Effects of Dietary Flaxseed on Symptoms of Cardiovascular Disease in Patients With Peripheral Arterial Disease: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effects of Dietary Flaxseed on Symptoms of Cardiovascular Disease in Patients With Peripheral Arterial Disease (NCT00781950), a randomized phase 2, phase 3 study. The primary outcome is Number of Participants With All-cause Mortality, Cardiovascular Mortality, Stroke, and Myocardial Infarctions.

2. Clinical Question

The clinical question is framed as a comparison between two assigned dietary regimens, rather than as a comparison of flaxseed with no food intervention. Both groups received food products, and the placebo products were intended to replace the flaxseed products. The trial was randomized and triple masked according to the registry record. Those design features are relevant to how group differences are interpreted, but the registry record does not describe the masking procedures or who was masked.

The primary endpoint title groups several serious cardiovascular outcomes. The record gives a combined count for each arm, but does not provide separate counts for all-cause mortality, cardiovascular mortality, stroke, or myocardial infarction. It also does not give a more detailed rule for how participants were counted if they experienced more than one of the listed outcomes. Those details limit what can be concluded about the individual components.

3. Trial Design

NCT00781950 is listed as a randomized, triple-masked, parallel-group trial with phase classifications of phase 2 and phase 3. The registry status is completed. Enrollment was 110 participants: 52 assigned to placebo and 58 assigned to flaxseed. The record identifies Dr. Grant Pierce as sponsor. The study start is listed as 2008-10, and primary completion as 2011-03.

The flaxseed group was assigned food products containing 30 g of milled flaxseed daily for one year. The placebo group was assigned food products containing wheat and wheat bran to replace flaxseed daily for one year. Both arm descriptions list bagels, muffins, bars, pasta, buns, and milled seeds. The record identifies both interventions as dietary supplements. It does not give further details about adherence, how products were distributed, or how intake was monitored.

The primary outcome is a participant count for all-cause mortality, cardiovascular mortality, stroke, and myocardial infarctions, with a one-year timeframe. Secondary topics listed include exercise performance, blood pressure, and circulating lipid levels. The registry indicates one secondary outcome posted, although the study summary also describes exercise tolerance as an additional topic. More detailed outcome definitions and results for the secondary measures are not reported in the registry record.

Randomization means that assignment to the two groups was intended to be determined by chance. In general, random allocation can help make groups comparable at the start, while masking can reduce the influence of expectations on care or assessment. These are general design principles; the registry record does not report the allocation sequence, concealment procedures, masking roles, or how masking was maintained. The original design assumptions and sample-size justification 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

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 Number of Participants With All-cause Mortality, Cardiovascular Mortality, Stroke, and Myocardial Infarctions, measured over 1 year.

The primary endpoint is titled “Number of Participants With All-cause Mortality, Cardiovascular Mortality, Stroke, and Myocardial Infarctions.” Its unit is participants, and its timeframe is one year. The posted arm counts are 4 participants in the placebo group and 5 in the flaxseed group. These are counts, not rates or event totals. The number at risk was 52 in the placebo group and 58 in the flaxseed group.

A participant-count endpoint can describe how many people experienced an outcome in each group during the stated period. Combining serious outcomes can provide a broad summary of events relevant to the trial’s cardiovascular question. In general, a combined endpoint may capture more kinds of clinically important events than any one component alone, but it can also conceal differences among components. The registry record does not provide separate counts for mortality, stroke, and myocardial infarction, or explain the precise counting rule for participants with multiple outcomes.

The endpoint is suitable for describing the posted one-year counts, but the record does not report the timing of individual events, follow-up completeness, or a time-to-event analysis. It also does not explain why this endpoint was selected or how the one-year timeframe was chosen. Those protocol details are not reported in the registry record. The additional stated interest in exercise tolerance and the posted secondary topics concern different outcomes and should not be treated as components of this primary endpoint.

7. Results Posted in the Registry

• Flaxseed: 8.6% (5/58) versus 7.7% (4/52) on control; risk difference 0.9 percentage points (95% CI -9.3 to 11.2), risk ratio 1.12 (0.32–3.95); unadjusted two-proportion z-test p = 0.859.

8. Statistical Interpretation

9. Statistical Methods Explained

The posted comparison is an unadjusted comparison of the flaxseed group with the placebo group for a binary endpoint: whether a participant was counted as having the listed primary outcome during the one-year timeframe. The arm summaries report participant counts and group sizes. The comparison gives a risk difference, a risk ratio, an odds ratio, confidence intervals, and a p-value. The registry record does not describe an adjusted model or a formal analysis plan, and it lists zero analyses.

What does a risk difference describe?

In general, a risk difference subtracts the proportion with an outcome in one group from the proportion in the comparison group, with the direction depending on the stated contrast. It is expressed on an absolute scale. A value of zero corresponds to equal proportions under that definition. The posted estimate is positive, and its confidence interval includes values on both sides of zero. This makes clear that the estimated direction should not be mistaken for a precise or definitive difference. The group counts are the primary descriptive information; the registry’s risk-difference estimate is an unadjusted summary of those groups.

How do risk ratios and odds ratios differ?

In general, a risk ratio compares the proportions experiencing the outcome, while an odds ratio compares the odds of the outcome. A ratio of 1 represents no difference on that ratio scale. The posted risk ratio is 1.121, and the posted odds ratio is 1.132. The confidence intervals for both measures include 1, so the results remain compatible with no difference on those scales as well as with differences in either direction. Odds and risks are related but are not interchangeable, and an odds ratio should not be read as a direct absolute change in the proportion of participants with an outcome.

What does the p-value address?

In general, a p-value describes how compatible the observed result is with a specified statistical null model, assuming that model and its assumptions hold. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. The posted p-value is 0.859. That value is consistent with the broad uncertainty reflected in the interval, but it does not demonstrate that the groups are identical. The registry record does not state the test used to obtain the p-value or provide further model details.

Why are confidence intervals useful?

In general, a confidence interval conveys uncertainty around an estimate and indicates which values are compatible with the analysis under its assumptions. Here, the risk-difference interval extends below and above zero. The ratio intervals include 1. These features mean the posted results do not isolate a single direction of effect. The width of an interval also matters: a wide interval allows a broader range of possible effects than a narrow interval. The limited number of participants counted with the endpoint is relevant to the precision of these comparisons, although the registry record does not report a separate precision analysis.

Randomization supports a comparison between assigned groups, but the registry record does not report details of the allocation procedure or the analysis population. It does not state whether participants were analyzed according to their randomized group, how missing outcome information was handled, or whether any exclusions occurred. The record also does not report model diagnostics, adjustment variables, or a multiplicity procedure. These omissions prevent assessment of those aspects of the analysis from the registry record alone.

The endpoint is binary at the participant level, and the reported summaries are counts. General methods for binary outcomes rely on assumptions about how outcomes are defined and how participants contribute to the analysis. The registry record does not report whether a participant could contribute more than one component event, how recurrent events were handled, or how event ascertainment was conducted. It also does not provide an event-by-event dataset, so the analysis cannot be independently reconstructed beyond the posted summaries.

10. Confidence Intervals and Precision

Precision is limited for the primary comparison. The registry reports 4 participants with the endpoint among 52 in the placebo group and 5 among 58 in the flaxseed group. The risk-difference confidence interval crosses zero, extending from a negative lower bound to a positive upper bound. Thus the interval includes no difference and possible differences in either direction. Its breadth means the posted estimate does not tightly determine the size of the group contrast.

The risk ratio is 1.121, and its confidence interval includes 1. The odds ratio is 1.132, and its confidence interval also includes 1. On both ratio scales, the no-difference value remains within the interval. These measures are consistent with the same general reading as the risk-difference interval: the estimates are uncertain, and the registry results do not narrowly identify a particular effect size or direction.

In general, confidence intervals are more informative than a single point estimate because they show a range of values compatible with the data and analysis assumptions. They do not guarantee that the true effect lies within the reported range, and they do not resolve limitations in outcome definition, follow-up, or missing information. The registry record does not report confidence intervals for component outcomes or secondary outcomes, nor does it provide a separate precision assessment for those measures.

The number of participants with the endpoint is small relative to the groups’ sizes, so the comparison has limited information for distinguishing modest differences. This is a general interpretation of the posted counts and interval uncertainty, not a new calculation. The exact upper limit of the risk-difference interval and some lower limits for ratio intervals are not repeated because they are recorded with more than three decimal places. The original trial’s target precision and design assumptions are not reported in the registry record.

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 figures are planning illustrations based on the observed effect, not the trial’s original sample-size justification. For this binary participant-count endpoint, the listed numbers are participants per arm, not total events. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning row uses the stated proportion of the observed effect as the effect to detect. The trial’s own original design assumptions are not reported in the registry record.

The 80% power column gives the illustrated number of participants per arm for a design with 80% power under those assumptions. In general, power is the probability that a specified statistical procedure will detect an effect of the size assumed, if that effect is present and the assumptions hold. The 90% power column gives the corresponding planning number for 90% power. These columns are design illustrations, not descriptions of the trial’s achieved power.

The rows consider planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For 100% of the observed effect, the figures are 13,643 participants per arm for 80% power and 18,264 for 90% power. For 75% of the observed effect, they are 23,940 and 32,048 participants per arm, respectively. For 50% of the observed effect, they are 53,156 and 71,160 participants per arm, respectively. Smaller effects require more participants under the stated assumptions, because they are harder to distinguish from sampling variation.

The curve represents the same planning relationship across effect sizes: planning for smaller effects requires larger groups. These values should be treated cautiously because they are calculated from the observed effect, which is itself uncertain, and the observed comparison has a confidence interval spanning both directions. The figures are not observed power and do not show what the completed trial was capable of detecting under its original design. That design information is not reported in the registry record.

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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.077; treatment proportion p₁ = 0.086; average p̄ = 0.082.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.3871 = 0.7586.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.3870 = 0.3257.
4. n = (0.7586 + 0.3257)² / (0.0093)² = 13,642.7, rounded up to 13,643 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
p0 <- 0.0769230769230769                          # control proportion
p1 <- 0.0862068965517241                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(781950)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 13,643 (80% power), 18,264 (90% power)
 75% of observed effect: n per arm = 23,940 (80% power), 32,048 (90% power)
 50% of observed effect: n per arm = 53,156 (80% power), 71,160 (90% power)
power.prop.test: 13642.7 
Simulated power at n = 13,643 per arm: 0.798 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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 a primary outcome and identifies secondary topics that include exercise performance, blood pressure, and circulating lipid levels. One secondary outcome is posted. The primary endpoint title groups all-cause mortality, cardiovascular mortality, stroke, and myocardial infarctions, but the record does not provide separate component results. It also does not give a detailed hierarchy or clarify whether the component events were analyzed separately.

When several outcomes or comparisons are tested, the chance of at least one apparently unusual result can increase. In general, a prespecified multiplicity strategy can address that issue, but the registry record does not report whether one was planned or used. No adjustment for multiple testing is described. The record lists zero analyses, and does not provide a full statistical analysis plan, outcome hierarchy, or a set of secondary estimates. It is therefore not possible to determine how the posted primary comparison relates to any broader family of planned tests.

Information about missing data and analysis populations is also limited. The registry does not report how many participants completed follow-up, whether every randomized participant had endpoint information, how missing outcomes were handled, or whether exclusions occurred. It does not specify whether the analysis followed randomized assignment or used another population definition. Those details are not reported in the registry record, so the effect of missing information or departures from assigned treatment cannot be assessed.

The registry record does not describe interim analyses, stopping rules, or monitoring procedures. It also does not give details of outcome adjudication or how the listed events were verified. These matters can influence interpretation, but no assumptions about them can be made from the record. The reported group counts and unadjusted comparison should consequently be read alongside the missing analysis details, rather than as a complete account of the trial’s statistical methods.

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 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: increased claudication (12.1%), myocardial infarction (5.8%), stroke (5.2%), rest pain in limbs (3.4%), iliac artery stenosis (1.9%).

The serious adverse event summary lists 9 affected participants among 52 at risk in the placebo group and 15 among 58 at risk in the flaxseed group. The other adverse event summary lists 0 among 52 at risk in the placebo group and 3 among 58 at risk in the flaxseed group. These are counts of participants as displayed in the registry record; they should not be interpreted as proof that an event was caused by the assigned food product. The record does not provide a causal assessment or additional detail about event severity, timing, or relatedness.

The registry lists serious event terms with percentages: Increased Claudication, 12.1%; Myocardial Infarction, 5.8%; Stroke, 5.2%; Rest Pain in Limbs, 3.4%; Iliac Artery Stenosis, 1.9%; and Increased Numbess in Extremities, 1.9%. The record does not specify an arm for these listed terms in the posted summary, so they should not be assigned to a particular group. It also does not report deaths by arm. Safety counts and event terms are descriptive and do not, on their own, establish comparative risk or causation.

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

The posted result means that the registry recorded 4 participants with the primary endpoint in the placebo group and 5 in the flaxseed group during the one-year timeframe. The unadjusted comparison is uncertain: the risk-difference interval spans zero, the ratio intervals include 1, and the p-value is 0.859. These features indicate that the record does not establish a clear difference between the groups for this endpoint. They do not establish that the groups had exactly the same outcome.

The result does not show which primary endpoint components occurred, how many participants experienced each component, or whether participants had multiple components. It therefore cannot support a component-by-component interpretation. It also does not answer the listed questions about exercise performance, blood pressure, or circulating lipid levels because detailed results for those outcomes are not reported in the registry record.

In general, a non-significant comparison is not proof of no effect. A confidence interval that includes the no-difference value can still include effects in either direction, and the width of the interval indicates that considerable uncertainty remains. The comparison is unadjusted, and the record does not describe missing-data handling, analysis populations, or the original statistical plan. These gaps further limit how far the posted result can be interpreted.

The results should not be read as advice about dietary choices or as evidence that flaxseed does or does not work. They describe the outcomes recorded for the randomized groups and the uncertainty of the posted comparison. The safety summary is also descriptive: it reports participant counts and event terms, but does not establish that an event was caused by either assigned regimen. Conclusions about outcomes not reported in the registry record cannot be drawn from the primary endpoint alone.

16. Why This Trial Matters Statistically

This trial is statistically instructive because the posted point estimates and uncertainty need to be read together. The group counts are close in absolute terms, but counts alone do not describe the range of plausible group differences. The risk-difference interval crosses zero, and both ratio intervals include 1. These interval features make the uncertainty explicit and caution against treating the direction of a point estimate as a settled finding.

The record also illustrates why endpoint definition matters. The primary outcome groups several serious events under one participant-count label, yet component-specific counts and a detailed counting rule are absent. A combined endpoint can be useful for a broad summary, but it can obscure which components account for the total. Without those component results, interpretation must remain at the level of the combined outcome as posted.

The sample-size illustration shows how planning depends on the effect size one seeks to detect: smaller effects require more participants under the stated assumptions. However, those calculations use the observed effect, which is uncertain, and are not the trial’s original design justification. Keeping planning illustrations distinct from achieved power and from the trial’s own design rationale is essential for sound statistical interpretation.

Finally, a completed trial record may still leave important analytical details unavailable. Here, the registry does not report the original statistical plan, missing-data methods, analysis populations, or a multiplicity strategy. Recognizing those limits helps prevent a posted comparison from being treated as a complete report of every methodological decision or outcome. Statistical interpretation depends not only on a point estimate, but also on how the endpoint, analysis, and uncertainty are documented.

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 endpoint description combines all-cause mortality, cardiovascular mortality, stroke, and myocardial infarctions, but the registry does not report component-specific counts or a detailed definition of the combined participant count. This prevents assessment of whether the posted total is driven by one component or distributed across several. The record also does not report whether participants could contribute more than one event to the endpoint or how such cases were counted.

Follow-up and analysis details are limited. The primary timeframe is one year, but the record does not report the number with complete follow-up, losses to follow-up, missing outcome handling, adherence, or the analysis population. It does not describe event ascertainment or adjudication. The comparison is unadjusted, and adjusted estimates are not reported in the registry record.

The record does not provide the trial’s original sample-size assumptions or justification, a full statistical analysis plan, or information on interim analyses. It does not report whether multiplicity was addressed across the primary components or secondary outcomes. Although exercise performance, blood pressure, and circulating lipid levels are named as secondary topics, detailed results for these outcomes are not reported in the registry record.

The posted safety summary provides participant counts and selected serious event terms, but does not identify the arm associated with each listed term or report deaths by arm. It does not provide event timing or relatedness assessments. These limitations mean the safety information is descriptive and incomplete for comparative interpretation. In addition, the sample-size illustrations are based on the observed effect rather than the trial’s original planning assumptions, so they should not be treated as evidence about the study’s original design or its achieved power.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Effects of Dietary Flaxseed on Symptoms of Cardiovascular Disease in Patients With Peripheral Arterial Disease — NCT00781950.
• Registry record last updated 2016-12-12; status last verified 2016-10.
• Results first posted 2014-12-12.
• 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

NCT00781950 is a completed randomized, triple-masked, parallel-group trial listed as phase 2 and phase 3. It enrolled 110 participants with peripheral arterial disease. The flaxseed arm received food products containing 30 g of milled flaxseed daily for one year; the placebo arm received wheat- and wheat-bran-based products for one year.

The primary endpoint was the number of participants with all-cause mortality, cardiovascular mortality, stroke, and myocardial infarctions over one year. The registry reports 4 participants in the placebo group and 5 in the flaxseed group. Its unadjusted comparison is imprecise, with a risk-difference interval spanning zero and a p-value of 0.859. Component-specific results, detailed secondary results, and several analysis-plan details are not reported in the registry record.