Effect of Fish Oil (Omega-3 Fatty Acids) on Arteries: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effect of Fish Oil (Omega-3 Fatty Acids) on Arteries (NCT00935766), a randomized phase 3 study. The primary outcome is Change in Pulse Wave Velocity in Active vs. Placebo-treated Patients..

2. Clinical Question

3. Trial Design

The study was registered as a Phase 3, randomized, triple-masked, parallel-group trial comparing omega-3 with placebo. Its status is terminated. The registry lists a start date of 2009-09 and a primary completion date of 2012-03. It lists enrollment of 76. The reason for termination and any consequences for recruitment or follow-up are not reported in the registry record.

The primary-outcome description characterizes the study as prospective, randomized, and double-blinded, and describes patients at risk for cardiovascular disease who received omega-3 or matched placebo daily. The registry's masking field says triple masking. The record does not identify which participant, investigator, or assessor roles were masked, nor does it explain the different masking descriptions.

The listed primary outcome is mean change in pulse wave velocity, expressed in cm/sec, measured at baseline and 3 months. The primary-outcome description calls the measure brachial-ankle PWV. Two secondary outcomes are posted: change in LpPLA2, expressed in ng/mL, and change in hsCRP, expressed in mg/L. Both secondary outcomes are defined over baseline to 3 months.

The record lists the Denver Health and Hospital Authority as sponsor. It does not report the original sample-size justification, recruitment targets by arm, the reason for termination, or the planned statistical analysis in enough detail to establish how the registered plan was intended to address the reported results.

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: The study was discontinued early due to lack of funding and slow enrollment

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 Change in Pulse Wave Velocity in Active vs. Placebo-treated Patients., measured over Baseline, 3 months.

Pulse wave velocity (PWV) is a measure of how quickly a pressure wave travels through the arteries. The posted primary outcome is change in brachial-ankle PWV from baseline to 3 months, measured in cm/sec. The registry describes this as the principal outcome measure in the primary-outcome text. Its broader study aims also refer to vascular function measured by brachial artery reactivity (BAR), but the posted primary outcome is PWV; the record does not explain how these measures relate in the study's endpoint hierarchy.

As a general statistical concept, PWV is used as a vascular measure because it reflects arterial properties and can be assessed as a continuous outcome. A change score compares a participant's later measurement with their baseline measurement. Comparing average changes between randomized arms can describe whether the observed shifts differed between the assigned groups. The posted summaries report mean change and standard deviation for each arm.

A change in a physiological marker is not itself a direct measure of a clinical event or patient experience. The registry record does not report a clinical-event primary outcome in this trial. The posted results therefore address the measured vascular marker, not whether the intervention altered the occurrence of cardiovascular disease or improved health in other ways.

7. Results Posted in the Registry

• Omega 3: mean -97.00 versus -33.00 on control; difference -64.00 (95% CI -186.43 to 58.43), standardized effect d = -0.25; z-test p = 0.306.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Change in Lipoprotein-associated Phospholipase A2 (LpPLA2)

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Omega 3: mean -18.10 versus -6.10 on control; difference -12.00 (95% CI -30.73 to 6.73), standardized effect d = -0.33; z-test p = 0.209.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Omega 3 and the control. The interval gives the range of effects that remain compatible with the data.

Change in hsCRP

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Omega 3: mean -0.90 versus 0.90 on control; difference -1.80 (95% CI -3.67 to 0.07), standardized effect d = -0.46; z-test p = 0.059.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Omega 3 and the control. The interval gives the range of effects that remain compatible with the data.

The secondary outcomes cover two circulating markers: LpPLA2 and hsCRP. Their posted results do not give a uniform pattern of movement across the measures, and their unadjusted confidence intervals include zero. The sponsor's mixed models p-values are also not identical to those from the recalculations. Together, the secondary findings are best read as uncertain estimates rather than as a consistent, conclusive pattern.

These outcomes complement the primary vascular measure by assessing inflammatory or cardiovascular risk markers. They do not replace the primary comparison, which is change in PWV. The registry's stated aims include vascular function and circulating inflammatory markers, but the posted results do not establish how the secondary outcomes were ranked or whether they were intended to support a confirmatory claim about the primary outcome.

Unadjusted secondary results carry less weight when several outcomes are tested because the chance of observing an apparently notable result by chance can increase across multiple comparisons. As a general statistical principle, multiplicity procedures or prespecified outcome hierarchies can address that concern. The registry record does not report whether either was used. The secondary p-values should consequently be treated as exploratory or descriptive unless a fuller analysis plan establishes otherwise.

The posted outcomes are limited to change in LpPLA2 and hsCRP. Although the registry lists a count of three outcome measures, only these two secondary results are posted. The status of any additional measure and the reason for its absence are not reported in the registry record. No conclusion should be extended to unposted markers or outcomes.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Change in Lipoprotein-associated Phospholipase A2 (LpPLA2)
• Change in hsCRP

9. Statistical Interpretation

10. Statistical Methods Explained

The posted outcome values are means of continuous measures, with standard deviations describing variation within each arm. A mean gives the arithmetic average of observed changes. A standard deviation describes how dispersed individual observations are around that average; it is not the uncertainty in the mean itself. The registry reports this information for the primary outcome and both posted secondary outcomes.

What does the unadjusted comparison represent?

The recalculated comparison contrasts the omega-3 mean change with the placebo mean change. A negative difference means the posted omega-3 mean is numerically lower than the placebo mean under that subtraction order. This is an unadjusted comparison reconstructed from the posted summary statistics. It does not account for participant-level data, covariates, repeated measurements, or any features of the sponsor's model that are not available in the registry record.

The sponsor reports a mixed models analysis for each posted outcome. In general, mixed models can represent correlated observations, such as repeated measurements on the same participant, and can accommodate modeled variation across participants or other units. Whether those features were used in a particular way depends on the model specification. The model specification, covariates, covariance structure, missing-data handling, and analysis population are not reported in the registry record. The sponsor's p-values should therefore be understood as outputs of the reported mixed models analysis, without inferring details beyond the stated method.

How should the confidence interval be read?

A confidence interval expresses uncertainty around an estimated effect under the method used to calculate it. In general, a wider interval indicates less precision than a narrower interval. An interval containing zero is compatible with no difference as well as with differences in either direction, within the interval's limits. It does not show that all values in the interval are equally likely, and it does not directly state the probability that the true effect lies in the interval.

The recalculated intervals are based on the posted group summaries. They may not match intervals from a participant-level model, especially if that model adjusts for other information or accounts for repeated observations. The registry does not post sponsor-model estimates or confidence intervals, so the numerical intervals available for interpretation are those from the unadjusted recalculations.

Why does dispersion matter?

In general, variation among participants affects how precisely a group mean and a between-group contrast can be estimated. When the observed values are widely dispersed relative to the difference between group means, the comparison tends to be less precise. The reported standard deviations describe substantial variation in the measurements, while the confidence intervals express uncertainty in the contrasts. For count outcomes, over-dispersion can mean the observed variation exceeds what a simple count model assumes; these outcomes are continuous measures, so that issue is not the central feature of these comparisons.

The registry does not report diagnostic checks or model fit results. It is therefore not possible to assess whether model assumptions were evaluated or whether alternative specifications were considered. Such checks matter because statistical conclusions depend on how well the model represents the outcome data.

What does the p-value add?

A p-value summarizes how unusual a result at least as extreme as the observed result would be if a specified null model were true, subject to the model's assumptions. It is not a measure of effect size and does not indicate the probability that a result will replicate. The unadjusted p-values are derived from the posted summary statistics; the sponsor's p-values are reported from mixed models. The registry does not identify a prespecified significance threshold for the sponsor's analyses, so the p-values should be read alongside the estimates and their uncertainty rather than as stand-alone conclusions.

The planning illustrations use a two-sided significance level of 0.05, equal allocation between arms, and a normal approximation. These assumptions describe the posted planning calculations, not the original trial design. No sample-size rationale or original design assumptions are reported in the registry record.

11. Confidence Intervals and Precision

The primary unadjusted mean difference is -64.0 cm/sec, with a 95% confidence interval from -186.4 to 58.43. The interval spans zero and includes both a negative difference and a positive difference. Thus, the estimated direction is not precise: the posted summaries are compatible with effects that differ substantially in direction and magnitude. The interval's breadth also indicates that the primary estimate is not tightly determined by these data.

The standard deviations for the primary outcome are 306.0 cm/sec in the placebo group and 182.0 cm/sec in the omega-3 group. As a general matter, variation within arms contributes to uncertainty in a comparison of means. The posted confidence interval reflects uncertainty in the recalculated contrast, not the range in which individual participants' changes occurred.

The sponsor's mixed models result is reported as p = 0.36, but no corresponding estimate or confidence interval is posted. It is therefore not possible to assess the precision of the sponsor-model effect estimate from the registry record. The unadjusted interval should not be treated as if it were the confidence interval from that model.

A confidence interval is not a guarantee that the true effect lies within its endpoints. It is a measure constructed using a statistical procedure and its assumptions. The registry does not report a clinical-importance threshold for the endpoint, so the interval cannot be classified against a stated threshold for meaningful change.

12. Planning a Similar Trial: Sample Size

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

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

The 80% power column represents the number of participants per arm estimated, under those planning assumptions, to give an 80% chance of detecting the selected effect if that effect were the true one. The 90% power column uses a higher target chance of detection and therefore requires more participants per arm for the same assumed effect. These are design-planning quantities, not descriptions of the precision actually achieved in this trial.

Rows planning for 100%, 75%, and 50% of the observed effect use progressively smaller effects as the target. Smaller effects are harder to distinguish from random variation, so the planning calculations require more participants per arm. The figures are sensitive to the assumptions and to the observed effect used as their starting point. They should not be interpreted as proof that the original trial was adequately or inadequately sized, because its own assumptions are not reported.

This is not observed power. Observed power is not a useful substitute for interpreting the estimate and its confidence interval after results are available. The planning illustrations instead show how enrollment requirements would change for specified assumed effects under the stated calculation assumptions.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so 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 = -64.000; pooled standard deviation σ = 259.642.
2. n = 2 × (1.96 + 0.842)² × 259.642² / -64.000² = 258.4, rounded up to 259 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 <- -64                      # observed difference in means
sigma <- 259.642318071098                     # 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(935766)
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 = 259 (80% power), 346 (90% power)
 75% of observed effect: n per arm = 460 (80% power), 615 (90% power)
 50% of observed effect: n per arm = 1,034 (80% power), 1,384 (90% power)
power.t.test: 259.3 
Simulated power at n = 259 per arm: 0.799 (20000 replicates)

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

14. Analyses Reported by the Sponsor

The sponsor's reported analysis for the primary outcome is a mixed models analysis with p = 0.36. The registry does not report a model estimate, confidence interval, detailed specification, or covariate adjustments for that analysis. The recalculated comparison is an unadjusted contrast of the posted group means, with an estimated mean difference of -64.0 cm/sec and a 95% confidence interval from -186.4 to 58.43; its p-value is 0.306.

These results are not identical because they come from different analysis approaches: the sponsor reports a mixed models result, while the recalculation uses posted summary statistics. The record does not flag a discrepancy. The sponsor's analysis is the trial's reported analysis, but its p-value alone cannot supply the missing model estimate or explain how the model was specified. The recalculation gives a transparent comparison of the posted means, but it is not a reproduction of the sponsor's model.

For LpPLA2, the sponsor reports p = 0.21, compared with the unadjusted recalculation p = 0.209. For hsCRP, the sponsor reports p = 0.08, compared with the unadjusted recalculation p = 0.059. Small differences between these values do not by themselves indicate an error; they may reflect differences between model-based and summary-statistic analyses. The record does not provide enough model detail to determine the source of each difference.

15. Multiplicity, Missing Data and Analysis Populations

The registry record posts a primary outcome and two secondary outcomes, but does not report a multiplicity adjustment, a prespecified hierarchy for testing, or a detailed plan distinguishing confirmatory from exploratory analyses. When several outcomes are tested, interpreting each unadjusted p-value as if it were the only test can overstate the strength of evidence. Whether that concern applies to the sponsor's conclusions depends on the analysis plan, which is not reported in the registry record.

Missing-data methods are also not described. The record does not state how incomplete baseline or follow-up measurements were handled, whether all randomized participants were included in each analysis, or whether any imputation or sensitivity analyses were conducted. It does not provide participant flow or the number of missing observations for the posted endpoints. Without these details, it is not possible to judge whether the reported summaries reflect all randomized participants or a subset with available measurements.

The analysis populations are not defined. The record does not say whether the sponsor used an intention-to-treat population, a per-protocol population, or another definition. Nor does it report exclusions after randomization or reasons for any exclusions. This information is important when assessing how the randomized comparison was preserved in the analysis.

The registry reports both a total enrollment figure and outcome-specific arm sizes, but does not explain their relationship. The reason for the terminated status is not reported. Protocol deviations, interim analyses, stopping criteria, and the original statistical analysis plan are also not reported in the registry record. These omissions limit assessment of selective reporting, the handling of incomplete data, and the degree to which the posted results reflect prespecified analyses.

16. 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.

For serious adverse events, the registry reports 0 affected among 42 at risk in the placebo group and 0 affected among 34 at risk in the omega-3 group. For other adverse events, it likewise reports 0 affected among 42 at risk in the placebo group and 0 affected among 34 at risk in the omega-3 group. These figures describe what is recorded for the listed groups; they do not establish that no adverse events occurred outside the recorded categories or observation period.

No deaths are reported as values in the record, and no top serious-event terms are listed. The record does not provide further detail about adverse-event definitions, collection methods, severity grading, observation duration, or missing safety data. The safety figures should therefore be interpreted as registry reporting, not as a complete assessment of possible harms. They do not support a broader conclusion about safety beyond the recorded counts.

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

The posted results describe changes in continuous vascular and inflammatory markers over baseline to 3 months. For PWV, the unadjusted estimate favors a more negative mean change in the omega-3 arm than in placebo, but its confidence interval is broad and includes zero. The sponsor's mixed models analysis reports p = 0.36. These data do not precisely establish the size or direction of a between-arm difference in the primary endpoint.

The findings do not answer whether omega-3 changed cardiovascular events, symptoms, or longer-term health outcomes. Those outcomes are not reported as results in the registry record. Nor does a change in a biomarker alone demonstrate a clinical benefit or harm. The registry's study aims describe risk markers and pre-clinical cardiovascular markers, rather than a posted clinical-event result.

The secondary findings also remain uncertain, and the record does not report whether statistical testing across outcomes was adjusted. The missing analysis details, participant-flow information, and explanation for the terminated status further constrain interpretation. These limits are relevant to how much confidence can be placed in the estimates, but they do not establish that the unreported analyses or data favored either arm.

The results apply to the outcomes and follow-up described in this registry record. They should not be generalized to other populations, doses, durations, or clinical settings without additional evidence. The record's descriptions of population and dose are not fully aligned across fields, and it does not provide enough detail to resolve those differences. The soundest reading is narrow: the registry posts imprecise marker comparisons and does not provide the information needed for broader clinical conclusions.

18. Why This Trial Matters Statistically

This trial illustrates the distinction between an estimated effect and the certainty surrounding it. The primary recalculation gives a numerical contrast, but the confidence interval is wide and spans zero. Reporting the estimate together with its uncertainty is more informative than treating a p-value as a verdict. The sponsor's mixed models p-value and the unadjusted recalculation also show why the analysis method matters when interpreting results.

The registry record also demonstrates why outcome definitions and analysis details are important. Its study aims refer to brachial artery reactivity, while its posted primary outcome is change in brachial-ankle PWV. It describes masking in different ways, and the dosing descriptions are not reconciled. These details affect how readers understand what was tested and how the results map to the stated aims.

Finally, the record offers an example of the limits of registry results when information about missing data, analysis populations, multiplicity, and the reason for termination is absent. Those omissions make it difficult to assess the full context of the estimates. Clear reporting of these elements helps biostatisticians and clinical researchers distinguish a measured result from the assumptions and decisions that shape its interpretation.

19. Limitations

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

Several trial-specific reporting gaps restrict interpretation. The registry's overall enrollment is 76, while the posted primary and secondary outcome groups have reported sizes of 35 and 27. The record does not explain the difference. It also does not provide participant flow, reasons for nonparticipation in outcome analyses, or missing measurement counts, so the completeness of the outcome summaries cannot be assessed.

The descriptions of the intervention are not fully aligned: the primary-outcome text describes 4-g daily omega-3 fatty acids, while the arm description says 4 1 mg capsules daily. The primary-outcome description calls the study double-blinded, whereas the registry masking field says triple. The study aims mention BAR, while the posted primary endpoint is PWV. The record does not reconcile these details.

The sponsor's mixed models are not specified beyond the method label and p-values. Model estimates, confidence intervals, covariates, population definitions, missing-data procedures, and diagnostics are not reported. The registry also does not report multiplicity handling, the original sample-size rationale, interim analyses, or the reason for termination. These limitations leave uncertainty about the analysis context and prevent a complete assessment of robustness or selective reporting.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Effect of Fish Oil (Omega-3 Fatty Acids) on Arteries — NCT00935766.
• Registry record last updated 2014-09-29; status last verified 2014-09.
• Results first posted 2014-09-29.
• 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.

23. Record Summary

The registry describes a randomized, parallel-group Phase 3 trial of omega-3 versus placebo, with triple masking listed and a terminated status. The primary posted outcome is mean change in brachial-ankle PWV from baseline to 3 months. LpPLA2 and hsCRP changes are posted as secondary outcomes. The record lists Denver Health and Hospital Authority as sponsor, enrollment of 76, start in 2009-09, and primary completion in 2012-03.

The primary unadjusted mean difference is -64.0 cm/sec, with a 95% confidence interval from -186.4 to 58.43; the sponsor reports p = 0.36 from a mixed models analysis. The secondary comparisons also have uncertainty, and analysis details needed to assess missing data, multiplicity, and participant flow are not reported in the registry record.