0.07. The Humatrope group had a least-squares mean change of 0.97, also with a standard error of 0.07. The posted summary-statistic recalculation estimates the unadjusted mean difference as 0.88 SDS, with a 95% confidence interval from 0.686 to 1.074 and p < 0.001. The interval describes uncertainty around the recalculated group contrast; it is not a range containing every participant’s outcome.
The registry’s reported ANCOVA analysis gives a mean difference in final values of 0.9 SDS, with a 95% confidence interval from 0.7 to 1.1 and p < 0.001. These reported values are close to the recalculated unadjusted contrast. The analyses are not identical: the recalculation uses the posted group summaries, while the registry identifies its analysis as ANCOVA and labels the reported parameter as a mean difference in final values. The registry’s reported analysis is the study’s own analysis; the recalculation is a separate, unadjusted summary-statistic comparison.
Both analyses point in the same direction: the posted mean change or final-value contrast is higher for the Humatrope group than for control. The confidence intervals indicate the precision of the respective estimates under their analyses. Neither a small p-value nor a group-average difference establishes that every participant had the same experience, and neither alone describes clinical importance. A threshold for a meaningful difference is not reported in the registry record.
The randomized comparison is the most direct basis for interpreting the primary result because it retains assignment groups. The secondary as-treated analyses answer related but distinct questions and may not retain the same protection from confounding as the randomized comparison. The primary result concerns height SDS, not every listed outcome or all possible benefits and risks. Interpretation should therefore remain tied to the outcome, population, and analysis actually posted.
10. Statistical Methods Explained
The primary outcome is continuous: height SDS can take values along a scale, rather than representing only whether an event occurred. The registry reports least-squares means and standard errors for the primary as-randomized groups. A mean describes the central level of an outcome across a group. A standard error describes the uncertainty in an estimated mean; it is not the spread of individual participants’ measurements. Confusing standard error with standard deviation can make a result seem more or less variable than it is.
What does the randomized comparison estimate?
The primary analysis keeps participants in their randomized groups, regardless of treatment received. This is an as-randomized, intent-to-treat approach as described in the registry. Randomization aims to make assigned groups comparable at the start, on average, including for factors that may not have been measured. Keeping participants in those groups helps preserve that design feature. The registry says the analysis used the most mature height measurement available, but further details about missing measurements and how they were handled are not reported in the registry record.
The primary group summaries are least-squares means. These are model-based estimates, and the registry’s reported comparison is an ANCOVA analysis. ANCOVA, or analysis of covariance, compares outcomes while accounting for specified covariates. Which covariates were included in the sponsor’s model is not reported in the registry record. The posted group summaries alone do not reveal the full model or allow its adjusted result to be reconstructed exactly.
What is the recalculated contrast?
The recalculated primary mean difference is 0.88 SDS, with a 95% confidence interval from 0.686 to 1.074 and p < 0.001. This is a simple, unadjusted comparison based on posted summary statistics. It is not the same calculation as the registry’s ANCOVA. The recalculation uses the group means and standard errors to estimate the contrast and its uncertainty; the standard deviation used in the recalculation is approximate because it is derived from the posted standard errors. It should therefore be read as a check of the scale and direction of the summary result, not as a replacement for the study’s model.
A confidence interval gives a range of values compatible with the data under the assumptions of the analysis. In repeated use of the same method under its assumptions, intervals constructed in this way would cover the underlying parameter at the stated rate. For a reader, the interval is useful for seeing both the estimated contrast and its precision. It does not describe the range of individual responses or prove that a particular value is the true effect.
What does a p-value contribute?
A p-value measures how unusual data at least as inconsistent with a specified null hypothesis would be if that hypothesis and the analysis assumptions held. The posted primary p-values are less than 0.001 for both the sponsor’s ANCOVA and the recalculated comparison. This is evidence against a zero-difference null under those analyses. A p-value is not the probability that the null hypothesis is true, nor does it measure the size or clinical importance of the group difference. It also does not account for every uncertainty about design, missing data, or outcome selection.
The registry reports a 95% confidence interval for the sponsor analysis and for the recalculated contrast. The sponsor interval is rounded to one decimal place, while the recalculated interval is reported to three decimal places. More digits do not make the recalculation more authoritative; the recalculation is approximate and unadjusted. The distinction between a model-based analysis and a summary-statistic re-analysis is important when comparing the estimates.
Why do over-dispersion and outcome type matter?
General statistical explanation: over-dispersion occurs when observed variation is greater than the model assumes. If a model underestimates variability, standard errors can be too small and confidence intervals too narrow. The primary outcome is continuous, and the posted primary analysis uses mean-based methods; over-dispersion is not a reported feature of the primary result. For binary outcomes, event counts and denominators describe proportions, and methods must account for the discrete nature of the data. The registry reports a Fisher exact test for the posted pure-tone audiometry comparison.
General statistical explanation: analyses of several outcomes or repeated assessments create opportunities for chance findings. If many tests are considered, unadjusted p-values do not by themselves control the overall chance of a false-positive result across that family of tests. The registry record does not report a multiplicity adjustment or a plan defining families of hypotheses. Thus, secondary p-values should be read as individual, unadjusted evidence unless the registry states otherwise.
The report includes both randomized and as-treated populations. The as-treated secondary analyses categorize participants according to growth-hormone treatment received. That can be informative descriptively, but treatment received may be associated with participant characteristics or events after randomization. An as-treated contrast therefore does not necessarily preserve the comparability of randomized groups. The registry’s reported primary comparison remains the more direct answer to the randomized clinical question.
11. Confidence Intervals and Precision
The sponsor’s reported ANCOVA estimate is a mean difference of 0.9 SDS, with a 95% confidence interval from 0.7 to 1.1. The unadjusted recalculation from the posted summaries is 0.88 SDS, with a 95% confidence interval from 0.686 to 1.074. Both intervals are centered around a positive group contrast and their reported bounds are above zero. The estimates are close, while the analyses differ in method and adjustment.
A confidence interval communicates statistical precision by showing a range of effect estimates compatible with the data under the analysis assumptions. It is not a prediction interval for an individual participant, and it does not mean that the true value has a 95% probability of lying in this particular interval. The interval also does not settle whether the estimated difference is important in practice; the registry record does not report a threshold for meaningful change in height SDS.
The recalculated interval is based on an unadjusted summary-statistic method and an approximate standard deviation derived from standard errors. Its extra decimal places should not be mistaken for extra certainty. The sponsor’s ANCOVA interval is the interval for the study’s reported analysis. Neither interval captures every possible source of uncertainty, including uncertainty related to missing outcome data, model specification, or conduct of the trial.
The primary group estimates are least-squares means with standard errors of 0.07 in each group. A standard error describes uncertainty in the estimated group mean, not individual variability. Individual-level distributions and the full sponsor model are not reported in the registry record, limiting assessment of the underlying spread and model assumptions.
12. 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.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 8 | 11 |
| 75% of the observed effect | 14 | 19 |
| 50% of the observed effect | 31 | 41 |
The planning estimates are expressed as participants per arm for the continuous outcomes in this trial. For time-to-event outcomes, the stated convention is total events; there are no time-to-event planning figures in the results. The estimates illustrate sample sizes under a planning calculation based on an effect size, rather than report the trial’s actual enrollment or an original design target.
The calculation assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is set at the stated fraction of the observed effect. The 80% power column describes the number of participants per arm estimated to give an 80% chance of detecting that specified effect under those assumptions if it is present. The 90% power column describes the corresponding planning target for a 90% chance. These are planning probabilities, not guarantees about a future study.
For the primary outcome, the illustration ranges from 8 participants per arm for planning at 100% of the observed effect to 31 participants per arm for planning at 50% of the observed effect, in the 80% power column. At 90% power, the corresponding figures are 11 and 41 participants per arm. The intermediate planning scenario is 75% of the observed effect. Smaller effects require more participants because a smaller group contrast is harder to distinguish from sampling variability under the same assumptions.
These estimates are not observed power. They are not evidence that the trial was originally designed using these assumptions. The trial’s own original sample-size justification and planning assumptions are not reported in the registry record. The displayed scenarios are retrospective planning illustrations based on the observed effect, and may not reflect the study’s actual design considerations.
13. 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 z1−α/2 = 1.960) and the desired power (z1−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
- Observed difference Δ = 0.880; pooled standard deviation σ = 0.614.
- n = 2 × (1.96 + 0.842)2 × 0.6142 / 0.8802 = 7.6, rounded up to 8 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 <- 0.88 # observed difference in means
sigma <- 0.614299986720015 # 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(191113)
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 = 8 (80% power), 11 (90% power)
75% of observed effect: n per arm = 14 (80% power), 19 (90% power)
50% of observed effect: n per arm = 31 (80% power), 41 (90% power)
power.t.test: 8.7
Simulated power at n = 8 per arm: 0.762 (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.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| ANCOVA | Mean Difference (Final Values) 0.9 | 0.7 to 1.1 | < 0.001 |
The registry’s reported primary analysis is an ANCOVA comparison of final values. It estimates a mean difference of 0.9 SDS, with a 95% confidence interval from 0.7 to 1.1 and p < 0.001. This is the trial’s own reported analysis and should be distinguished from the separate recalculation based only on posted group summaries.
The recalculated unadjusted mean difference is 0.88 SDS, with a 95% confidence interval from 0.686 to 1.074 and p < 0.001. It is close to the registry estimate in direction and magnitude. The recalculation does not reproduce ANCOVA, because the model’s covariates and other details are not reported in the registry record. It uses the posted means and standard errors, with an approximate standard deviation, and therefore serves as a simple unadjusted check rather than a substitute for the study analysis.
The registry does not flag a discrepancy between the analyses. The slight differences in reported estimates and interval endpoints are consistent with the different methods and rounding. The sponsor result retains the status of the reported trial analysis, while the recalculation offers a transparent summary-statistic comparison. Neither analysis alone addresses issues such as missing-data assumptions or the clinical importance of the difference.
15. Multiplicity, Missing Data and Analysis Populations
The primary endpoint is clearly identified in the registry record, and the primary analysis is described as an intent-to-treat, as-randomized analysis using the most mature measurement available. Beyond this, several statistical-plan details are not reported in the registry record. These include the original sample-size justification, the full analysis plan, any interim analyses, the covariates in the ANCOVA model, and procedures for handling missing primary outcome data.
The record lists 18 outcome measures and 14 analyses, and it reports 16 secondary outcomes as posted. Multiple outcomes and analyses raise the issue of multiplicity: when many hypotheses are tested, the chance of at least one apparently unusual result can increase if each is interpreted without adjustment. The registry record does not report a multiplicity correction, a hierarchy among secondary outcomes, or a prespecified family of tests. Consequently, it is not possible to determine from the record whether or how the study controlled the overall type I error across secondary comparisons.
The primary population is all randomized patients, analyzed according to assigned group. The registry states that the most mature available measurement was used, but does not report how many randomized participants contributed a primary outcome, the reasons for unavailable measurements, or whether missing data were imputed. The group summaries list 78 in control and 76 in Humatrope, but those numbers alone do not establish that every participant had a usable endpoint measurement or describe missingness.
The secondary growth outcome is explicitly as-treated, with groups defined as no growth hormone and growth Humatrope. Such analyses may be affected by differences between participants who did and did not receive treatment, including differences arising after randomization. The registry record does not explain the reasons for treatment receipt or provide enough information to evaluate those differences. The primary randomized comparison and secondary as-treated analyses therefore address different estimands and should not be conflated.
The record also does not report a detailed plan for handling protocol deviations, sensitivity analyses, or subgroup analyses. These omissions do not establish that such procedures were absent; they mean that they are not reported in the registry record. They limit how fully readers can assess whether the posted analyses followed a prespecified plan.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Treated-As-Randomized Control | 10 | 54 | 18.5% |
| Treated-As-Randomized Humatrope | 22 | 74 | 29.7% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Treated-As-Randomized Control | 53 of 54 |
| Treated-As-Randomized Humatrope | 74 of 74 |
Most frequent serious adverse event terms
| Event term | Organ system | Treated-As-Randomized Control | Treated-As-Randomized Humatrope |
|---|---|---|---|
| Tympanoplasty | Surgical and medical procedures | 0 of 54 | 3 of 74 |
| Arm fracture | Injury, poisoning and procedural complications | 0 of 54 | 2 of 74 |
| Appendectomy | Surgical and medical procedures | 2 of 54 | 0 of 74 |
| Pterygium operation | Surgical and medical procedures | 1 of 54 | 1 of 74 |
| Anemia iron deficiency | Blood and lymphatic system disorders | 0 of 54 | 1 of 74 |
| Hypochromic microcytic anemia | Blood and lymphatic system disorders | 0 of 54 | 1 of 74 |
| Idiopathic thrombocytopenic purpura | Blood and lymphatic system disorders | 1 of 54 | 0 of 74 |
| Cardiac arrest | Cardiac disorders | 1 of 54 | 0 of 74 |
| Cellulitis of foot | Infections and infestations | 0 of 54 | 1 of 74 |
| Gastroenteritis | Infections and infestations | 0 of 54 | 1 of 74 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Treated-As-Randomized Control | Treated-As-Randomized Humatrope |
|---|---|---|---|
| Cold | Infections and infestations | 39 of 54 | 42 of 74 |
| Headache | Nervous system disorders | 25 of 54 | 46 of 74 |
| Sore throat | Respiratory, thoracic and mediastinal disorders | 28 of 54 | 37 of 74 |
| Fever | General disorders | 20 of 54 | 36 of 74 |
| Flu | Infections and infestations | 20 of 54 | 36 of 74 |
| Vomiting | Gastrointestinal disorders | 21 of 54 | 29 of 74 |
| Otitis media | Infections and infestations | 13 of 54 | 31 of 74 |
| Cough | Respiratory, thoracic and mediastinal disorders | 14 of 54 | 27 of 74 |
| Ear infection | Infections and infestations | 12 of 54 | 27 of 74 |
| Rhinitis | Infections and infestations | 11 of 54 | 17 of 74 |
Serious events with the highest arm-level rate: tympanoplasty (4.1%), appendectomy (3.7%), arm fracture (2.7%), idiopathic thrombocytopenic purpura (1.9%), cardiac arrest (1.9%).
Serious adverse event figures are reported for treated-as-randomized groups, which are not the same population labels as the primary as-randomized efficacy analysis. The control group had 10 serious adverse events among 54 participants at risk, and the Humatrope group had 22 among 74 at risk. These are counts of participants affected and denominators at risk as posted; they do not by themselves establish whether an event was caused by treatment or whether the groups differed in risk after accounting for follow-up and other factors.
The listed serious-event terms include tympanoplasty at 4.1%, appendectomy at 3.7%, arm fracture at 2.7%, idiopathic thrombocytopenic purpura at 1.9%, cardiac arrest at 1.9%, and pneumonia at 1.9%. The registry also reports other adverse events in 53 of 54 control participants and 74 of 74 Humatrope participants. The record does not provide enough detail in these figures to evaluate event timing, duration, severity beyond the serious classification, or causal attribution. Death counts are not reported in the registry record.
These safety summaries are descriptive. Differences in denominators, duration of observation, and participant characteristics may matter, but further details are not reported in the registry record. The counts should not be treated as a causal comparison or as a complete assessment of safety.
17. What the Result Does, and Does Not, Mean
The primary result describes a higher average change in height SDS in the randomized Humatrope group than in the randomized control group. The registry’s ANCOVA estimate is 0.9 SDS, with a 95% confidence interval from 0.7 to 1.1 and p < 0.001. The unadjusted recalculation is similar in direction and magnitude. The result is about the average standardized height outcome in this trial population and analysis, not an individual prediction.
The result does not show that every participant’s height increased by the same amount, or that every participant would have a response matching the group average. It does not establish how the difference should be judged clinically, because a threshold for meaningful change is not reported in the registry record. A low p-value supports evidence against a zero-difference hypothesis under the stated analysis; it does not measure importance or certainty about every possible consequence.
The outcome is height SDS, not a complete measure of health or development. The record also lists centimeters, hearing, and fasting-glucose outcomes, but the primary finding does not determine the findings for those outcomes. The available safety counts are descriptive and do not prove that events were caused by the assigned treatment. Nor does the primary result by itself establish the balance of benefits and risks.
Interpretation is also bounded by the information available in the registry record. Detailed handling of missing outcomes, model covariates, the original design assumptions, multiplicity procedures, and a full statistical plan are not reported. These gaps do not negate the posted estimate, but they limit independent evaluation of all assumptions behind it. The most direct conclusion is therefore about the reported randomized comparison of change in height SDS, with its stated confidence interval and limitations.
18. Why This Trial Matters Statistically
This trial illustrates the value of distinguishing a primary randomized analysis from secondary analyses organized by treatment received. The primary comparison follows randomized assignment, while the as-treated growth outcomes classify participants according to receipt of growth hormone. These approaches can answer related but not identical questions, and their estimates should not be interpreted as interchangeable.
It also demonstrates why a point estimate and its uncertainty should be read together. The reported ANCOVA contrast and the recalculated unadjusted contrast are close, and both have confidence intervals that exclude zero. The recalculation is useful as a transparent check from summary statistics, but it does not reproduce the sponsor’s model. The difference between these analyses highlights the importance of reporting the analysis method and recognizing what a summary-statistic reconstruction can and cannot establish.
The registry record offers a further lesson about trial interpretation: a statistically clear primary result does not answer every question about clinical meaning, missing data, safety, or secondary outcomes. The record’s identification of the primary endpoint and randomized population helps frame the main comparison, while unreported statistical-plan details leave limits on assessment. Secondary analyses across growth, hearing, and glucose outcomes require attention to multiplicity and analysis populations. Taken together, these features make the trial a useful case for reading estimates in context rather than relying on a p-value alone.
19. 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 registry describes a long-running study, with a recorded start of 1989-02 and primary completion of 2007-12, but does not report detailed follow-up distributions or the timing of each participant’s last measurement. The primary endpoint uses the most mature height measurement available, and the timeframe includes the end of a 4-year addendum. Without individual follow-up details, the degree to which measurement timing varied across participants cannot be assessed from the registry record.
The study is identified as unmasked. The registry record does not describe masking of outcome assessors or other procedures that might limit awareness of assigned treatment. It also does not report the method for random sequence generation or allocation concealment. These details would help readers assess potential sources of bias, but their absence from the record does not establish how the trial was conducted beyond the reported design features.
The registry gives least-squares means and standard errors for the primary outcome, but does not report the ANCOVA covariates, diagnostic checks, or missing-data methods. The recalculated comparison is unadjusted and uses an approximate standard deviation derived from standard errors, so it cannot replace a full reanalysis of individual data. A complete evaluation of model assumptions is not possible from group summaries alone.
Secondary as-treated growth analyses are potentially vulnerable to differences between participants who received and did not receive growth hormone. The registry does not report enough information to assess the reasons for treatment receipt or resulting comparability. The record also does not report a multiplicity plan, the original sample-size justification, or detailed results for every listed secondary outcome. Finally, safety figures are descriptive, use treated-as-randomized denominators, and do not provide enough detail to establish causation or account for differences in follow-up.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Somatropin Treatment to Final Height in Turner Syndrome — NCT00191113.
- Registry record last updated 2010-01-27; status last verified 2009-12.
- Results first posted 2010-01-27.
- 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.
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23. Record Summary
NCT00191113 is a completed, randomized, controlled phase 3 parallel-group trial sponsored by Eli Lilly and Company, with no masking reported. It enrolled 154 girls with Turner syndrome who were at least 7 years old and younger than 13 at study entry. The comparison was Humatrope somatropin versus a control arm without Humatrope; both arm descriptions include later ethinyl estradiol and medroxyprogesterone acetate.
The primary outcome was change from baseline in height SDS, referenced to NCHS standards, using the most mature measurement available in the as-randomized population. The registry’s ANCOVA estimate was a mean difference of 0.9 SDS, with a 95% confidence interval from 0.7 to 1.1 and p < 0.001. An unadjusted summary-statistic recalculation estimated a mean difference of 0.88 SDS, with a 95% confidence interval from 0.686 to 1.074 and p < 0.001.
The registry also lists secondary growth, hearing, and fasting-glucose outcomes and descriptive adverse-event counts. Details of the original sample-size justification, full statistical plan, missing-data handling, and multiplicity procedures are not reported in the registry record.