Vitamin D and Breast Cancer Biomarkers in Female Patients: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Vitamin D and Breast Cancer Biomarkers in Female Patients (NCT01224678), a randomized phase 3 study. The primary outcome is Percent Change (Between Baseline and Month 12) in Mammographic Density by the Boyd Method Compared Between Arms.

2. Clinical Question

3. Trial Design

The registry describes a phase 3, randomized, double-masked, parallel-group trial. Participants were assigned to vitamin D or placebo. The vitamin D arm received oral vitamin D, 2000 IU once daily for 12 months; the placebo arm received oral placebo once daily for the same duration. The registry lists breast cancer as the condition and describes the trial as studying vitamin D and breast cancer biomarkers in female patients.

The planned enrollment was 300. The registry reports that 86 of the 300 patients were analyzed for the primary endpoint, and the posted endpoint results give arm-specific analyzed counts of 40 for vitamin D and 46 for placebo. The record does not explain the difference between planned enrollment and the reported endpoint analysis population, nor does it provide participant flow or reasons for exclusion from this analysis.

The study began in 2010-10, had a primary completion date of 2014-12, and is listed as completed. The primary outcome was percent change in mammographic density by the Boyd method between baseline and month 12. Although the record describes the target population for the endpoint as premenopausal women, it does not report additional eligibility criteria, the randomization procedure, allocation concealment, or the details of how masking was maintained. The trial's original statistical design assumptions and its prespecified 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.

Overall Study

Analysis population for the primary outcome, as defined in the registry: 86 of the 300 patients were analyzed for the primary endpoint

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.

Population: All patients were used for baseline analysis

6. Primary Endpoint

The registry lists the primary outcome as Percent Change (Between Baseline and Month 12) in Mammographic Density by the Boyd Method Compared Between Arms, measured over 12 months.

The primary endpoint is the percent change in mammographic density from baseline to month 12, assessed using the Boyd method. Mammographic density is a breast imaging measure; in this trial it serves as a biomarker rather than a direct measure of breast cancer incidence, survival, or another clinical event. The record describes the endpoint as a way to evaluate change after one year of vitamin D supplementation compared with placebo in premenopausal women.

The reported outcome is continuous, and the registry summarizes each arm with a mean and standard deviation. A mean describes the average percent change among participants included in the endpoint analysis. The standard deviation describes how spread out individual measurements were around that arm's mean. These summaries can help convey both the direction of the average change and variation among analyzed participants, but they do not describe every participant's response.

Using a biomarker can allow a trial to study a measurable biological or imaging outcome over a defined period. However, a difference in a biomarker does not by itself establish a difference in cancer occurrence or other patient-important outcomes. The registry record does not report secondary outcome results or link the mammographic-density result to subsequent clinical outcomes.

7. Results Posted in the Registry

• Vitamin D: mean -1.40 versus -3.40 on control; difference 2.00 (95% CI -2.22 to 6.22), standardized effect d = 0.21; z-test p = 0.353.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry reports a continuous endpoint summarized as a mean, with standard deviation as the measure of dispersion. The primary contrast is a mean difference between arms. The reported estimate of 2.0 is expressed in percentage-change units and compares the vitamin D arm with placebo. The arm means are -1.4 for vitamin D and -3.4 for placebo. The registry's comparison also reports a 95% confidence interval and an unadjusted p-value.

What does a mean difference describe?

A mean difference compares the average observed outcome in one group with the average in another. It retains the outcome's units, which makes it possible to interpret the estimate on the scale of percent change in mammographic density. The contrast's direction depends on which arm is subtracted from which. Here, the posted comparison is vitamin D minus placebo, so positive values indicate a higher mean percent change in the vitamin D arm than in the placebo arm. This describes the direction of the comparison, not whether the difference is clinically important.

A group mean does not show the distribution of individual observations. The standard deviation gives a measure of spread around the mean: a larger standard deviation indicates more variation in the measured values within that group. The reported standard deviations are 11.9 for vitamin D and 7.1 for placebo. They describe variability in the analyzed endpoint values; they are not standard errors and do not directly express uncertainty about the estimated mean difference.

How should the p-value be read?

General statistical explanation: a p-value describes how unusual data at least as incompatible with a specified null hypothesis would be under the assumptions of a particular statistical test. It is not the probability that the null hypothesis is true, nor is it the probability that the result occurred by chance. The posted unadjusted p-value is 0.353. Because the registry record does not report the test, its assumptions, or the prespecified inferential plan, this value cannot by itself provide all details needed to reproduce the analysis.

The term “unadjusted” indicates that the posted p-value is presented without a reported adjustment for multiple comparisons. The registry lists one outcome measure, no posted secondary outcome results, and zero analyses. It does not report whether other comparisons were planned or whether any multiplicity procedure was specified. Therefore, the record does not establish whether or how multiplicity was handled in the trial's original analysis.

What does the confidence interval add?

General statistical explanation: a confidence interval gives a range of values compatible with the observed data under the method's assumptions. It communicates uncertainty about an estimate and is more informative about possible effect sizes than a p-value alone. The reported interval for the mean difference ranges from -2.22 to 6.22. Because it spans negative and positive values, the posted results do not pin down the direction of the underlying difference with high precision. A confidence interval is not a range containing a known proportion of individual participant outcomes, and it does not remove uncertainty about the analysis population or missing data.

The registry record does not state how the interval was calculated, whether the comparison was adjusted for baseline values or other covariates, or whether any model was used. It also does not report assumptions concerning the distribution of the outcome or the handling of outliers. These analysis details matter because statistical estimates and their uncertainty depend on the method used. Without a reported plan and method, the posted summaries can be described, but the analysis cannot be fully reproduced from the registry record.

What limits a reanalysis?

The record provides arm-level sample sizes, means, standard deviations, and a comparison estimate with its interval and p-value. It does not provide individual participant measurements or enough details to reconstruct all analysis choices. The primary endpoint population is described as 86 of the 300 patients, while the results report analyzed arm counts of 40 and 46. The record does not explain which participants were excluded, whether endpoint data were missing, or how such data were treated. No recalculated analysis is needed to describe the posted comparison, and no alternative inferential result should be inferred from these summary statistics alone.

10. Confidence Intervals and Precision

The estimated mean difference in percent change in mammographic density was 2.0, comparing vitamin D with placebo. Its 95% confidence interval runs from -2.22 to 6.22. The interval is wide enough to include negative values, zero, and positive values. In practical terms, the posted estimate does not narrowly determine either the direction or size of the difference compatible with the analysis.

General statistical explanation: a confidence interval reflects sampling uncertainty under the statistical method used to construct it. A narrower interval generally indicates greater precision for the estimated contrast, while a wider interval leaves more uncertainty about plausible effect sizes. The interval is not a statement about the range of individual changes, and it does not capture every source of uncertainty, such as uncertainty from missing data, measurement procedures, or choices in the analysis plan.

The registry record does not report the method used to calculate the interval, the prespecified primary analysis, or adjustments for baseline measurements or other variables. It reports 86 participants analyzed for the endpoint, with 40 in the vitamin D arm and 46 in the placebo arm. The endpoint analysis group is smaller than the planned enrollment of 300, but the record does not explain the participant flow or the reason for the difference. These details limit what can be concluded about why the interval has its observed precision and how representative the analyzed group is of all enrolled participants.

The interval should be considered alongside the arm-level standard deviations, 11.9 for vitamin D and 7.1 for placebo, which describe variability among the analyzed outcome values. Neither the standard deviations nor the confidence interval alone establish clinical importance. The endpoint is a biomarker, and the registry does not report a threshold for a meaningful change in mammographic density or a relationship between this contrast and later clinical outcomes.

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 planning figures are participants per arm, not total event counts. They are illustrations based on the observed mean difference, not a report of the trial's original design calculation. The listed assumptions are a two-sided significance level of 0.05, equal allocation between arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The registry record does not report the trial's own original sample-size assumptions.

For each stated effect assumption, the 80% power column gives the participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting that effect under the listed assumptions, if the assumptions hold. The 90% power column gives the corresponding planning number for a 90% chance. These are design illustrations; they are not the number of participants actually analyzed and do not describe the probability that the trial's observed result is true.

The entries consider planning for 100%, 75%, and 50% of the observed effect. The estimated participants per arm increase as the effect being planned for becomes smaller: detecting a more modest difference generally requires more information, often obtained by enrolling more participants. This relation is a general feature of statistical power planning, not evidence that a particular sample size guarantees a definitive result.

The displayed planning values are not observed power. The record does not establish that these calculations were used to design the trial, and they should not be read as an explanation of the difference between planned enrollment and the reported primary endpoint analysis population. The registry does not report why 86 of the 300 patients were analyzed for the primary endpoint.

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 = 2.000; pooled standard deviation σ = 9.631.
2. n = 2 × (1.96 + 0.842)² × 9.631² / 2.000² = 364.0, rounded up to 365 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 <- 2                      # observed difference in means
sigma <- 9.63082847645295                     # 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(1224678)
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 = 365 (80% power), 488 (90% power)
 75% of observed effect: n per arm = 648 (80% power), 867 (90% power)
 50% of observed effect: n per arm = 1,457 (80% power), 1,950 (90% power)
power.t.test: 365 
Simulated power at n = 365 per arm: 0.801 (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 lists one outcome measure and reports the primary endpoint as percent change in mammographic density between baseline and month 12. It lists zero posted secondary outcomes and zero analyses. This describes what is present in the registry record; it does not establish that the trial had no other planned outcomes, comparisons, or analyses.

The record does not report a multiplicity strategy, such as a prespecified method to control the chance of false-positive findings across multiple tests. The posted p-value is described as unadjusted. Without a full protocol or statistical analysis plan in the registry, it is not possible to determine whether other endpoints or analyses were prespecified, whether any multiplicity adjustment was planned, or how the primary endpoint was prioritized among potential analyses.

The primary endpoint population is reported as 86 of the 300 patients, and the results give analyzed counts of 40 for vitamin D and 46 for placebo. The registry does not report a participant flow diagram, reasons for non-analysis, the number with missing month 12 measurements, or how missing measurements were handled. It also does not state whether the analysis followed intention-to-treat, per-protocol, or another population definition. These omissions make it difficult to assess whether the analyzed participants differed from those not included in the endpoint summaries.

The record does not report imputation procedures, sensitivity analyses for missing data, covariate adjustment, or the statistical model used for the comparison. It also does not report the trial's original sample-size justification, interim analyses, or a full analysis plan. These details should not be inferred from the posted arm summaries or from the planning illustration. Consequently, the registry supports a description of the reported endpoint results, but not a complete assessment of the trial's analysis choices or robustness to missing data and multiplicity.

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 0% reporting threshold.

Most frequent non-serious adverse event terms

The registry reports serious adverse event counts of 0 among 150 participants at risk in the placebo arm and 0 among 150 participants at risk in the vitamin D arm. It reports other adverse event counts of 1 among 150 at risk in each arm. The listed counts are registry summaries and should be read with their stated at-risk denominators.

The record does not list serious adverse event terms. It does not report event descriptions, severity gradings, attribution to study treatment, timing, or the method used to collect and classify events. The serious adverse event counts should not be interpreted as evidence that no events of any kind occurred: the registry separately lists other adverse events, and the event categories are not interchangeable.

Deaths are not reported in the registry record. The adverse-event at-risk counts are distinct from the primary endpoint analysis counts described for mammographic density; the record does not explain their relation to enrollment or follow-up. These safety figures are descriptive and do not by themselves provide a complete comparative safety assessment.

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

The posted primary endpoint results describe mean percent change in mammographic density at month 12. The mean was -1.4 in the vitamin D arm and -3.4 in the placebo arm, and the estimated mean difference was 2.0 percentage points for vitamin D minus placebo. The 95% confidence interval, from -2.22 to 6.22, spans values on either side of zero, and the unadjusted p-value is 0.353. The results therefore leave uncertainty about the direction and size of the difference compatible with the analysis.

These findings concern a continuous imaging biomarker in the reported endpoint analysis population. They do not directly report breast cancer incidence, cancer progression, survival, or another clinical endpoint. The registry rationale refers to possible prevention, but the posted primary outcome is mammographic density, not a measure of whether cancer developed or changed over time. No conclusion about a clinical benefit or lack of benefit follows from this biomarker comparison alone.

The result also cannot be treated as a complete description of every participant's response. Arm means summarize analyzed measurements, while the standard deviations describe variation among those measurements. The record reports 86 patients analyzed for the primary endpoint, but does not explain why that population differs from planned enrollment or how missing endpoint data were handled. This limits assessment of how the reported averages relate to all enrolled participants.

Finally, the registry record does not provide the full statistical analysis plan, the test or model used, or details on adjustments and sensitivity analyses. The reported estimate and interval are useful for describing the posted comparison, but the available record does not support stronger claims about mechanism, clinical importance, or outcomes beyond the measured endpoint and follow-up period.

16. Why This Trial Matters Statistically

This trial is statistically informative because it illustrates the difference between an estimated effect and the precision with which that effect is known. The mean difference is reported as 2.0 percentage points, while the confidence interval extends from -2.22 to 6.22. A single point estimate can look definite when read alone; the interval makes clear that multiple directions and sizes of difference remain compatible with the posted result.

The endpoint is continuous and measured as percent change in mammographic density. The arm means and standard deviations communicate both average change and within-arm spread, while the between-arm estimate addresses the comparative question. These statistics answer different questions: the standard deviations describe observed variation, and the confidence interval describes uncertainty about the estimated contrast under the analysis method. They should not be treated as interchangeable measures.

The record also highlights why analysis populations matter. Planned enrollment was 300, while the registry says 86 patients were analyzed for the primary endpoint. The result includes arm-specific analysis counts, but the registry does not explain participant flow, missing measurements, or the analysis population definition. Without these details, readers cannot fully assess selection into the endpoint analysis or reconstruct how the comparison was obtained.

Finally, a biomarker endpoint should be distinguished from a clinical outcome. Mammographic density is the measured outcome in this record; breast cancer incidence and other clinical outcomes are not reported as primary results. The example underscores that statistical interpretation depends not only on a p-value, but also on the outcome's meaning, the analysis population, the uncertainty interval, and the completeness of the reported methods.

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 primary endpoint analysis includes 86 of the planned 300 patients, according to the registry record. Although the posted results report arm-specific analyzed counts, the record does not explain participant flow, reasons for non-analysis, or whether endpoint values were missing. It also does not describe the analysis population definition or how missing data were handled. These gaps limit assessment of whether the analyzed group represents all enrolled participants.

The registry does not report baseline mammographic density by arm, participant characteristics for the analyzed population, or details of adherence to the daily study regimens. It does not describe the methods used to measure or assess mammographic density beyond naming the Boyd method. Further information about measurement procedures, quality control, and assessor masking is not reported in the registry record.

The statistical plan is also incomplete in the registry. The analysis method, any adjustment for baseline values or other factors, the construction method for the confidence interval, and the prespecified significance threshold are not reported. The registry lists zero analyses and zero secondary outcome results; it does not clarify whether other analyses were planned or conducted. The original sample-size assumptions and any interim analyses are not reported.

The reported endpoint is a biomarker assessed at month 12. The record does not provide later follow-up results or report breast cancer incidence and other clinical outcomes. Safety information is limited to the posted serious and other adverse event counts; event descriptions, attribution, and deaths are not reported. These limitations restrict interpretation to the registry's reported summaries and do not support broader conclusions about clinical outcomes or the full safety profile.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Vitamin D and Breast Cancer Biomarkers in Female Patients — NCT01224678.
• Registry record last updated 2024-10-08; status last verified 2024-09.
• Results first posted 2018-06-25.
• 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

The registry lists a completed, phase 3, randomized, double-masked, parallel-group trial of oral vitamin D versus oral placebo in female patients with breast cancer. Both interventions were taken once daily for 12 months. Planned enrollment was 300, and the primary endpoint was percent change in mammographic density by the Boyd method between baseline and month 12.

The registry reports that 86 patients were analyzed for the primary endpoint. The mean percent change was -1.4 in the vitamin D arm and -3.4 in the placebo arm. The estimated mean difference was 2.0, with a 95% confidence interval from -2.22 to 6.22 and an unadjusted p-value of 0.353. The record does not report the full statistical analysis plan, participant flow, or missing-data handling.

Serious adverse events were recorded as 0 among 150 at risk in each arm; other adverse events were recorded as 1 among 150 at risk in each arm. Deaths are not reported in the registry record. The primary result is a biomarker comparison and does not report a clinical breast cancer outcome.