Dietary Fat, Eicosanoids and Breast Cancer Risk: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Dietary Fat, Eicosanoids and Breast Cancer Risk (NCT01824498), a randomized na study. The primary outcome is E2.

2. Clinical Question

3. Trial Design

The registry record describes a randomized, unmasked crossover trial. Its listed dietary conditions were a high-fat diet, a low-fat diet, and a low-fat diet with high n3 fatty acids. Six different orders of these diets are listed, consistent with participants receiving diets in different sequences. The registry does not report how the sequences were assigned, the length of any interval between diets, or whether the analysis accounted for period or carryover effects.

Enrollment was 18. Each diet's posted outcome entry has an n of 18. Because this is a crossover design, those entries should not be added as if they necessarily represented separate groups of people: the same participant may contribute measurements under more than one diet. The registry record does not give a participant flow or explain whether every enrolled participant completed every diet period.

The primary outcome was E2, described as estradiol, with a timeframe of 8 weeks. The posted values are least-squares means with standard errors. The two reported comparisons use the high-fat diet as the reference and estimate mean differences for the low-fat diet and the low-fat, high n3 diet. The record lists the study as completed and gives its start as 2004-01 and primary completion as 2008-12. The trial's original sample-size assumptions and the detailed analysis plan are not reported in the registry record.

4. Participant Flow and Accounting

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

Before assignment: Subjects enrolled prior to randomization (N=18)

1st Intervention (8 Weeks)

Washout (8 Weeks)

Reasons for not completing this period:

2nd Intervention (8 Weeks)

Washout (8 Weeks)

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 7 groups are shown.

6. Primary Endpoint

The registry lists the primary outcome as E2, measured over 8 weeks.

The primary endpoint was estradiol, identified as E2 and measured in pmol/L. Estradiol is a sex hormone, so its concentration is a biochemical measure relevant to the study's stated question about whether diets designed to increase circulating n3 fatty acids affect sex hormone distribution. The registry frames the question around biochemical markers associated with sex hormone-mediated cancer risk.

The outcome timeframe was 8 weeks. For each diet condition, the registry reports a least-squares mean and a standard error. A least-squares mean is a model-based estimate of an average; the registry record does not describe the model or its adjustment variables. The standard error describes uncertainty in that estimated mean, rather than the spread of individual participants' measurements.

Estradiol concentration is not a measure of breast cancer occurrence, diagnosis, or mortality. The posted endpoint therefore addresses a short-term biochemical outcome, not whether any diet changes cancer risk. The registry record does not report the specimen collection method, timing within the diet period, or a clinically meaningful threshold for interpreting a difference in E2.

7. Results Posted in the Registry

• Low Fat Diet: mean 35.60 versus 52.80 on control; difference -17.20 (95% CI -31.76 to -2.64), standardized effect d = -0.77; z-test p = 0.021.
• Low Fat, High n3 Diet: mean 39.80 versus 52.80 on control; difference -13.00 (95% CI -27.14 to 1.14), standardized effect d = -0.60; z-test p = 0.071.

8. Statistical Interpretation

9. Statistical Methods Explained

What does a least-squares mean represent?

In general, a least-squares mean is an estimated average from a statistical model. It can differ from a simple arithmetic average when the model includes factors or adjustments. The registry labels the primary outcome values as least-squares means, but the model specification, adjustment variables, and handling of the crossover observations are not reported in the registry record. For that reason, the values can be described as model-based means, but the exact model cannot be reconstructed from the record.

What does the mean difference represent?

The posted contrasts are expressed as the mean for a diet compared with the high-fat diet. A negative value indicates that the estimated mean for the named diet is lower than the high-fat estimate, under that subtraction order. The reported differences are -17.2 pmol/L for low fat versus high fat and -13.0 pmol/L for low-fat, high n3 versus high fat. They are estimates of contrasts, not counts of participants or individual changes. The registry does not post a contrast between the two low-fat conditions.

What does the standard error describe?

In general, a standard error describes the precision of an estimated quantity across repeated samples under a statistical model. A smaller standard error indicates less sampling uncertainty for that estimate, whereas it does not describe how much individual observations vary. The posted standard errors for the three diet means are 5.1, 5.4, and 5.1 pmol/L, respectively. The record does not provide the model details needed to assess whether the standard errors account for within-participant correlation, sequence, or period.

Why does crossover structure matter?

In general, a crossover study compares conditions experienced by the same participants over time. Measurements from one person may be correlated, so analyses often need to account for that repeated-measure structure. Time trends, period effects, and persistence of an earlier condition can also matter. These are general design considerations, not claims about what occurred in this trial. The registry identifies the model as crossover and lists six diet orders, but the analysis used to estimate E2 contrasts and its treatment of these design features are not reported in the registry record.

How should the p-values be read?

A p-value evaluates how compatible the observed data are with a specified null hypothesis under the assumptions of the statistical model. It is not the probability that the null hypothesis is true, and it does not measure the size or practical importance of a difference. The registry reports unadjusted p-values of 0.021 and 0.071 for the two contrasts. “Unadjusted” indicates that these values are not reported as corrected for multiple comparisons. The record does not describe a multiplicity plan or identify a threshold used in the trial's original analysis.

What does the confidence interval add?

In general, a confidence interval gives a range of values compatible with the data and the assumptions of the analysis at a stated confidence level. Its width conveys precision: a wider interval leaves more uncertainty about the size and potentially the direction of the contrast. The intervals reported for these results are 95% confidence intervals. Their interpretation depends on the unreported analysis model being appropriate for the study's crossover data.

The registry lists two outcome measures overall and no secondary results posted for the outcome summaries described in this analysis. It does not report a statistical analysis plan, analysis populations, a missing-data approach, or whether interim analyses occurred. Those omissions limit what can be said about model choice, prespecification, and the handling of incomplete observations. The posted results can still be described as reported, but the unreported methods should not be inferred from the numerical estimates alone.

10. Confidence Intervals and Precision

The low-fat versus high-fat contrast was -17.2 pmol/L, with a 95% confidence interval from -31.76 to -2.642. The interval is entirely below zero, which indicates that the posted estimate is more precise about the direction of this contrast than an interval that spans zero. It still covers a range of possible sizes, so it does not pin down one exact difference.

For low-fat, high n3 versus high fat, the estimate was -13.0 pmol/L and the 95% confidence interval was -27.14 to 1.136. This interval includes zero and extends to both negative and positive values. It therefore leaves uncertainty about whether the contrast is below or above zero, as well as about its magnitude. The unadjusted p-value for this comparison was 0.071.

Confidence intervals describe uncertainty in an estimated contrast under the analysis assumptions; they are not ranges containing a specified proportion of individual participants' E2 measurements. Their coverage interpretation also depends on the analysis being appropriate. Since the registry record does not explain the model used for the crossover data, the extent to which the intervals reflect within-participant dependence or other design features cannot be assessed from the record.

The posted results do not give a clinical-importance threshold for E2 differences. Statistical precision alone therefore cannot establish whether a difference matters clinically. Nor do these intervals address cancer outcomes, which are not reported as trial results.

11. Planning a Similar Trial: Sample Size

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

The sample-size planning figures are participants per arm, not total events. They are planning illustrations based on the observed effect, not the trial's own original design assumptions. The calculation assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The planning effect is set at the stated fraction of the observed effect: 100%, 75%, or 50%. The trial's own original sample-size justification is not reported in the registry record.

The 80% power column gives the planned number of participants per arm for a design with an 80% chance of detecting the specified effect under those assumptions, if that effect and the assumptions are correct. The 90% power column gives the corresponding planning number for a 90% chance. These are design probabilities for hypothetical studies, not probabilities that the posted result is true. They are not observed power.

The figures are calculated separately for each reported comparison. For low fat versus high fat, planning for 100% of the observed effect gives 27 participants per arm for 80% power and 36 for 90% power; planning for 75% gives 47 and 63, and for 50% gives 106 and 142. For low-fat, high n3 versus high fat, the corresponding figures are 44 and 59; 78 and 104; and 174 and 233. Smaller effects require more participants for the same target power under the stated assumptions.

These are simplified illustrations, not a reconstruction of the crossover trial's design. The stated assumptions use equal allocation between two arms and a normal approximation, while the registry describes a crossover study. The planning figures do not establish what sample size the investigators intended or whether the completed study met a prespecified target.

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 = -17.200; pooled standard deviation σ = 22.283.
2. n = 2 × (1.96 + 0.842)² × 22.283² / -17.200² = 26.3, rounded up to 27 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 <- -17.2                      # observed difference in means
sigma <- 22.2829531256519                     # 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(1824498)
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 = 27 (80% power), 36 (90% power)
 75% of observed effect: n per arm = 47 (80% power), 63 (90% power)
 50% of observed effect: n per arm = 106 (80% power), 142 (90% power)
power.t.test: 27.3 
Simulated power at n = 27 per arm: 0.788 (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 reports two mean comparisons against the high-fat diet, and the p-values are labeled unadjusted. When multiple hypotheses are tested, the chance of at least one apparently notable result can increase. In general, a multiplicity procedure can address that issue by adjusting the testing strategy or interpretation. The registry does not report whether the investigators prespecified a multiplicity approach, which comparisons were considered primary for inference, or whether any adjustment was applied elsewhere. The reported p-values should therefore be understood as unadjusted values, not as evidence of a documented family-wise testing plan.

The record does not describe an analysis population, such as whether analyses included all randomized participants or only those with measurements under specified conditions. Enrollment was 18, and each diet outcome entry has an n of 18, but the record does not provide participant flow or explain the relationship between these entries and completion of all crossover periods. The diet entries should not be treated as independent groups simply because each has an n listed.

Missing-data methods are not reported in the registry record. There is no posted account of whether outcome measurements were missing, why they might have been missing, or how any missing observations were handled. The record also does not state whether interim analyses took place. No conclusions about these procedures can be drawn from the posted estimates.

The crossover model raises further analysis questions: whether within-person correlation, period, sequence, or carryover were included in the analysis. Those methods are not reported. These omissions do not change the numerical values posted, but they limit independent assessment of how the estimates and their uncertainty were obtained.

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.

The registry lists serious adverse events and other adverse events by diet condition. For each of the high-fat, low-fat, and low-fat, high n3 entries, 18 were listed as at risk and 0 as affected for serious adverse events. The corresponding other-adverse-event entries also list 18 at risk and 0 affected. Death counts are not reported in the registry record.

These figures describe what is recorded in the adverse-event entries; they do not show that no adverse events of any kind could have occurred. The record does not provide event terms, definitions, collection procedures, follow-up details, or an explanation of how adverse events were attributed across diet periods. The crossover design also means the diet-specific at-risk entries should not be added as if they necessarily represented separate participants.

Zero affected in the posted entries is a count, not proof of zero underlying risk. The record does not report enough detail to assess how complete event ascertainment was or how the safety summaries were constructed. These data should be read as registry-recorded counts, not as a comprehensive safety conclusion.

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

The posted results describe E2 concentrations under three dietary conditions and provide two contrasts against the high-fat diet. The low-fat diet estimate was lower than the high-fat estimate, with a 95% confidence interval that remained below zero. The estimate for the low-fat, high n3 diet was also lower than the high-fat estimate, but its 95% confidence interval included zero. These findings describe the endpoint and comparisons reported in the registry; they do not establish a causal explanation beyond the analysis represented by those estimates.

The trial summary links its question to sex hormone distribution and biochemical markers associated with hormone-mediated cancer risk. A measured difference in estradiol is not itself evidence of a change in breast cancer incidence or risk. The registry record does not post cancer outcomes or a threshold defining a clinically meaningful change in E2. It therefore cannot support conclusions about cancer prevention, treatment, or clinical benefit.

The results also do not answer whether adding high n3 to a low-fat diet changes E2 relative to low fat alone, because that direct comparison is not reported. The record does not report the detailed crossover analysis, missing-data procedures, multiplicity plan, or participant flow. These gaps limit assessment of the robustness and scope of the comparisons.

In general, a statistically estimated difference and its confidence interval are only part of an interpretation. The outcome, trial design, analysis assumptions, and relevance of the measured change all matter. Here, the most defensible reading is specific: the registry reports estimates of estradiol after 8 weeks and their uncertainty for two comparisons with the high-fat diet. Broader claims about health outcomes are outside the posted results.

16. Why This Trial Matters Statistically

This trial is statistically notable for its crossover structure. In general, crossover designs can compare conditions within participants, which may help distinguish condition differences from stable differences between people. They also require attention to repeated measurements, sequence, time period, and possible carryover. The registry identifies the design and lists six diet orders, but the analysis handling those features is not reported. That makes the design an important part of interpreting the posted means and contrasts.

The results also illustrate why a point estimate should be read together with its confidence interval. The low-fat comparison has an interval below zero, whereas the low-fat, high n3 comparison has an interval that includes zero. The latter does not demonstrate equivalence; rather, it leaves uncertainty about the direction and size of the contrast. Unadjusted p-values alone do not convey that full picture.

Finally, the endpoint is a biochemical measure, while the trial's rationale refers to cancer risk. Keeping those levels distinct is essential: an estimate for estradiol does not directly answer a question about cancer incidence. The registry's lack of detailed analysis methods and outcome context further shows why statistical interpretation should remain tied to the precise endpoint and comparisons reported.

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 registry record leaves important trial details unreported. It does not describe eligibility criteria beyond the population language in the study summary, nor does it report participant flow, completion by diet period, or reasons for any missing measurements. The enrollment and diet-specific outcome entries do not clarify whether all participants contributed data under every condition.

The record identifies a crossover model and lists six treatment orders, but it does not explain the duration of diet periods, any washout interval, or the model used for analysis. It is therefore not possible to assess from the registry record whether period effects, sequence, carryover, or within-participant correlation were addressed. The reported least-squares means and standard errors are not accompanied by model specifications.

The original sample-size justification, prespecified analysis plan, multiplicity strategy, missing-data approach, and analysis populations are not reported in the registry record. A direct comparison between the two low-fat conditions is also not posted. The outcome is estradiol at 8 weeks, and the record does not provide a clinical-importance threshold or cancer outcome results. These limits constrain interpretation to the stated biochemical measurements and the two reported contrasts.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Dietary Fat, Eicosanoids and Breast Cancer Risk — NCT01824498.
• Registry record last updated 2018-08-31; status last verified 2018-08.
• Results first posted 2013-09-25.
• 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 record describes a completed, randomized, unmasked crossover study of dietary fat and n3 fatty acids, with enrollment of 18. The three listed diets were high fat, low fat, and low fat with high n3. The primary outcome was estradiol (E2), measured in pmol/L at 8 weeks and reported as least-squares means with standard errors.

Two mean contrasts against the high-fat diet are posted. The low-fat estimate was -17.2 pmol/L relative to high fat, with a 95% confidence interval of -31.76 to -2.642. The low-fat, high n3 estimate was -13.0 pmol/L, with a 95% confidence interval of -27.14 to 1.136. The registry record does not report cancer outcomes or the detailed statistical analysis methods needed to assess crossover-specific modeling.