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 Determine the Efficacy, Safety and Tolerability of Denosumab (AMG 162) in the Treatment of Postmenopausal Women With Low Bone Mineral Density (NCT00043186), a randomized phase 2 study. The primary outcome is Lumbar Spine Bone Mineral Density Percent Change From Baseline at Month 12 for the Placebo and Denosumab Arms.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00043186 |
| Phase | Phase 2 |
| Condition | Low Bone Mineral Density |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Quadruple |
| Enrollment | 412 |
| Arms in the primary outcome | 8 |
| Lead sponsor | Amgen |
| Results posted | Yes |
2. Clinical Question
The registry record describes a study of postmenopausal women with low bone mineral density. Its primary question was whether lumbar spine bone mineral density changed differently over 12 months in participants assigned to denosumab or placebo. The outcome was percent change from baseline, measured by dual energy X-ray absorptiometry.
Population
Postmenopausal women with low bone mineral density. The primary analysis population was randomized participants with a non-missing baseline value and a non-missing Month 12 value.
Intervention
Several denosumab schedules were studied: doses of 6 mg, 14 mg, or 30 mg every 3 months, and doses of 14 mg, 60 mg, 100 mg, or 210 mg every 6 months.
Comparator
Placebo was the comparator for the primary endpoint. The registry also lists an alendronate arm, but it was not included in the posted primary comparison results.
Primary question
What was the difference between each denosumab schedule and placebo in mean percent change in lumbar spine bone mineral density from baseline to Month 12?
The study was designed to assess a measured bone-density outcome and tolerability. The posted primary results address the bone-density comparison; they do not by themselves answer broader questions about fractures, symptoms, long-term health, or comparative safety. Those outcomes and their interpretation require evidence beyond this single endpoint.
3. Trial Design
This was a randomized, parallel-group phase 2 study. The registry describes quadruple masking and identifies the study as placebo-controlled and multi-dose. The registry record lists an enrollment of 412. That is the trial enrollment figure, not the number included in each Month 12 endpoint analysis.
Participants were assigned to placebo or one of several denosumab regimens. The dose schedules differed in both dose and frequency. The arm descriptions also show that some assigned regimens changed after Month 21: several continued with denosumab 60 mg every 6 months from Month 24 through Month 42, while other schedules included placebo injections during part of that extension. The 60 mg every 6 months arm continued that schedule through Month 42. The placebo injections continued through Month 42.
An open-label alendronate 70 mg arm is also described. Participants in that arm received weekly oral tablets through Month 24 and no treatment from Month 24 to Month 48. The primary endpoint, however, is explicitly framed as a comparison of placebo and denosumab arms at Month 12. Alendronate is not part of the posted primary comparison set.
The study's stated primary timeframe was baseline and Month 12, although the registry also includes bone-density outcomes at later visits. The trial is marked completed. Its own detailed sample-size justification, randomization procedures, and operational details beyond the registry descriptions are not reported in the registry record. Results apply to the endpoint populations and comparisons described in the record, rather than automatically to every randomized participant or every possible treatment contrast.
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.
Only the first 6 of 9 groups are shown.
Overall Study
| Stage | Placebo | Denosumab 6 mg Q3M | Denosumab 14 mg Q3M | Denosumab 30 mg Q3M | Denosumab 14 mg Q6M | Denosumab 60 mg Q6M |
|---|---|---|---|---|---|---|
| STARTED | 46 | 44 | 44 | 41 | 54 | 47 |
| COMPLETED | 29 | 29 | 24 | 19 | 36 | 39 |
| NOT COMPLETED | 17 | 15 | 20 | 22 | 18 | 8 |
Reasons for not completing this period:
| Reason | Placebo | Denosumab 6 mg Q3M | Denosumab 14 mg Q3M | Denosumab 30 mg Q3M | Denosumab 14 mg Q6M | Denosumab 60 mg Q6M |
|---|---|---|---|---|---|---|
| Physician Decision | 0 | 0 | 3 | 0 | 1 | 0 |
| Adverse Event | 2 | 2 | 2 | 3 | 2 | 1 |
| Withdrawal by Subject | 11 | 8 | 11 | 13 | 14 | 6 |
| Death | 0 | 0 | 1 | 0 | 0 | 0 |
| Disease progression | 1 | 0 | 0 | 3 | 0 | 0 |
| Ineligibility determined | 0 | 0 | 0 | 0 | 0 | 0 |
| Lost to Follow-up | 3 | 5 | 1 | 1 | 1 | 1 |
| Noncompliance | 0 | 0 | 1 | 1 | 0 | 0 |
| Other | 0 | 0 | 1 | 1 | 0 | 0 |
Analysis population for the primary outcome, as defined in the registry: Randomized participants with non-missing Baseline and non-missing value at Month 12.
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.
Only the first 6 of 10 groups are shown.
| Characteristic | Unit | Placebo | Denosumab 6 mg Q3M | Denosumab 14 mg Q3M | Denosumab 30 mg Q3M | Denosumab 14 mg Q6M | Denosumab 60 mg Q6M |
|---|---|---|---|---|---|---|---|
| Participants analysed | 46 | 44 | 44 | 41 | 54 | 47 | |
| Age Continuous | Years | 63.7 (SD 9.1) | 62.8 (SD 8.6) | 62.3 (SD 6) | 61.2 (SD 8.5) | 61.4 (SD 8.1) | 63.1 (SD 8.1) |
| Sex: Female, Male: Female | Participants | 46 | 44 | 44 | 41 | 54 | 47 |
| Sex: Female, Male: Male | Participants | 0 | 0 | 0 | 0 | 0 | 0 |
| Race/Ethnicity, Customized: White or Caucasian | Participants | 37 | 33 | 42 | 36 | 49 | 39 |
| Race/Ethnicity, Customized: Black or African American | Participants | 0 | 1 | 1 | 2 | 1 | 1 |
| Race/Ethnicity, Customized: Hispanic or Latino | Participants | 8 | 8 | 1 | 3 | 3 | 5 |
| Race/Ethnicity, Customized: Asian | Participants | 1 | 1 | 0 | 0 | 0 | 2 |
| Race/Ethnicity, Customized: Japanese | Participants | 0 | 0 | 0 | 0 | 1 | 0 |
| Race/Ethnicity, Customized: American Indian or Alaska Native | Participants | 0 | 1 | 0 | 0 | 0 | 0 |
6. Primary Endpoint
The registry lists the primary outcome as Lumbar Spine Bone Mineral Density Percent Change From Baseline at Month 12 for the Placebo and Denosumab Arms, measured over Baseline and Month 12.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | Percent change |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is percent change in lumbar spine bone mineral density from baseline to Month 12. The record describes bone mineral density assessment by dual energy X-ray absorptiometry and defines the change as the Month 12 value minus the baseline value, divided by the baseline value, then multiplied by 100. The unit is percent change.
The posted arm values are least-squares means, with standard errors as the measure of spread. The analysis population is randomized participants with non-missing baseline and Month 12 values. Thus, the endpoint describes the mean change among participants contributing those measurements, as specified in the registry.
As a continuous measure, percent change retains information about the size and direction of measured change rather than reducing results to a binary category. Comparing group means can describe how the average measured change differed between assigned groups. The endpoint is used because the trial's stated objective was to examine the effect of denosumab relative to placebo on lumbar spine bone mineral density over 12 months.
Bone-density change is not itself a report of fractures, symptoms, or other clinical events. The registry record does not establish from this endpoint alone how an observed difference relates to those outcomes. It also does not report a minimum clinically important difference for interpreting the size of the mean changes.
7. Results Posted in the Registry
- Denosumab 6 mg Q3M: mean 4.41 versus -0.81 on control; difference 5.22 (95% CI 3.86 to 6.58), standardized effect d = 1.73; z-test p = <0.001.
- Denosumab 14 mg Q3M: mean 4.71 versus -0.81 on control; difference 5.52 (95% CI 4.16 to 6.88), standardized effect d = 1.83; z-test p = <0.001.
- Denosumab 30 mg Q3M: mean 6.69 versus -0.81 on control; difference 7.50 (95% CI 6.08 to 8.92), standardized effect d = 2.46; z-test p = <0.001.
- Denosumab 14 mg Q6M: mean 3.03 versus -0.81 on control; difference 3.84 (95% CI 2.58 to 5.10), standardized effect d = 1.28; z-test p = <0.001.
Mean difference: Denosumab 6 mg Q3M
95% CI: 3.86 to 6.58
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 |
|---|---|---|---|---|
| Lumbar Spine Bone Mineral Density Percent Change From Baseline at Month 24 | Continuous Endpoint | Mean difference | 8.67 (6.77 to 10.57) | 4 per arm |
| Lumbar Spine Bone Mineral Density Percent Change From Baseline at Month 36 | Continuous Endpoint | Mean difference | 10.37 (8.12 to 12.62) | 3 per arm |
| Lumbar Spine Bone Mineral Density Percent Change From Baseline at Month 48 | Continuous Endpoint | Mean difference | 11.74 (8.69 to 14.79) | 4 per arm |
Lumbar Spine Bone Mineral Density Percent Change From Baseline at Month 24
- 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:
- Denosumab 6 mg Q3M: mean 7.42 versus -1.25 on control; difference 8.67 (95% CI 6.77 to 10.57), standardized effect d = 2.20; z-test p = <0.001.
- Denosumab 14 mg Q3M: mean 7.21 versus -1.25 on control; difference 8.46 (95% CI 6.58 to 10.34), standardized effect d = 2.15; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Denosumab 6 mg Q3M than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Denosumab 14 mg Q3M than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Lumbar Spine Bone Mineral Density Percent Change From Baseline at Month 36
- 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:
- Denosumab 6 mg Q3M: mean 8.57 versus -1.80 on control; difference 10.37 (95% CI 8.12 to 12.62), standardized effect d = 2.32; z-test p = <0.001.
- Denosumab 14 mg Q3M: mean 9.17 versus -1.80 on control; difference 10.97 (95% CI 8.60 to 13.34), standardized effect d = 2.45; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Denosumab 6 mg Q3M than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Denosumab 14 mg Q3M than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Lumbar Spine Bone Mineral Density Percent Change From Baseline at Month 48
- 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:
- Denosumab 6 mg Q3M: mean 9.35 versus -2.39 on control; difference 11.74 (95% CI 8.69 to 14.79), standardized effect d = 1.98; z-test p = <0.001.
- Denosumab 14 mg Q3M: mean 9.93 versus -2.39 on control; difference 12.32 (95% CI 9.12 to 15.52), standardized effect d = 2.08; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Denosumab 6 mg Q3M than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Denosumab 14 mg Q3M than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The posted secondary bone-density results extend observation beyond the Month 12 primary endpoint, with measurements listed at Month 24, Month 36, and Month 48. The overall pattern is that most denosumab arms have positive mean percent changes at these later visits, while the placebo mean is negative at each of those listed time points. The size and ordering of arm means vary across visits, so the later results should not be reduced to a claim that all schedules followed the same trajectory.
These results provide context for the primary finding because they describe the same measured outcome at later times. They do not replace the Month 12 primary comparison or establish that observed differences persist in the same way for every regimen. The arm descriptions indicate that treatment schedules changed over time for some groups, and the alendronate arm had its own treatment period. Later means therefore reflect the regimens and analysis populations at those visits, not a single uniform exposure pattern.
The registry lists 36 outcome measures and 279 analyses, with 35 secondary outcomes posted. With many endpoints, time points, and comparisons, the chance of at least one apparently unusual result can increase if many tests are considered without adjustment. The multiplicity plan is not reported in the registry record. As a result, secondary findings with unadjusted inferential results carry less weight than a prespecified primary result with an explicitly described analysis plan. They are best treated as supportive and exploratory descriptions, especially when considering patterns across multiple visits and treatment arms.
The registry also includes secondary outcomes involving serum CTX and urine NTX/creatinine, but the registry entries do not give their numerical results. Their findings and relation to bone-density changes are not reported in the registry record.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Serum CTX Percent Change From Baseline at Month 12
- Urine NTX/Creatinine Percent Change From Baseline at Month 12
- Lumbar Spine Bone Mineral Density Percent Change From Baseline at Month 12 for the Alendronate Arm
- Lumbar Spine Bone Mineral Density Percent Change From Baseline at Month 24
- Lumbar Spine Bone Mineral Density Percent Change From Baseline at Month 36
- Lumbar Spine Bone Mineral Density Percent Change From Baseline at Month 42
- Lumbar Spine Bone Mineral Density Percent Change From Baseline at Month 48
- Serum CTX Percent Change From Baseline at Month 24
9. Statistical Interpretation
At Month 12, the placebo arm's least-squares mean percent change was -0.81. The corresponding denosumab arm means ranged from 3.03 for 14 mg every 6 months to 6.69 for 30 mg every 3 months. The other posted denosumab means were 4.41 for 6 mg every 3 months, 4.71 for 14 mg every 3 months, 4.55 for 60 mg every 6 months, 5.52 for 100 mg every 6 months, and 5.07 for 210 mg every 6 months.
The posted recalculated unadjusted mean differences between denosumab and placebo are positive for each listed schedule. They range from 3.84 to 7.50 percentage points, with 95% confidence intervals that do not cross zero. The associated recalculated unadjusted p-values are all p < 0.001. These are summary-statistic re-calculations, not the sponsor's adjusted ANCOVA analyses. Each interval expresses uncertainty for its own contrast and should not be read as a direct comparison among denosumab doses.
The registry's own ANCOVA results likewise report positive mean differences for each denosumab-versus-placebo primary comparison, with p < 0.001 for each. The sponsor's estimates and confidence intervals are described separately because they are the analyses reported by the trial record. The small differences between some posted re-calculations and sponsor estimates do not change the broad descriptive pattern, but the sponsor analysis is the primary reported analysis.
The arm means and contrasts describe average bone-density changes among participants with the measurements required for the primary analysis. They do not demonstrate that every participant changed in the same way. Nor do the differences establish effects on fractures or other outcomes not measured by this primary endpoint. The p-values address compatibility with a null contrast under their respective statistical procedures; they do not quantify the probability that a treatment is effective, nor do they describe the clinical importance of the observed differences.
Multiple dose schedules were compared with the same placebo group. The record lists many analyses across outcomes, but the multiplicity strategy for the primary contrasts is not reported in the registry record. Therefore the unadjusted re-calculated p-values should be treated as descriptive inferential results, rather than as proof that the family of comparisons was controlled for false-positive findings.
10. Statistical Methods Explained
The primary endpoint is continuous: it is a percentage change in bone mineral density. A mean summarizes the average measured change in an arm. The registry reports least-squares means, which are model-based means, and reports standard errors to convey the estimated uncertainty in those means. Details of the sponsor's full ANCOVA specification, including its covariates, are not reported in the registry record.
What does the mean difference represent?
A mean difference compares the average outcome in one group with the average outcome in another. For the primary endpoint, the contrast is denosumab minus placebo. A positive contrast means the posted denosumab mean is higher than the placebo mean for percent change. It is a difference in percentage points, not a relative percentage increase. No further transformation is needed to understand the contrast.
The recalculated comparisons use the posted arm means and standard errors to produce simple unadjusted estimates. The record marks the pooled spread used for these calculations as approximate. This matters because a standard error is an estimate of uncertainty in a mean, while a standard deviation describes variation among individual observations. Recovering a spread from summary information requires assumptions and can be less direct than using participant-level data. These recalculations do not reproduce the trial's adjusted ANCOVA model.
How should a confidence interval be read?
A confidence interval gives a range of values compatible with the data under the analysis procedure, while reflecting sampling uncertainty. Narrower intervals indicate greater precision for the estimate; wider intervals indicate less precision. For a difference between means, an interval that includes zero is compatible with no difference under that interval procedure. An interval entirely on one side of zero is evidence that the estimated contrast is not centered on zero at the stated confidence level. This general interpretation does not establish clinical importance.
The recalculated intervals are unadjusted and are based on summary statistics. The sponsor's reported intervals come from ANCOVA. The two approaches need not produce identical estimates or limits because they use different statistical information and modeling. The sponsor results are the registry's own reported analyses; a summary-statistic re-calculation is a supplementary check, not a replacement for the sponsor's model.
What does a p-value say?
A p-value measures how unusual data at least as inconsistent with a specified null hypothesis would be if that null hypothesis and the analysis assumptions were true. It is not the probability that the null hypothesis is true, the probability that the result happened by chance, or a measure of the size of the difference. A small p-value can coexist with uncertainty about the magnitude or clinical meaning of an effect.
The re-calculated p-values are unadjusted for the set of comparisons. The sponsor results report p-values from ANCOVA. The registry's multiplicity procedures are not reported, so the stated p-values should not be interpreted as documenting family-wise error control across multiple doses and outcomes.
Why does over-dispersion matter?
Over-dispersion is a general concern when observed variability is greater than a statistical model assumes. A model that understates variability can make standard errors too small and confidence intervals too narrow, which can make results appear more precise than they are. The primary endpoint is continuous, and the record does not identify an over-dispersion issue or provide diagnostics for it. The concept is useful generally, but it should not be inferred that over-dispersion occurred in this trial.
More broadly, statistical precision depends on both the amount of information and the variability in measurements. Missing endpoint values can reduce the information available for a particular analysis. The primary population excludes participants without both baseline and Month 12 values, but the registry does not report the missing-data method beyond that population definition. No assumptions about imputation, sensitivity analyses, or model handling of missing outcomes should therefore be attributed to the trial.
11. Confidence Intervals and Precision
The Month 12 recalculated 95% confidence intervals are positive for all listed denosumab-versus-placebo contrasts. Their widths differ across dose schedules, reflecting differences in the estimates and the standard errors used in the calculations. For example, the interval for 14 mg every 6 months is 2.577 to 5.103, while the interval for 30 mg every 3 months is 6.084 to 8.916. These intervals describe uncertainty in separate contrasts; they do not directly test whether those two schedules differ from one another.
The sponsor's reported ANCOVA intervals are also positive for every primary comparison. For 14 mg every 6 months, the reported mean difference is 3.84 with a 95% confidence interval from 2.60 to 5.07. For 30 mg every 3 months, it is 7.50 with a 95% confidence interval from 6.13 to 8.87. The distinction between sponsor intervals and recalculated intervals is important: the latter are simple unadjusted re-calculations from posted summary statistics, while the former come from the reported ANCOVA analyses.
A confidence interval is a range reflecting statistical uncertainty, not a range containing most individual participants' outcomes. It also does not account automatically for selection, missing-data, measurement, or multiplicity concerns. Precision of an estimate is only one part of interpreting a result; the endpoint's meaning and the trial's design and analysis limitations also matter.
The primary record does not report a clinically important threshold for this outcome. Consequently, the intervals can describe statistical precision around the mean differences, but they cannot determine by themselves whether the differences are important to patients or translate into differences in other outcomes.
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 | 6 | 8 |
| 75% of the observed effect | 10 | 13 |
| 50% of the observed effect | 22 | 29 |
The sample-size illustrations are expressed as participants per arm for the continuous-outcome comparisons in this trial, not as total event counts. They are planning illustrations based on the observed contrast and the variability estimated from posted summaries. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set as the stated fraction of the observed effect.
The 80% power column means the illustrated number of participants per arm for a design that would have an 80% chance of detecting the chosen effect under those assumptions, if the assumed effect and variability were correct. The 90% power column means the corresponding planning number for a 90% chance. These are design calculations, not guarantees that a future study would detect an effect.
The rows for 100% of the observed effect use the full observed contrast as the planning target. The 75% and 50% rows use smaller target effects. Smaller effects need more participants to detect under otherwise similar assumptions, so the illustrations generally require more participants per arm as the target effect is reduced.
These figures are not observed power. They do not describe the probability that this completed trial detected its result, and they should not be read as evidence that the original trial was planned with these assumptions. The original trial's sample-size justification and design assumptions are not reported in the registry record.
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 = 5.220; pooled standard deviation σ = 3.019.
- n = 2 × (1.96 + 0.842)2 × 3.0192 / 5.2202 = 5.3, rounded up to 6 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 <- 5.22 # observed difference in means
sigma <- 3.01891335381422 # 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(43186)
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 = 6 (80% power), 8 (90% power)
75% of observed effect: n per arm = 10 (80% power), 13 (90% power)
50% of observed effect: n per arm = 22 (80% power), 29 (90% power)
power.t.test: 6.4
Simulated power at n = 6 per arm: 0.769 (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) 5.87 | 4.59 to 7.16 | < 0.001 |
| ANCOVA | Mean Difference (Final Values) 6.33 | 5.01 to 7.65 | < 0.001 |
| ANCOVA | Mean Difference (Final Values) 5.35 | 4.07 to 6.64 | < 0.001 |
| ANCOVA | Mean Difference (Final Values) 3.84 | 2.60 to 5.07 | < 0.001 |
| ANCOVA | Mean Difference (Final Values) 7.50 | 6.13 to 8.87 | < 0.001 |
| ANCOVA | Mean Difference (Final Values) 5.52 | 4.19 to 6.85 | < 0.001 |
The registry reports the sponsor's primary comparisons using ANCOVA and labels the parameter as a mean difference in final values. For the denosumab schedules, the reported mean differences range from 3.84 to 7.50, and each comparison has p < 0.001. Each reported 95% confidence interval is above zero. These results are the trial's own reported inferential analyses.
The recalculated contrasts are simple, unadjusted calculations from the posted arm summaries. They closely track the sponsor's estimates in broad terms, but they are not the same analysis: ANCOVA is a model-based comparison, whereas the recalculation uses group summaries and an approximate pooled spread. The sponsor's analysis takes precedence as the trial-reported analysis. The registry record does not flag a discrepancy between the re-calculation and sponsor results.
That distinction does not mean that either estimate should be interpreted without context. The sponsor's adjusted model details, including its covariates, are not reported in the registry record. The recalculation is useful as a transparent descriptive check, but it cannot verify unreported model choices or replace analysis of participant-level data.
15. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when several statistical hypotheses are tested. Even if each test uses the same nominal significance threshold, the probability of at least one false-positive result across a family of tests can be greater than for a single test. This general issue is relevant in a multi-dose trial with several endpoints and time points.
The registry record lists 36 outcome measures and 279 analyses. It posts results for the primary Month 12 endpoint and multiple secondary outcomes, including later bone-density time points. The primary comparisons include several denosumab schedules against placebo. The sponsor reports p-values for those contrasts, while the recalculated p-values are unadjusted. Whether a multiplicity adjustment was planned or applied to the sponsor analyses is not reported in the registry record. The family of tests and any hierarchy among them are also not reported.
The primary analysis population is defined as randomized participants with non-missing baseline and Month 12 values. This makes clear that participants lacking either required measurement do not contribute to that endpoint analysis. The number excluded for missing values, reasons for missingness, and method for handling missing outcomes beyond the stated population are not reported in the registry record. No imputation or missing-at-random assumption should be inferred.
The registry does not report detailed protocol deviations, analysis-set definitions beyond the primary population, or sensitivity analyses for missing data. The full ANCOVA covariates and diagnostics are likewise not reported. These omissions limit the ability to assess how robust the estimates are to modeling decisions, missing outcomes, and multiple testing. They do not invalidate the posted results, but they constrain how strongly the inferential findings can be interpreted beyond the described analyses.
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 |
|---|---|---|---|
| Placebo | 5 | 46 | 10.9% |
| Denosumab 6 mg Q3M | 7 | 43 | 16.3% |
| Denosumab 14 mg Q3M | 13 | 44 | 29.5% |
| Denosumab 30 mg Q3M | 9 | 40 | 22.5% |
| Denosumab 14 mg Q6M | 7 | 53 | 13.2% |
| Denosumab 60 mg Q6M | 5 | 47 | 10.6% |
| Denosumab 100 mg Q6M | 9 | 41 | 22.0% |
| Denosumab 210 mg Q6M | 6 | 46 | 13.0% |
| Alendronate 70 mg | 8 | 46 | 17.4% |
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 |
|---|---|
| Placebo | 43 of 46 |
| Denosumab 6 mg Q3M | 38 of 43 |
| Denosumab 14 mg Q3M | 39 of 44 |
| Denosumab 30 mg Q3M | 35 of 40 |
| Denosumab 14 mg Q6M | 44 of 53 |
| Denosumab 60 mg Q6M | 42 of 47 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo | Denosumab 6 mg Q3M | Denosumab 14 mg Q3M | Denosumab 30 mg Q3M | Denosumab 14 mg Q6M | Denosumab 60 mg Q6M |
|---|---|---|---|---|---|---|---|
| Angina pectoris | Cardiac disorders | 1 of 46 | 2 of 43 | 0 of 44 | 0 of 40 | 0 of 53 | 0 of 47 |
| Osteoarthritis | Musculoskeletal and connective tissue disorders | 0 of 46 | 1 of 43 | 0 of 44 | 0 of 40 | 2 of 53 | 0 of 47 |
| Syncope | Nervous system disorders | 0 of 46 | 1 of 43 | 1 of 44 | 1 of 40 | 0 of 53 | 0 of 47 |
| Coronary artery disease | Cardiac disorders | 0 of 46 | 0 of 43 | 0 of 44 | 1 of 40 | 0 of 53 | 1 of 47 |
| Non-cardiac chest pain | General disorders | 0 of 46 | 0 of 43 | 1 of 44 | 0 of 40 | 1 of 53 | 0 of 47 |
| Breast cancer in situ | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 0 of 46 | 0 of 43 | 2 of 44 | 0 of 40 | 0 of 53 | 0 of 47 |
| Colon cancer | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 1 of 46 | 1 of 43 | 0 of 44 | 0 of 40 | 0 of 53 | 0 of 47 |
| Endometrial hyperplasia | Reproductive system and breast disorders | 0 of 46 | 0 of 43 | 0 of 44 | 1 of 40 | 1 of 53 | 0 of 47 |
| Chronic obstructive pulmonary disease | Respiratory, thoracic and mediastinal disorders | 1 of 46 | 0 of 43 | 1 of 44 | 0 of 40 | 0 of 53 | 0 of 47 |
| Acute coronary syndrome | Cardiac disorders | 0 of 46 | 0 of 43 | 0 of 44 | 1 of 40 | 0 of 53 | 0 of 47 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo | Denosumab 6 mg Q3M | Denosumab 14 mg Q3M | Denosumab 30 mg Q3M | Denosumab 14 mg Q6M | Denosumab 60 mg Q6M |
|---|---|---|---|---|---|---|---|
| Upper respiratory tract infection | Infections and infestations | 11 of 46 | 15 of 43 | 10 of 44 | 8 of 40 | 13 of 53 | 16 of 47 |
| Arthralgia | Musculoskeletal and connective tissue disorders | 14 of 46 | 7 of 43 | 13 of 44 | 9 of 40 | 12 of 53 | 11 of 47 |
| Back pain | Musculoskeletal and connective tissue disorders | 6 of 46 | 8 of 43 | 13 of 44 | 5 of 40 | 10 of 53 | 8 of 47 |
| Nasopharyngitis | Infections and infestations | 7 of 46 | 11 of 43 | 9 of 44 | 4 of 40 | 4 of 53 | 11 of 47 |
| Pain in extremity | Musculoskeletal and connective tissue disorders | 8 of 46 | 6 of 43 | 6 of 44 | 7 of 40 | 11 of 53 | 7 of 47 |
| Influenza like illness | General disorders | 5 of 46 | 4 of 43 | 4 of 44 | 3 of 40 | 10 of 53 | 11 of 47 |
| Sinusitis | Infections and infestations | 9 of 46 | 4 of 43 | 2 of 44 | 6 of 40 | 10 of 53 | 6 of 47 |
| Hypertension | Vascular disorders | 2 of 46 | 4 of 43 | 8 of 44 | 5 of 40 | 12 of 53 | 5 of 47 |
| Gastrooesophageal reflux disease | Gastrointestinal disorders | 2 of 46 | 8 of 43 | 2 of 44 | 5 of 40 | 8 of 53 | 8 of 47 |
| Headache | Nervous system disorders | 8 of 46 | 1 of 43 | 6 of 44 | 3 of 40 | 9 of 53 | 6 of 47 |
Serious events with the highest arm-level rate: angina pectoris (4.7%), breast cancer in situ (4.5%), non-cardiac chest pain (4.3%), osteoarthritis (4.3%), acute coronary syndrome (2.5%).
The adverse-event figures give the number at risk and the number affected by serious adverse events and other adverse events in each listed group. For example, the placebo group lists 5 serious adverse events among 46 at risk, and the denosumab 14 mg every 3 months group lists 13 among 44 at risk. These are counts for the registry's reported safety groups; they should not be converted into comparative risk estimates without an appropriate analysis.
Other adverse events are listed separately: 43 participants were affected among 46 at risk in the placebo group, and 39 among 44 at risk in the denosumab 14 mg every 3 months group. The figures are descriptive and do not establish that an event was caused by treatment. The registry also lists serious-event terms with percentages, including angina pectoris at 4.7%, breast cancer in situ at 4.5%, non-cardiac chest pain at 4.3%, and osteoarthritis at 4.3%. The record does not establish from these term figures a causal relationship or provide their arm-specific distribution.
Death counts are not reported in the registry record. Safety comparisons require attention to definitions, follow-up, exposure, and the number at risk; the posted counts alone do not support a general conclusion about comparative safety.
17. What the Result Does, and Does Not, Mean
The primary results describe average changes in a measured outcome: lumbar spine bone mineral density from baseline to Month 12. In the posted data, the placebo mean is negative and the denosumab arm means are positive. The reported ANCOVA comparisons and the recalculated unadjusted comparisons both place the estimated denosumab-versus-placebo mean differences above zero.
This is a finding about a continuous bone-density measure in the participants included in the endpoint analysis. It does not mean that every participant experienced an increase, and the group mean does not reveal the distribution of individual responses. It does not establish an effect on fractures, symptoms, quality of life, or other outcomes that are not reported as results in the registry record. Nor does a statistical difference alone establish that a difference is clinically important.
The trial studied several regimens and reports separate comparisons with placebo. The results do not provide a randomized head-to-head statistical comparison among all denosumab schedules. Comparing their displayed means or individual placebo contrasts is not a substitute for a direct dose-to-dose test. The record also does not provide enough information to infer a dose-response relationship or select a preferred regimen.
The results should be interpreted alongside the endpoint population definition, uncertainty intervals, missing-data information, and multiplicity limitations. The primary population includes randomized participants with both baseline and Month 12 measurements; the registry does not report further missing-data methods. The record's inferential details and multiplicity procedures are incomplete. These constraints call for a measured interpretation of the posted statistical results rather than a broad claim about treatment effects or clinical outcomes.
18. Why This Trial Matters Statistically
Statistically, this trial is informative because it reports a continuous primary endpoint across several dose and frequency schedules, with a placebo comparator and both arm-level means and sponsor ANCOVA contrasts. Those details let readers distinguish a description of group averages from a model-based comparison, and compare the sponsor's stated analysis with simple unadjusted re-calculations from the posted summaries.
The contrast between the primary Month 12 endpoint and later bone-density measurements also illustrates why time point and regimen matter. The trial includes multiple dose schedules, and some arm descriptions show changes in assigned treatment over the follow-up period. Later outcomes therefore need to be read in their own treatment and follow-up context rather than treated as interchangeable repetitions of the primary endpoint.
The record also illustrates an important limit of registry reporting. The results give detailed means, standard errors, confidence intervals, and p-values, but do not report the complete analysis plan, multiplicity procedure, missing-data method, or sample-size justification. Statistical estimates can be numerically precise while some design and analysis context remains unavailable. Transparent interpretation requires noting both what is quantified and what is not reported.
Finally, the sample-size illustrations are useful for understanding how planning requirements depend on the target effect, but they are not the original trial's design rationale and are not observed power. Keeping planning calculations separate from the completed trial's results prevents a common misreading of statistical summaries.
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 primary endpoint analysis is limited to randomized participants with non-missing baseline and Month 12 measurements. The registry record does not report the number of participants with missing endpoint values, why values were missing, or how missingness was handled beyond defining the analysis population. The Month 12 arm counts in the outcome results are therefore not a substitute for the trial's overall enrollment figure.
The registry does not report the sponsor ANCOVA covariates or the full model specification. The re-calculated comparisons use approximate pooled spread derived from summary information and are unadjusted; they are not participant-level analyses. The record does not report the multiplicity plan for the several dose comparisons and numerous outcome analyses.
The primary endpoint concerns bone mineral density at a particular anatomical site and time point. It does not report clinical events such as fractures as primary results in the registry entries, and the registry does not state a clinically important threshold for the measured change. Results at later visits involve different follow-up times and, for some arms, treatment schedules that changed after Month 21. The posted later outcomes should not be interpreted as if every arm received an unchanged regimen throughout follow-up.
The safety figures are descriptive counts and do not include death counts in the registry record. The registry entries do not provide a detailed adverse-event analysis plan or causal attribution. The record also does not report the original sample-size assumptions or the rationale for the selected enrollment. These trial-specific omissions limit assessment of design adequacy, robustness, and comparative safety from the registry results alone.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Determine the Efficacy, Safety and Tolerability of Denosumab (AMG 162) in the Treatment of Postmenopausal Women With Low Bone Mineral Density — NCT00043186.
- Registry record last updated 2013-09-18; status last verified 2013-09.
- Results first posted 2010-07-28.
- 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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Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.
23. Record Summary
NCT00043186 is a completed randomized, parallel-group phase 2 study of denosumab dose schedules compared with placebo in postmenopausal women with low bone mineral density. The registry lists enrollment of 412 and quadruple masking.
The primary endpoint was percent change in lumbar spine bone mineral density from baseline to Month 12, assessed by dual energy X-ray absorptiometry. The record reports positive denosumab-versus-placebo mean differences for each primary comparison, with sponsor ANCOVA p-values of p < 0.001. Recalculated unadjusted comparisons show the same overall direction.
Later bone-density outcomes and descriptive safety counts are also posted. Interpretation is limited by unreported details of multiplicity, missing-data handling, the full ANCOVA model, and the original sample-size justification. The results concern the measured endpoint and do not alone establish effects on other clinical outcomes.