Soy Protein and Breast Cancer Risk Reduction: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Soy Protein and Breast Cancer Risk Reduction (NCT00204477), a randomized phase 2 study. The primary outcome is Mammographic Density (Baseline).

2. Clinical Question

3. Trial Design

The registry describes a randomized, parallel-group phase 2 trial with quadruple masking. Its title is Soy Protein and Breast Cancer Risk Reduction, and the official title is Soybean Diet and Breast Density. The study is marked completed. The record gives a total enrollment of 321. Its listed start is 2002-04, and the primary completion date is 2011-07-22. Those dates describe the registry record; they do not by themselves explain how long individual participants received the drinks or how long they were followed.

The two dietary groups were soy milk and cow’s milk. The soy arm description specifies soy protein and calcium, and the cow’s milk arm description specifies casein protein and calcium. Both descriptions give the same intended schedule: two drinks in place of a small meal, five days per week. These are descriptions of the interventions, not evidence that every participant consumed the intended amount. Adherence information is not reported in the registry record.

Random allocation means that assignment was intended to use chance rather than a participant’s or clinician’s choice. A parallel design assigns participants to a group and compares groups, rather than having each participant receive both interventions in sequence. The registry labels masking as quadruple but does not identify which roles were masked or describe how masking was maintained. Further detail about randomization procedures, allocation concealment, eligibility, and the trial’s original statistical plan is not reported in the registry record.

The reported primary endpoint is mammographic density at baseline. The result includes 157 observations in each group, while the endpoint description notes missing or corrupt images. These endpoint counts and the record’s overall enrollment are different measures and should not be treated as interchangeable. The registry record lists no posted secondary results in the information.

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.

Baseline

One Year After Diet

Reasons for not completing this period:

Two Years After Diet

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: 4 participants images in the cow's milk and 3 images in soy milk were either missing or corrupt.

5. Baseline Characteristics

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

6. Primary Endpoint

The registry lists the primary outcome as Mammographic Density (Baseline), measured over Baseline.

Mammographic density is reported as the percentage of glandular tissue in the breast. The endpoint description says breast images were acquired by digital mammography, fibroglandular tissue was segmented from fatty tissue, and the total breast area was defined as the sum of those two tissue areas. Density is the fibroglandular area expressed as a percentage of the total breast area.

This measure represents breast composition rather than a cancer diagnosis. The trial summary identifies breast density and ovarian hormones as breast cancer risk markers and proposes that a dietary intervention might affect them. That rationale explains why density was of interest, but a marker is not itself a clinical cancer outcome. A difference in a marker would not, on its own, establish a change in cancer risk.

The primary endpoint is specifically labeled Baseline. The reported means therefore describe density at baseline in the two assigned groups. They do not describe an after-treatment value or a change from baseline. No post-intervention mammographic-density result is reported in the registry record. The endpoint description notes that 4 cow’s milk images and 3 soy milk images were missing or corrupt. It does not explain how these missing images were handled in the analysis.

7. Results Posted in the Registry

• Cow's Milk: mean 28.24 versus 29.21 on control; difference -0.97 (95% CI -3.54 to 1.60), standardized effect d = -0.08; z-test p = 0.459.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: mammographic density is recorded as a percentage, and the registry reports a mean and standard deviation for each group. A mean describes the center of a set of measurements, while a standard deviation describes how dispersed individual measurements are around that mean. These summaries are useful for comparing group averages, but they do not show the complete distribution or identify possible outliers.

What does the mean difference represent?

The comparison reports Cow’s Milk relative to Soy Milk. It uses the listed means of 28.24 and 29.21 and reports a difference of -0.97. The negative sign indicates that the reported Cow’s Milk mean is lower than the Soy Milk mean. This is a contrast in baseline values. It is not a treatment-effect estimate, because the reported endpoint is baseline mammographic density rather than change after treatment or an endpoint measured after treatment.

In general, a difference between group means is easy to interpret in the original measurement units. Here, the units are percentage of glandular tissue in the breast. A standardized mean difference expresses a contrast in standard-deviation units, which can help describe the size of a contrast relative to observed variability. The registry reports a standardized difference of -0.084. Standardization does not make the result a causal treatment effect and does not replace interpretation in the original units.

What do the standard deviations tell the reader?

The reported standard deviations are 11.44 for Soy Milk and 11.77 for Cow’s Milk. They describe variation among the measurements within each group, not uncertainty in the group means. The standard error is a measure of sampling uncertainty in a mean estimate; the reported standard errors are 0.913 and 0.939. In general, standard errors are used to construct confidence intervals and test statistics. They should not be read as a description of how far apart individual participants’ measurements are likely to be.

The comparison also reports a pooled standard deviation of 11.61. In general, pooling combines information about within-group variability under an approach that treats the groups’ variability as sufficiently comparable for that calculation. A standardized mean difference based on a pooled standard deviation uses that common scale. The registry record does not report a separate justification for the variance assumptions or additional diagnostics.

How should the p-value be understood?

The unadjusted p-value is 0.459. In general, a p-value is calculated under a specified null model and describes how often results at least as incompatible with that model would arise through sampling variation if the model were true. It is not the chance that an observed result occurred “by chance,” the probability that there is no effect, or a measure of clinical importance. A comparatively large p-value does not establish equivalence or rule out meaningful differences.

“Unadjusted” indicates that the reported p-value has not been adjusted for multiple comparisons. The registry record does not report how many hypotheses were planned, whether this comparison was selected before examining the data, or what multiplicity procedure, if any, was prespecified. No adjustment should be inferred from the trial design label or from the fact that the record lists multiple outcome measures.

Why does the confidence interval matter?

The reported 95% confidence interval for the mean difference extends from -3.537 to 1.597. In general, a confidence interval is a range generated by a procedure that, under its assumptions and repeated use, would cover the target parameter at the stated rate. For a single trial, it gives a range of estimates compatible with the data and model, rather than a guarantee that the true value lies inside it. This interval includes no difference and also includes values in both directions. Its width signals that the point estimate should not be treated as exact.

Confidence intervals depend on the analysis and its assumptions, including how observations are treated and how variability is estimated. The registry record does not describe a full analysis model, adjustment covariates, missing-data method, or sensitivity analyses. The reported summary statistics allow a simple unadjusted comparison to be described, but they do not reveal whether an adjusted analysis was planned or performed. The record lists zero analyses, so no additional analysis details can be inferred from a posted analysis entry.

Why can over-dispersion matter in other settings?

In general, over-dispersion means that observed variability is greater than a statistical model expects. If ignored, standard errors can be too small, confidence intervals too narrow, and p-values misleading. This issue is especially relevant to count outcomes modeled under assumptions about variability. The primary endpoint is continuous and reported with means and standard deviations; the registry record does not report an over-dispersion analysis. The general concept should not be mistaken for a finding about this trial.

Finally, statistical significance and scientific meaning are different questions. The estimate, its uncertainty, the endpoint’s timing, the measurement process, and the analysis population all matter. In this trial record, the baseline timing is especially important: even a precise baseline difference would not by itself demonstrate an effect of the assigned dietary regimen.

10. Confidence Intervals and Precision

The mean-difference estimate is -0.97, with a reported 95% confidence interval from -3.537 to 1.597. The point estimate gives a single best estimate under the reported comparison, but the interval shows that the estimate is uncertain. It includes no difference and extends to values in both directions. Thus the data do not pin down the direction of a baseline group difference with precision.

In general, a confidence interval is a measure of statistical uncertainty, not a range containing a specified proportion of individual participants’ measurements. It also is not a statement that every value inside the interval is equally likely. The interval is tied to the statistical procedure and assumptions used to calculate it. Details of a complete model and missing-data handling are not reported in the registry record.

The standard deviations, 11.44 for Soy Milk and 11.77 for Cow’s Milk, describe variation across the observed measurements. They are much larger than the absolute point estimate, consistent with substantial variation relative to the observed separation of the means. The reported standard errors, 0.913 and 0.939, describe uncertainty in the group means rather than variation among individuals.

Precision should be considered alongside endpoint timing. The interval concerns a baseline comparison; it does not quantify uncertainty in a post-treatment contrast or in a change from baseline. Nor does the interval establish equivalence: no equivalence margin or equivalence analysis is reported. The unadjusted p-value of 0.459 and the confidence interval address related questions about the baseline mean contrast, but neither resolves the absence of a reported post-intervention primary result.

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 participants or total events. They are illustrative calculations based on the observed effect, rather than the trial’s original design. The record gives the planning assumptions: a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses the stated fraction of the observed effect as the effect to detect.

The 80% power column describes the number of participants per arm in a hypothetical study that would have an 80% probability of detecting the specified effect under those assumptions, if that effect were the true one and the model assumptions held. The 90% power column represents a higher target probability of detection for that same specified effect. These are planning targets, not guarantees about what a future study will find. The displayed values are not observed power.

The planning scenarios consider 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. The corresponding participants-per-arm figures are 2,248 and 3,009 for 80% and 90% power at 100% of the observed effect; 3,996 and 5,349 at 75%; and 8,990 and 12,035 at 50%. The pattern illustrates a general principle: smaller effects are harder to detect, so they require more participants under otherwise unchanged assumptions.

These illustrations should not be read as a claim about what the completed trial was designed to detect. The trial’s own original sample-size assumptions and justification are not reported in the registry record. The observed comparison is a baseline mean difference, so planning from it does not establish the sample size needed for a post-intervention effect or for another endpoint. The plotted planning curve represents the same general relationship between the assumed effect size and required sample size; its values remain hypothetical planning quantities.

12. How the Sample Size Is Derived

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

Formula

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

Worked calculation for this trial

1. Observed difference Δ = -0.970; pooled standard deviation σ = 11.606.
2. n = 2 × (1.96 + 0.842)² × 11.606² / -0.970² = 2,247.4, rounded up to 2,248 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 <- -0.970000000000002                      # observed difference in means
sigma <- 11.6061729265077                     # 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(204477)
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 = 2,248 (80% power), 3,009 (90% power)
 75% of observed effect: n per arm = 3,996 (80% power), 5,349 (90% power)
 50% of observed effect: n per arm = 8,990 (80% power), 12,035 (90% power)
power.t.test: 2248.3 
Simulated power at n = 2,248 per arm: 0.800 (20000 replicates)

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

13. Multiplicity, Missing Data and Analysis Populations

The registry record lists 11 outcome measures and zero analyses. It also lists no posted secondary results in the information. Those counts do not establish how many hypotheses were tested or whether analyses were conducted outside the registry record. The analysis plan, prespecified outcome hierarchy, and any multiplicity adjustment are not reported in the registry record.

Multiplicity arises when several outcomes, time points, subgroups, or statistical tests are considered. In general, testing many hypotheses can increase the chance that at least one result appears noteworthy even if none reflects a real effect. Statistical approaches can address this issue, but the appropriate approach depends on the planned questions and analysis. It cannot be determined from the listed count of outcome measures whether the reported unadjusted p-value was part of a larger family of tests or how any other tests were handled.

The primary endpoint description states that 4 cow’s milk images and 3 soy milk images were missing or corrupt. The outcome summaries report 157 observations for each arm. The record does not explain how the unavailable images affected the analysis, whether missingness was related to participant or image characteristics, or whether any imputation or sensitivity analysis was used. In general, missing-data methods rely on assumptions; different assumptions can lead to different estimates. No particular method should be attributed to this trial from the available record.

The analysis population is also not described in sufficient detail to determine whether the reported summaries include all randomized participants, only participants with usable images, or another defined set. Although the study is identified as randomized, the record does not specify whether analyses followed assigned groups or whether participants were excluded after randomization. Such details matter for interpreting comparisons and potential bias.

Participant flow, protocol deviations, and reasons for missing images are not reported in the registry record. The record also does not provide a statistical analysis plan, model covariates, interim-analysis information, or sensitivity analyses. These absences limit assessment of whether the reported result corresponds to the intended analysis and how robust it may be to alternative assumptions.

14. Safety Results

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

Deaths

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 serious adverse event figures report zero affected participants in each group: the Soy Milk group lists 161 at risk and 0 affected, and the Cow’s Milk group lists 160 at risk and 0 affected. Deaths are reported as 0 in each group. The record gives no top serious adverse-event terms.

Other adverse events are reported as 28 affected in the Soy Milk group, with 161 at risk, and 21 affected in the Cow’s Milk group, with 160 at risk. These are counts as recorded, not estimates of comparative risk. No percentages or rate comparisons are reported, and none should be inferred by treating the counts as a complete account of all possible harms.

In general, an adverse event is an event recorded during a study and is not necessarily caused by the intervention. The registry record does not provide event definitions, severity details for the other events, timing, duration, attribution, or information about repeated events in the same participant. The counts therefore describe the posted safety summaries, not a causal comparison. The listed at-risk counts should not be conflated with the endpoint-analysis counts for mammographic density.

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

The posted result describes baseline mammographic density in the two randomized groups. The Soy Milk mean is 29.21 and the Cow’s Milk mean is 28.24. The reported mean difference for Cow’s Milk relative to Soy Milk is -0.97, and its 95% confidence interval runs from -3.537 to 1.597. The interval includes no difference and values in either direction, so the estimate does not establish a clear baseline separation.

That finding is not a test of whether soy milk reduced mammographic density. The endpoint is explicitly labeled Baseline, and the reported comparison does not describe change after the dietary intervention. The trial summary proposes a hypothesis involving ovarian steroid hormones and density, but the record does not provide a post-intervention result for the primary endpoint or a posted secondary result. The result therefore cannot establish an effect on hormones, density over time, breast cancer incidence, or breast cancer risk.

A nonsignificant or imprecise comparison is not proof that two groups are identical. Demonstrating equivalence would require an appropriate design, a prespecified margin for an acceptable difference, and a suitable analysis. Those elements are not reported in the registry record. Conversely, the fact that the trial was randomized does not make every reported contrast a treatment effect: timing and analysis matter, and the reported density measure is at baseline.

The safety summary reports zero serious adverse events and zero deaths in each group, alongside counts for other adverse events. Those descriptive counts do not establish that an intervention is safe or unsafe, because event definitions, follow-up, attribution, and detailed analysis are not reported. Taken together, the available results are informative about the recorded baseline density summaries and posted adverse-event counts, but they do not answer the proposed treatment-effect question.

16. Why This Trial Matters Statistically

This trial illustrates why an endpoint’s timing is essential to interpretation. Mammographic density is described as a percentage of glandular tissue, and the study summary identifies density as a breast cancer risk marker. Yet the primary result is labeled Baseline. A group comparison at baseline describes the groups before the endpoint is being used to evaluate a treatment response; it cannot substitute for a comparison of post-intervention outcomes or changes.

The record also demonstrates the difference between a point estimate and its precision. A mean difference of -0.97 is accompanied by a confidence interval that includes values on both sides of no difference. Reporting the interval makes clear that a small point estimate is not the same as a precise estimate of no effect. Likewise, a p-value alone cannot establish equivalence or clinical importance.

There is a second statistical lesson in distinguishing measurement variation from uncertainty in the group means. The standard deviations describe variation among observed density measurements, whereas standard errors and confidence intervals concern uncertainty in estimated means and contrasts. Keeping these quantities separate helps avoid interpreting a group summary as if it described every participant.

Finally, randomization, masking, and an intervention description do not fill gaps in outcome reporting. The registry identifies randomized allocation and quadruple masking, but the masking roles, missing-image handling, analysis population, and trial-specific analysis plan are not reported. Statistical conclusions depend on these details as well as on the design label. The record therefore offers a useful example of how to read the result that is posted while keeping the proposed clinical question distinct from the outcome information actually available.

17. Limitations

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

The main limitation for interpreting the primary result is that mammographic density is reported at baseline. No post-intervention primary result or change-from-baseline estimate is reported in the registry record. The comparison therefore cannot be interpreted as the effect of soy milk relative to cow’s milk.

The endpoint description notes 4 missing or corrupt images in the cow’s milk group and 3 in the soy milk group. The record does not explain why images were unavailable, how the missing observations were handled, or whether results were checked under alternative missing-data assumptions. The reported endpoint counts are not accompanied by enough information to identify the analysis population or participant flow.

The record does not report eligibility criteria or characteristics needed to describe how participants compare with a broader population. It also does not give adherence results, so the intervention descriptions indicate the intended regimen rather than what participants actually consumed. Details of the masking procedures and the specific roles masked are absent.

The analysis plan, covariate adjustment, multiplicity handling, interim analyses, and original sample-size justification are not reported. The registry lists 11 outcome measures, zero analyses, and no posted secondary results in the information. The unadjusted comparison and planning illustrations cannot fill those gaps. Safety summaries also lack event definitions, detailed severity information for other events, timing, and attribution. These limitations restrict both causal interpretation and assessment of the completeness of outcome and safety reporting.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Soy Protein and Breast Cancer Risk Reduction — NCT00204477.
• Registry record last updated 2024-01-23; status last verified 2023-12.
• Results first posted 2024-01-23.
• 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

NCT00204477 is a completed phase 2 randomized, quadruple-masked, parallel-group trial comparing soy milk with cow’s milk. The registry gives enrollment as 321 and lists the start as 2002-04 and primary completion as 2011-07-22.

The primary outcome is mammographic density at baseline, measured as the percentage of glandular tissue in the breast. The reported means are 29.21 for Soy Milk and 28.24 for Cow’s Milk. The reported mean difference for Cow’s Milk relative to Soy Milk is -0.97, with a 95% confidence interval from -3.537 to 1.597 and an unadjusted p-value of 0.459.

The result is a baseline comparison, not a reported intervention effect. The record notes missing or corrupt images in both groups, but does not describe their handling. It reports zero serious adverse events and zero deaths in each group, and counts of other adverse events of 28 and 21. No secondary results are posted in the record.