Omega-3 Fatty Acids for Prevention of Post-Operative Atrial Fibrillation: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Omega-3 Fatty Acids for Prevention of Post-Operative Atrial Fibrillation (NCT00970489), a randomized phase 3 study. The primary outcome is Any First Post-op Atrial Fibrillation or Flutter (AF).

2. Clinical Question

This is a question about the comparative frequency of a defined post-operative event in the randomized groups. It is not a question about all possible arrhythmias, longer-term outcomes, or outcomes beyond the stated assessment window. The trial title identifies prevention of post-operative atrial fibrillation as its subject, but interpretation should rest on the posted endpoint definition and comparative results rather than on the title alone.

3. Trial Design

OPERA is recorded as a phase 3, randomized, quadruple-masked, parallel-group trial. It is marked completed. Brigham and Women's Hospital is listed as the sponsor. The registry reports enrollment of 1516, and the primary completion date is recorded as 2012-05. The trial summary describes a large multi-center study in patients undergoing cardiac surgery.

The comparison was between omega-3 fatty acid capsules and olive oil capsules. Each arm lists 758.0 participants. The results report 227.0 participants with the primary event in the omega-3 fatty acid capsule arm and 233.0 in the olive oil capsule arm. These are the posted arm-level counts; the registry information does not establish from these figures alone which participants were included in every analysis or how missing outcome data were handled.

The primary outcome was any first post-operative atrial fibrillation or flutter meeting the stated duration and confirmation requirements. It was assessed up to 10 days post-surgery or discharge, whichever came sooner. The record also lists secondary outcomes as post-op AF, other arrhythmias, and other endpoints, but does not provide their detailed definitions in the information available for this analysis.

Random allocation and masking are important design features for interpreting a treatment comparison. In general, randomization is intended to support comparability of groups at assignment, while masking can reduce the influence of knowledge of assigned treatment on care or assessment. The registry lists these design features but does not describe the randomization procedure, the parties included in quadruple masking, or the precise operational methods. The original sample-size assumptions and 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: Ineligible patients were most often excluded because they were not in sinus rhythm (40.5%), were on fish oil (28.9%), or were unwilling to provide informed consent (23.5%).

Overall Study

Reasons for not completing this period:

5. Baseline Characteristics

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

Population: Patients scheduled for cardiac surgery across 28 centers in the US, Italy, and Argentina, enrolled between Aug 2010 and Jun 2012. Inclusion criteria were broad; the main exclusions were regular use of fish oil or absence of sinus rhythm at enrollment. Forty-eight percent of screened patients and 94% of eligible patients were enrolled.

6. Primary Endpoint

The registry lists the primary outcome as Any First Post-op Atrial Fibrillation or Flutter (AF), measured over up to 10 days post-surgery or discharge, whichever sooner.

The primary endpoint counts participants with any first post-operative atrial fibrillation or flutter. The event had to last at least 30 seconds and be confirmed by a rhythm strip or 12-lead ECG. The definition includes definite AF and probable AF, where a supraventricular tachycardia is considered likely to be AF depending on rate and other characteristics. The observation window was up to 10 days post-surgery or discharge, whichever came sooner.

This is a binary endpoint: for the reported measure, each participant is counted as having or not having the defined event during the assessment window. The registry presents the number of participants with an event in each arm and compares the proportions. It does not report the total number of episodes per participant, the time to the first event, or the duration of events beyond the minimum definition.

In general, a prespecified, clearly defined event endpoint can make a clinical comparison easier to interpret because it states what is counted and when it is assessed. ECG or rhythm-strip confirmation gives an explicit basis for identifying an event. The inclusion of probable AF broadens the definition beyond definite AF, so interpretation should use the full registry definition rather than treating the outcome as only confirmed definite AF. The registry record does not report why this endpoint was selected over other possible outcomes or whether the definition was changed during the trial.

7. Results Posted in the Registry

• Omega-3 Fatty Acid Capsules: 29.9% (227/758) versus 30.7% (233/758) on control; risk difference -0.8 percentage points (95% CI -5.4 to 3.8), risk ratio 0.97 (0.84–1.13); unadjusted two-proportion z-test p = 0.737.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary measure is binary: each participant either met the registry definition of post-operative AF or flutter during the specified window or did not. The reported event counts are 227.0 for omega-3 fatty acid capsules and 233.0 for olive oil capsules. The reported arm sizes are 758.0 in each group. The comparison therefore concerns proportions of participants with an event, rather than event rates per unit of follow-up or total numbers of recurrent episodes.

What does a risk difference express?

The risk difference subtracts the comparator-arm risk from the intervention-arm risk under the stated comparison direction. The reported estimate is -0.008. A value of zero would represent equal risks on this scale; values below or above zero represent differences in opposite directions. The confidence interval is -0.054 to 0.038. Since this interval spans zero, the data do not pinpoint a single direction of difference with high precision. In general, the risk difference is often straightforward to interpret as an absolute contrast in outcome probability, while its practical importance depends on context and on what size of difference would matter. A clinically important threshold is not reported in the registry record.

How do relative measures differ?

The registry comparison also gives a risk ratio of 0.974 and an odds ratio of 0.963. In general, a risk ratio compares the risks directly, whereas an odds ratio compares the odds of the event. A value of one represents no relative difference for either measure. The risk-ratio confidence interval is 0.836 to 1.135, and the odds-ratio confidence interval is 0.774 to 1.199; both include one. Relative measures can convey direction and scale differently from an absolute risk difference. In particular, an odds ratio is not itself a risk difference. These estimates are complementary descriptions of the same outcome comparison, not independent replications.

What does the p-value indicate?

The posted unadjusted p-value is 0.737. In general, a p-value describes how unusual data at least as incompatible with a specified null model would be if that model and the test assumptions were true. It is not the probability that the null hypothesis is true, and it does not indicate the size or clinical importance of an effect. The registry record does not report the exact test used to obtain this value, whether a covariate-adjusted analysis was also conducted, or a full statistical analysis plan. Accordingly, the value should be described as the posted unadjusted p-value without attributing a particular test or model to it.

Why does the endpoint definition matter?

For a binary outcome, event classification determines which participants enter the event count. Here, the record requires at least 30 seconds of AF or flutter and confirmation by rhythm strip or 12-lead ECG, while also including probable AF as described in the definition. In general, any uncertainty or variation in classifying events can influence the resulting counts. Masking may help limit assessment influenced by treatment knowledge, but the registry does not explain how outcome adjudication was conducted or who was masked.

What can and cannot be inferred from the reported comparison?

The arm-level counts and contrast describe the recorded primary endpoint in the two randomized groups. In general, confidence intervals express uncertainty in an estimated quantity under the analysis assumptions; they do not include every possible source of uncertainty, such as limitations in event ascertainment or missing data. The registry record does not report the handling of missing endpoint data, the analysis population, or whether the primary analysis followed an intention-to-treat principle. Those details should not be inferred from the displayed counts.

The record lists three secondary outcomes and four outcome measures, but the detailed definitions and inferential results for the secondary outcomes are not reported in the registry information available for this analysis. It lists no posted analyses. The multiplicity approach and any prespecified hierarchy for outcomes are not reported in the registry record. In general, when several outcomes or analyses are considered, the chance of at least one apparently notable result can change unless the analysis strategy addresses multiplicity. No adjustment procedure can be assumed.

10. Confidence Intervals and Precision

The risk-difference estimate is -0.008, with a 95% confidence interval from -0.054 to 0.038. This interval is the main indication of the statistical precision of the absolute comparison. It includes zero and extends into both negative and positive differences, so the point estimate alone should not be treated as a precise description of the underlying contrast.

In general, a confidence interval gives a range of values compatible with the data under the method and assumptions used to construct it. It does not mean there is a 95% probability that the fixed true value lies in this particular interval. The registry record does not identify the method used to calculate the interval, so no specific calculation procedure should be inferred.

The relative measures also have intervals that include their no-difference values: 0.836 to 1.135 for the risk ratio and 0.774 to 1.199 for the odds ratio. These ranges indicate uncertainty on their respective scales. The risk difference is often more directly interpretable as an absolute contrast, while relative measures express a ratio; none removes the uncertainty in the underlying data.

Precision is distinct from clinical importance. The registry record does not report a threshold defining a clinically important difference, nor an equivalence or noninferiority margin. The confidence intervals therefore cannot establish equivalence or rule out all effects that might matter in a particular setting. They describe the uncertainty around the reported estimates, not the certainty of a clinical conclusion.

11. Planning a Similar Trial: Sample Size

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

The planning figures are participants per arm, not total event counts. The planning illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses the observed effect as its reference and considers planning for 100%, 75%, or 50% of that observed effect. For planning for 100% of the observed effect, the listed figures are 52,953 participants per arm for 80% power and 70,889 participants per arm for 90% power. For planning for 75% of the observed effect, they are 94,312 and 126,257 participants per arm. For planning for 50% of the observed effect, they are 212,590 and 284,597 participants per arm.

The 80% power column describes a planning target under the stated assumptions: if the assumed effect and model were correct, the planned design would have an 80% chance of rejecting the null under the specified test. The 90% column expresses the analogous target at a higher probability of detecting that assumed effect. These figures are planning illustrations, not observed power.

As the assumed effect becomes smaller, a study generally needs more participants to detect it at the same power and significance level. That pattern is reflected in the listed planning values. These calculations are based on the observed effect and are not evidence about the trial's original design process. The trial's original sample-size assumptions are not reported in the registry record. Any curve should be read as expressing this relationship between an assumed effect and the number of participants planned per arm, under the stated assumptions.

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 = 0.307; treatment proportion p₁ = 0.299; average p̄ = 0.303.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6502 = 1.2743.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6501 = 0.5472.
4. n = (1.2743 + 0.5472)² / (-0.0079)² = 52,952.6, rounded up to 52,953 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 <- 0.307387862796834                          # control proportion
p1 <- 0.299472295514512                          # 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(970489)
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 = 52,953 (80% power), 70,889 (90% power)
 75% of observed effect: n per arm = 94,312 (80% power), 126,257 (90% power)
 50% of observed effect: n per arm = 212,590 (80% power), 284,597 (90% power)
power.prop.test: 52952.6 
Simulated power at n = 52,953 per arm: 0.794 (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 endpoint and identifies three secondary outcomes: post-op AF, other arrhythmias, and other endpoints. It also records four outcome measures. The detailed definitions and results for the secondary outcomes are not reported in the registry information available for this analysis. The registry lists no posted analyses.

Multiplicity arises in general when investigators conduct several statistical tests or examine multiple outcomes, time points, or analysis choices. Without a stated strategy, a reader cannot determine how the probability of false-positive findings across multiple comparisons was controlled, or whether a hierarchy was used to prioritize outcomes. The multiplicity strategy is not reported in the registry record. The primary comparison is therefore described using the posted unadjusted p-value, not as part of a documented family-wise adjusted analysis.

Missing data can affect a binary endpoint if outcome status is unknown for some participants. The record does not report how missing primary outcome data were handled, whether any participants lacked endpoint assessment, or whether imputation or sensitivity analyses were used. The listed arm sizes and event counts should not be taken as evidence of a particular missing-data procedure.

The analysis population is also not reported in the registry record. The available information does not say whether the comparison used all randomized participants, participants with observed outcomes, or another defined population. Nor does it report whether the primary analysis followed an intention-to-treat principle or how protocol deviations were handled. These omissions limit assessment of whether the posted estimates reflect the originally assigned groups in full.

In general, these details matter because the results of a trial can depend not only on the outcome definition but also on which participants and comparisons enter the analysis. They cannot be reconstructed from event counts alone. No assumptions about missingness, analysis population, or multiplicity adjustment should be made beyond the information stated in the registry record.

14. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: cardiac (7.1%), bleeding (4.7%), infection (3.4%), pulmonary (3.0%), neurologic (2.0%).

The serious adverse event information lists 147 participants in the olive oil capsule arm and 136 in the omega-3 fatty acid capsule arm as affected by serious adverse events. The listed at-risk count is 758 in each arm. For other adverse events, the figures are 20 in the olive oil capsule arm and 19 in the omega-3 fatty acid capsule arm, again with 758 listed at risk in each arm.

The serious-event terms listed most prominently are cardiac, 7.1%; bleeding, 4.7%; infection, 3.4%; pulmonary, 3.0%; neurologic, 2.0%; and constitutional symptoms, 1.3%. These are the recorded percentages associated with the listed terms. The registry information does not provide further detail about the event definitions, severity gradations, timing, or whether terms could overlap within participants.

These figures describe reported safety events and should not be interpreted as proof that one arm is safer than the other. The death counts are not reported in the registry record. The available information also does not describe causal attribution, statistical comparisons for safety, or methods used to collect and classify adverse events. Serious adverse events and other adverse events are presented as separate summaries, and the record does not explain their relationship in further detail.

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

The primary endpoint records whether participants experienced any first qualifying post-operative AF or flutter during the stated assessment window. The posted comparison shows 227.0 events among 758.0 participants in the omega-3 fatty acid capsule arm and 233.0 among 758.0 in the olive oil capsule arm. The reported risk difference is -0.008, and its 95% confidence interval runs from -0.054 to 0.038. The unadjusted p-value is 0.737.

These results describe the observed event counts and the uncertainty around the estimated comparison. The interval includes no difference and allows estimates in either direction. The result is not proof that the treatments are identical, and it does not establish that every potentially important difference has been excluded. The registry record does not define a threshold for clinical importance or report an equivalence margin.

The endpoint and follow-up period also delimit what the result addresses. It concerns a first qualifying AF or flutter event, with the stated rhythm confirmation and duration criteria, up to 10 days post-surgery or discharge, whichever came sooner. It does not by itself address recurrent episodes, other arrhythmias, outcomes beyond that window, or every potential consequence of cardiac surgery.

The safety summaries give counts of participants with serious and other adverse events, along with listed serious-event terms. They do not provide enough detail to determine causation or to make a complete comparative safety assessment. Death counts are not reported in the registry record.

Overall, the posted primary data show a small observed contrast on the reported scales, with uncertainty spanning both directions. The statistical results should be read as an estimate for this defined endpoint and trial population, not as a general claim about all patients, all treatment regimens, or all outcomes.

16. Why This Trial Matters Statistically

This trial is statistically informative because it compares a defined binary post-operative event between randomized groups and reports both absolute and relative measures. The risk difference of -0.008 gives an absolute-scale estimate, while the risk ratio of 0.974 and odds ratio of 0.963 express the comparison on relative scales. Reading these measures together helps distinguish the scale of a contrast from the uncertainty around it.

The confidence intervals are particularly important. The risk-difference interval extends from -0.054 to 0.038, and the intervals for the risk ratio and odds ratio include their respective no-difference values. These ranges make clear that a point estimate alone is not enough to characterize the evidence. The reported p-value of 0.737 also needs to be interpreted as an unadjusted statistical summary, not as a measure of clinical importance or as the probability that a treatment effect is absent.

The endpoint definition illustrates how outcome construction shapes a statistical comparison. Requiring an event to last at least 30 seconds and be supported by rhythm-strip or 12-lead ECG evidence specifies what counts, while inclusion of probable AF affects the scope of the outcome. Clear operational definitions help readers understand what the counts represent, even though details of adjudication and missing-data handling are not reported.

The planning illustration provides a further statistical lesson: sample-size requirements depend on the effect assumed for planning. Smaller assumed effects require more participants to reach the same power target under the listed assumptions. These planning values are not observed power and do not establish the trial's original design rationale.

Finally, the record's lack of detail on multiplicity, analysis populations, and missing data illustrates why a result estimate cannot be fully assessed from counts and a p-value alone. Those details are part of understanding the robustness and scope of a trial's statistical conclusions.

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.

Several trial-specific details needed for a fuller interpretation are not reported in the registry record. The eligibility criteria and further characteristics of the cardiac surgery population are not described in the information available for this analysis. This limits assessment of how closely the enrolled population matches any particular clinical setting.

The registry does not report the dose or detailed schedule for the omega-3 fatty acid capsules, nor detailed administration information for the olive oil capsule. It also does not explain the randomization procedure or who was included in quadruple masking. The study is described as multi-center, but the number and characteristics of centers are not reported in the record information used.

For the primary endpoint, the record states the duration, confirmation requirements, and assessment window, but does not report the process for outcome adjudication or event classification. It does not describe missing outcome data, the analysis population, protocol deviations, or sensitivity analyses. The statistical test and any adjusted primary model are not reported in the registry record.

Detailed definitions and comparative results for the listed secondary outcomes are not reported in the information available for this analysis. The record also does not report a multiplicity strategy, the original sample-size assumptions, or a clinically important difference threshold. These gaps limit assessment of the broader outcome picture and of how the primary finding relates to the original design and analysis plan.

Finally, the outcome window ends at 10 days post-surgery or discharge, whichever came sooner. The posted primary comparison therefore does not describe later outcomes. Death counts are not reported in the registry record, and the available safety summary does not provide event-level details or causal attribution.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Omega-3 Fatty Acids for Prevention of Post-Operative Atrial Fibrillation — NCT00970489.
• Registry record last updated 2017-04-10; status last verified 2017-02.
• Results first posted 2017-04-10.
• 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

NCT00970489 is the completed phase 3 OPERA randomized, quadruple-masked, parallel-group trial sponsored by Brigham and Women's Hospital. It compared omega-3 fatty acid capsules with olive oil capsules in patients undergoing cardiac surgery; the registry describes the study as multi-center and lists enrollment of 1516.

The primary outcome was any first post-operative AF or flutter lasting at least 30 seconds and confirmed by rhythm strip or 12-lead ECG, assessed up to 10 days post-surgery or discharge, whichever came sooner. The reported event counts were 227.0 in the omega-3 arm and 233.0 in the olive oil arm, with 758.0 participants listed in each arm.

The reported risk difference was -0.008 (95% confidence interval -0.054 to 0.038), with an unadjusted p-value of 0.737. The registry also reports risk-ratio and odds-ratio estimates with confidence intervals that include their no-difference values. Details on missing data, analysis populations, multiplicity, and the original design assumptions are not reported in the registry record.