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Prevention & Control Phase 3 Binary Endpoint NCT01776424

Rivaroxaban for the Prevention of Major Cardiovascular Events in Coronary or Peripheral Artery Disease: Complete Statistical Analysis

The COMPASS trial compared rivaroxaban regimens with aspirin-based control in people with coronary or peripheral artery disease. The analysis focuses on the primary cardiovascular composite, sponsor-reported time-to-event results, unadjusted recalculations, and the limits of the registry record.

Trial start: 2013-02-28  ·  Enrollment: 27395  ·  Sponsor: Bayer
Scope of this record

This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.

1. Trial at a Glance

This page covers the registry results for Rivaroxaban for the Prevention of Major Cardiovascular Events in Coronary or Peripheral Artery Disease (NCT01776424), a randomized phase 3 study. The primary outcome is The First Occurrence of the Composite Primary Efficacy Outcome, Myocardial Infarction (MI), Stroke, or Cardiovascular (CV) Death.

27395
Enrollment
Phase 3
3
Arms
In the primary outcome
-0.8 pts
Risk difference
Rivaroxaban 2.5mg + Aspirin 100mg
-1.4 to -0.2 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01776424
PhasePhase 3
ConditionPrevention & Control
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment27395
Arms in the primary outcome3
Lead sponsorBayer
Results postedYes

2. Clinical Question

Population

Participants with coronary artery disease or peripheral artery disease were the intended population, as stated in the study objectives. The primary efficacy analysis included participants randomized to antithrombotic treatment in the initial study part. The registry record does not report detailed eligibility criteria or the clinical characteristics needed to describe how closely the enrolled participants represented particular patient groups.

Intervention

One regimen was rivaroxaban 2.5 mg twice daily with aspirin 100 mg once daily. A second regimen was rivaroxaban 5 mg twice daily with aspirin placebo. Treatments were administered orally. Some participants were also randomized to pantoprazole or matching placebo; this additional randomization was separate from the antithrombotic comparison.

Comparator

The control regimen was rivaroxaban placebo twice daily with aspirin 100 mg once daily. The posted results also include a comparison of rivaroxaban 5 mg twice daily with aspirin placebo against this control. Thus, the two experimental regimens differed in whether aspirin was active as well as in the rivaroxaban regimen.

Primary question

The primary question was whether the first occurrence of myocardial infarction, stroke, or cardiovascular death differed across the antithrombotic regimens. The registry describes two objectives: comparing rivaroxaban 2.5 mg twice daily plus aspirin with aspirin, and comparing rivaroxaban 5 mg twice daily with aspirin. The primary outcome is a composite, so it records whether any listed event occurred first; it does not, by itself, describe each component separately.

3. Trial Design

This was a completed phase 3 randomized controlled trial with a parallel-group design and quadruple masking. The registry reports enrollment of 27395 participants and identifies Bayer as the sponsor. The study began on 2013-02-28, and the listed primary completion date is 2017-07-21. These design features describe the trial structure, but do not establish how well randomization was implemented or how masking was maintained in practice.

The three antithrombotic groups were rivaroxaban 2.5 mg twice daily plus aspirin 100 mg once daily; rivaroxaban 5 mg twice daily plus aspirin placebo; and rivaroxaban placebo twice daily plus aspirin 100 mg once daily. The descriptions specify oral tablet administration. Participants who did not have a continuous need for a proton pump inhibitor could also be randomized to pantoprazole or its placebo. The registry record does not give the complete details of this additional randomization in the arm descriptions.

The primary efficacy population is described as the intention-to-treat set, including all participants randomized to antithrombotic treatment for the initial study part. It includes participants randomized to pantoprazole or placebo and participants who were not randomized to that additional treatment. The event window ran from randomization to the global rivaroxaban/aspirin outcomes cut-off date of 06 FEB 2017; the reported mean follow-up to that date was 702 days.

The record reports both counts of participants with events and log-rank hazard-ratio analyses. The original trial's sample-size justification, detailed allocation procedures, operational masking procedures, and planned interim analyses 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: Overall, 29872 participants were screened, of which 2477 participants were screen failures. A total of 27395 participants were randomized to antithrombotic treatment. 17598 participants were randomized to pantoprazole/placebo treatment. 12964 participants joined long-term open-label extension (LTOLE) part.

Antithrombotic Part (Double Blind)

StageRivaroxaban 2.5mg + Aspirin 100mgRivaroxaban 5mg + Aspirin PlaceboRivaroxaban Placebo + Aspirin 100mg
STARTED915291179126
Treated With Antithrombotic Treatment913491099107
Randomized to Study Pantoprazole/Placebo587858595861
COMPLETED913290989102
NOT COMPLETED201924

Reasons for not completing this period:

ReasonRivaroxaban 2.5mg + Aspirin 100mgRivaroxaban 5mg + Aspirin PlaceboRivaroxaban Placebo + Aspirin 100mg
Lost to Follow-up1089
Withdrawal by Subject101115

LTOLE Part (Open Label)

StageRivaroxaban 2.5mg + Aspirin 100mgRivaroxaban 5mg + Aspirin PlaceboRivaroxaban Placebo + Aspirin 100mg
STARTED439942924273
Treated in LTOLE Part437942744250
COMPLETED432042304195
NOT COMPLETED796278

Reasons for not completing this period:

ReasonRivaroxaban 2.5mg + Aspirin 100mgRivaroxaban 5mg + Aspirin PlaceboRivaroxaban Placebo + Aspirin 100mg
Lost to Follow-up625
Refused5211
Missing final visit685862

Analysis population for the primary outcome, as defined in the registry: ITT: included all participants randomized to antithrombotic treatment for the initial study part. The ITT set comprised both participants randomized to pantoprazole/placebo and participants not randomized to pantoprazole/placebo.

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: Intent-to-treat analysis set (ITT): included all participants randomized to antithrombotic treatment for the initial study part. The ITT set comprised both participants randomized to pantoprazole/placebo and participants not randomized to pantoprazole/placebo.

CharacteristicUnitRivaroxaban 2.5mg + Aspirin 100mgRivaroxaban 5mg + Aspirin PlaceboRivaroxaban Placebo + Aspirin 100mgTotal
Participants analysed91529117912627395
Age, ContinuousYears68.3 (SD 7.9)68.2 (SD 7.9)68.2 (SD 8.0)68.2 (SD 7.9)
Sex: Female, Male: FemaleParticipants2059197219896020
Sex: Female, Male: MaleParticipants70937145713721375
Race/Ethnicity, Customized: ChineseParticipants3883813761145
Race/Ethnicity, Customized: HispanicParticipants1769175117585278
Race/Ethnicity, Customized: White/CaucasianParticipants56735672568217027
Race/Ethnicity, Customized: South AsianParticipants107102106315
Race/Ethnicity, Customized: Other AsianParticipants9569389152809
Race/Ethnicity, Customized: Black/African AmericanParticipants769492262
Race/Ethnicity, Customized: OtherParticipants183179197559

6. Primary Endpoint

The registry lists the primary outcome as The First Occurrence of the Composite Primary Efficacy Outcome, Myocardial Infarction (MI), Stroke, or Cardiovascular (CV) Death, measured over For each participant, the first occurrence of the composite primary efficacy outcome after randomization up until the global rivaroxaban/aspirin outcomes cut-off date (06 FEB 2017) was considered. The mean time in follow-up until that date was 702 days..

ElementRegistry entry
Result typeCount Of Participants
Measure of spreadnot applicable
UnitParticipants
Endpoint classificationBinary Endpoint

The primary endpoint is the first occurrence of the composite of myocardial infarction, stroke, or cardiovascular death after randomization. A composite endpoint groups several clinically distinct events into one outcome. It can capture whether participants experience any event in the specified set, while the overall result does not show which component accounts for the pattern. Component-specific results for this primary endpoint are not reported in the registry record.

The registry describes the event as the first qualifying occurrence up to the global rivaroxaban/aspirin outcomes cut-off date, 06 FEB 2017. It also reports a mean follow-up of 702 days to that date. The endpoint description says that time from randomization to the first event was evaluated and that hazard ratios were calculated. This makes a time-to-event analysis relevant: it uses information about when an event occurred and can account for differing follow-up times, subject to the analysis method's assumptions.

Counts of participants with an event offer a more direct summary of how many people in each group had a recorded event during the specified follow-up. Those counts do not convey event timing. Because the counts and time-to-event analyses answer related but not identical statistical questions, they should not be treated as interchangeable. The reported log-rank hazard ratios are the sponsor's time-to-event comparisons; the recalculated risk differences are unadjusted comparisons based on the posted event counts.

7. Results Posted in the Registry

Risk difference: Rivaroxaban 2.5mg + Aspirin 100mg

-0.8

95% CI: -1.4 to -0.2 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals3.54.14.65.15.66.1Rivaroxaban 2.5mg + Aspirin 1… (n=9152)Rivaroxaban 5mg + Aspirin Pla… (n=9117)Rivaroxaban Placebo + Aspirin… (n=9126)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Rivaroxaban 2.5mg + Aspirin 1…Rivaroxaban Placebo + Aspirin…-1.58-0.99-0.400.190.781.37risk difference (percentage points) vs control (95% CI)

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.

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
The First Occurrence of Myocardial Infarction (MI), Ischemic Stroke, Acute Limb Ischemia (ALI), or Coronary Heart Disease (CHD) DeathBinary EndpointRisk difference-0.8 pts (-1.3 to -0.2)10,381 per arm
The First Occurrence of MI, Ischemic Stroke, ALI, or Cardiovascular (CV) DeathBinary EndpointRisk difference-0.7 pts (-1.3 to -0.1)13,377 per arm
All-cause MortalityBinary EndpointRisk difference-0.6 pts (-1.1 to -0.0)15,898 per arm

The First Occurrence of Myocardial Infarction (MI), Ischemic Stroke, Acute Limb Ischemia (ALI), or Coronary Heart Disease (CHD) Death

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Rivaroxaban 2.5mg + Aspirin 1…Rivaroxaban Placebo + Aspirin…-1.53-0.94-0.360.220.811.39risk difference (percentage points) vs control (95% CI)

The First Occurrence of MI, Ischemic Stroke, ALI, or Cardiovascular (CV) Death

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Rivaroxaban 2.5mg + Aspirin 1…Rivaroxaban Placebo + Aspirin…-1.54-0.92-0.300.310.931.55risk difference (percentage points) vs control (95% CI)

All-cause Mortality

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Rivaroxaban 2.5mg + Aspirin 1…Rivaroxaban Placebo + Aspirin…-1.29-0.86-0.43-0.010.420.85risk difference (percentage points) vs control (95% CI)

The registry posts three secondary outcomes: a composite involving myocardial infarction, ischemic stroke, acute limb ischemia, or coronary heart disease death; a composite involving myocardial infarction, ischemic stroke, acute limb ischemia, or cardiovascular death; and all-cause mortality. For each, results include sponsor-reported log-rank hazard ratios as well as participant counts and unadjusted recalculations. The overall pattern is that the sponsor-reported comparisons of rivaroxaban 2.5 mg plus aspirin with the aspirin-based control have hazard-ratio estimates below 1, while the 5 mg rivaroxaban regimen has estimates closer to 1 and with less consistent evidence across the reported secondary outcomes.

These outcomes provide related context for the primary composite, but they are not independent confirmations in the simple sense: some contain events that overlap with the primary outcome, and all-cause mortality is a broader endpoint. The secondary outcomes can help describe whether the primary pattern is accompanied by similar findings in related event groupings, but they do not replace the prespecified primary question. The registry record does not report component-level results for the primary composite.

Unadjusted secondary p-values carry less weight when many outcomes and comparisons are examined. General statistical explanation: testing multiple hypotheses increases the chance that at least one result appears statistically notable by chance, unless the analysis plan accounts for multiplicity. The registry record does not report a multiplicity adjustment or a testing hierarchy for the posted secondary analyses. Therefore, secondary estimates and p-values are best treated as supportive or exploratory signals rather than as stand-alone confirmatory conclusions. The posted results do not establish that every secondary finding was part of a familywise controlled analysis.

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

9. Statistical Interpretation

Clinical Biostats interpretation

For the primary composite, the sponsor-reported log-rank analysis comparing rivaroxaban 2.5 mg twice daily plus aspirin 100 mg once daily with rivaroxaban placebo plus aspirin reported a hazard ratio of 0.76, with a 95% confidence interval from 0.66 to 0.86 and p < 0.001. The interval lies below 1, and the reported p-value is small under the statistical test used. This is evidence of a difference in time to the first primary event in that comparison, as analyzed by the sponsor; it is not a direct measure of the absolute difference in the chance of an event.

The sponsor's comparison of rivaroxaban 5 mg twice daily with aspirin placebo against rivaroxaban placebo plus aspirin reported a hazard ratio of 0.90, with a 95% confidence interval from 0.79 to 1.03 and p = 0.115. This interval includes 1, and the reported test does not provide clear evidence of a time-to-event difference at conventional significance thresholds. The result should be read as uncertain rather than as proof that the groups are identical.

The unadjusted recalculation based on participant counts estimates a risk difference of -0.008 for the 2.5 mg rivaroxaban plus aspirin group versus the control group, with a 95% interval from -0.014 to -0.002 and p = 0.012. For rivaroxaban 5 mg twice daily versus control, the recalculated risk difference is 0.005, with a 95% interval from -0.001 to 0.012 and p = 0.112. These estimates are simple, unadjusted calculations from posted summary counts, not the sponsor's time-to-event analysis.

The record marks a discrepancy between the sponsor analyses and the recalculated results. The sponsor's own analysis therefore takes precedence when describing the trial's reported inferential result. The count-based recalculations can still help readers understand the direction and approximate scale of the observed event proportions, but their methods differ from the reported log-rank analyses. Neither set of results establishes what would occur in every individual or population. Interpretation also depends on the composite endpoint, follow-up, analysis population, and the multiplicity and missing-data details that the registry does not report.

10. Statistical Methods Explained

The posted primary results use two kinds of statistical summaries: participant event counts with unadjusted recalculations, and sponsor-reported log-rank hazard ratios. These summaries describe related aspects of the randomized comparisons, but they are not the same estimand and need not produce identical numerical estimates or p-values.

What a participant count captures

A binary event summary classifies each participant according to whether the specified event occurred within the recorded period. The primary arm counts are 379 of 9152 for rivaroxaban 2.5 mg plus aspirin, 448 of 9117 for rivaroxaban 5 mg plus aspirin placebo, and 496 of 9126 for rivaroxaban placebo plus aspirin. Such counts are easy to interpret as numbers of participants with a recorded event. On their own, however, they do not show when events occurred or whether follow-up differed among participants.

The recalculated risk difference is the estimated difference between the two event proportions, expressed as a proportion rather than as a relative comparison. A negative estimate means the event proportion is lower in the named experimental group in that calculation; a positive estimate means it is higher. The recalculated primary risk difference is -0.008 for rivaroxaban 2.5 mg plus aspirin versus control, and 0.005 for rivaroxaban 5 mg twice daily versus control. These are unadjusted calculations from the posted counts. They should not be presented as adjusted trial estimates or substituted for the sponsor's time-to-event analysis.

Why analyze time to event

General statistical explanation: time-to-event methods use both whether an event occurred and the time until the event or the end of observed follow-up. This can be useful when participants have different follow-up durations. A participant without a recorded event by the end of observation is commonly treated as censored at the last relevant observation, but the specific censoring rules used in the sponsor analysis are not reported in the registry record.

The sponsor reports log-rank analyses and hazard ratios. A hazard ratio compares the event rates over time between groups under the time-to-event framework. A value below 1 indicates a lower estimated event hazard in the first-named group relative to its comparator; it does not directly say how many fewer participants had events. The log-rank test evaluates evidence of a difference in the event-time distributions. The registry reports a hazard ratio, confidence interval, and p-value for each primary comparison, but does not report the full model specification or diagnostics.

Confidence intervals and p-values

General statistical explanation: a confidence interval communicates uncertainty around an estimate under the assumptions of the method. A narrower interval indicates greater statistical precision than a wider interval, while an interval containing the null value can include both directions of effect. For a risk difference, the null value is zero; for a hazard ratio, it is 1. A p-value describes how compatible the observed data are with a specified null hypothesis under the test assumptions. It is not the probability that the null hypothesis is true, nor does it measure clinical importance.

The sponsor's primary hazard-ratio results are based on log-rank analyses. The risk differences, risk ratios, odds ratios, and corresponding intervals in the recalculations are unadjusted derivations from summary counts. Because the registry flags a discrepancy, the sponsor's own analysis takes precedence for the trial's reported time-to-event inference. The recalculated results remain descriptive supplements, not a replacement for the sponsor's analysis.

What the analysis record leaves unspecified

The primary population is described as intention-to-treat and includes participants randomized to the initial antithrombotic study part, whether or not they were also randomized to pantoprazole or placebo. The registry does not report details of missing outcome handling, the precise censoring rules, adjustments for baseline variables, or the full statistical analysis plan. It also does not report whether the sponsor's analyses accounted for multiple comparisons or whether interim analyses were conducted. These omissions limit independent reconstruction of the inferential analysis from the registry record alone.

General statistical explanation: over-dispersion is relevant when data vary more than a model's assumed distribution allows, which can make standard errors too small if ignored. The primary outcome is reported as a binary participant event and as a time-to-event analysis, not as a count outcome with a dispersion estimate. The registry record does not report an over-dispersion assessment, and no such assessment can be inferred from the posted participant counts.

11. Confidence Intervals and Precision

Precision is described by the width and placement of an estimate's confidence interval. The sponsor's primary hazard ratio for rivaroxaban 2.5 mg plus aspirin versus control is 0.76, with a 95% confidence interval from 0.66 to 0.86. This interval is entirely below the hazard-ratio null value of 1. The sponsor's primary hazard ratio for rivaroxaban 5 mg twice daily versus control is 0.90, with a 95% confidence interval from 0.79 to 1.03; this interval includes 1 and permits uncertainty about the direction of the relative difference.

The unadjusted risk-difference interval for the 2.5 mg rivaroxaban plus aspirin comparison is -0.014 to -0.002. The corresponding interval for rivaroxaban 5 mg twice daily is -0.001 to 0.012. For a risk difference, zero is the null value. These count-based intervals therefore express uncertainty about the absolute difference in participant event proportions, while the sponsor intervals express uncertainty about the time-to-event hazard ratio. They should not be read as estimates of precisely the same quantity.

A confidence interval is not a guarantee that the true effect lies within its endpoints. General statistical explanation: under the model and repeated-sampling procedure used, a 95% confidence procedure would cover the fixed target parameter in 95% of repeated applications. The width reflects information and assumptions, and the endpoints do not describe the range of individual outcomes. The registry does not report the full methods needed to reproduce the sponsor intervals independently.

The count-based recalculations are marked as discrepant from the sponsor analyses. The sponsor's own analysis takes precedence for the trial's reported inferential result. The intervals should therefore be read alongside the stated method and analysis population rather than selected solely by which interval appears more favorable or more precise.

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.

Effect to detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect11,36315,211
75% of the observed effect20,61227,593
50% of the observed effect47,29863,319
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect10,00020,00050,000100,000200,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, pooled-variance normal approximation for two proportions (control proportion held at the observed value). Calculated for the comparison: Rivaroxaban 2.5mg + Aspirin 100mg.

The planning figures are illustrations based on the observed effect, not the trial's original design calculation. The registry does not report the original sample-size justification or the original design assumptions. For binary participant outcomes, the listed figures are participants per arm. The sample-size assumptions state a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each planning scenario uses the stated fraction of the observed effect as the effect to detect.

The 80% power column gives the planned number of participants per arm under the stated assumptions for a design with an 80% chance of rejecting the null hypothesis if the assumed effect were the true effect. The 90% power column gives the corresponding per-arm planning count for a 90% chance under those same assumptions. These are design probabilities conditional on the assumptions, not probabilities that the observed result is correct.

For example, planning for 75% of the observed effect requires more participants per arm than planning for 100% of the observed effect in the listed comparisons. Planning for 50% of the observed effect requires still more. This reflects a general principle: smaller effects are harder to distinguish from random variation, so larger samples are needed to achieve the same target power.

These figures are a planning illustration and not observed power. They should not be used to infer the probability that the completed trial detected a true effect. The trial's actual enrollment was 27395, but comparing that total directly with a per-arm planning figure would not be a like-for-like comparison. The time-to-event planning convention described in the assumptions is different: those figures represent total events, calculated using the Schoenfeld method. The primary binary endpoint planning figures are participants per arm.

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 z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n = [ z1−α/2 √(2p̄(1−p̄)) + z1−β √(p0(1−p0) + p1(1−p1)) ]2 / (p1 − p0)2

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 = 0.049; treatment proportion p1 = 0.041; average p̄ = 0.045.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.2940 = 0.5763.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.2940 = 0.2474.
  4. n = (0.5763 + 0.2474)2 / (-0.0077)2 = 11,362.7, rounded up to 11,363 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 <- 0.0491389711527915                          # control proportion
p1 <- 0.0414117132867133                          # 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(1776424)
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 = 11,363 (80% power), 15,211 (90% power)
 75% of observed effect: n per arm = 20,612 (80% power), 27,593 (90% power)
 50% of observed effect: n per arm = 47,298 (80% power), 63,319 (90% power)
power.prop.test: 11362.7 
Simulated power at n = 11,363 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.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Log RankHazard Ratio (HR) 0.760.66 to 0.86< 0.001
Log RankHazard Ratio (HR) 0.900.79 to 1.030.115
Where the two analyses differ, rely on the sponsor's. The simple re-calculation above reaches a different conclusion from the sponsor's analysis, usually because the sponsor adjusts for covariates, stratification or repeated measures, or (for event rates) uses a negative binomial model that allows for over-dispersion and so gives wider intervals.

The sponsor's primary analyses are log-rank comparisons reported as hazard ratios, with 95% confidence intervals and p-values. These are the trial's stated time-to-event results. The recalculations use posted participant counts to estimate unadjusted risk differences and related measures. They do not reproduce the sponsor's event-time analysis, because the counts alone do not retain event timing or the full follow-up information used for a time-to-event comparison.

The registry identifies a discrepancy between the recalculated results and the sponsor's analysis. Accordingly, the sponsor's own analysis takes precedence when reporting the trial's inferential conclusions. The recalculations can be useful as a transparent, count-based supplement: they show the direction and uncertainty of an unadjusted difference in event proportions. They should not be used to override the sponsor's time-to-event estimate or to imply that the analytic approaches are interchangeable.

For the primary comparison of rivaroxaban 2.5 mg plus aspirin with control, the sponsor reports a hazard ratio of 0.76 and p < 0.001; the recalculated risk difference is -0.008 with p = 0.012. For rivaroxaban 5 mg twice daily versus control, the sponsor reports a hazard ratio of 0.90 and p = 0.115; the recalculated risk difference is 0.005 with p = 0.112. Differences between the estimates and p-values are not, by themselves, evidence of an error: they arise from distinct summaries and methods, and the detailed sponsor analysis cannot be reconstructed fully from the registry record.

15. Multiplicity, Missing Data and Analysis Populations

The registry describes a primary composite and several secondary outcomes, with comparisons involving more than one antithrombotic regimen. It reports p-values for the sponsor's primary and secondary log-rank analyses, but a multiplicity-adjustment procedure, testing hierarchy, or allocation of the type I error rate is not reported in the registry record. Without those details, the p-values cannot be interpreted as though control of false-positive risk across all outcomes and comparisons has been established.

The registry describes the primary analysis population as intention-to-treat: all participants randomized to antithrombotic treatment for the initial study part, including those who were and were not randomized to pantoprazole or placebo. This definition is useful, but details on how participants with missing outcome information were handled are not reported in the registry record. The record also does not specify censoring rules, exclusions from particular analyses, or whether additional analysis populations were used.

The sample-size assumptions listed for the planning illustration are known, but the original trial's sample-size justification and design assumptions are not reported. Interim analyses, stopping boundaries, and any resulting adjustment to the analysis plan are not reported in the registry record. It is not possible to infer whether interim monitoring occurred from the completed status alone.

These omissions do not invalidate the posted results, but they constrain independent assessment of how the final analyses were selected and how uncertainty was controlled. General statistical explanation: when multiple hypotheses are tested, the chance of at least one false-positive result can increase; when outcome data are missing, conclusions can also depend on the reasons for missingness and the method used to handle it. Those issues require protocol or analysis-plan details not reported in the registry record.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Rivaroxaban 2.5mg + Aspirin 100mg69291347.6%
Rivaroxaban 5mg + Aspirin Placebo66491097.3%
Rivaroxaban Placebo + Aspirin 100mg63091076.9%
LTOLE Rivaroxaban Rivaroxaban 2.5mg + Aspirin 100mg292129032.3%
Participants with at least one serious adverse event
Serious adverse events by armRivaroxaban 2.5mg + Aspirin 1…7.6%Rivaroxaban 5mg + Aspirin Pla…7.3%Rivaroxaban Placebo + Aspirin…6.9%LTOLE Rivaroxaban Rivaroxaban…2.3%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Rivaroxaban 2.5mg + Aspirin 100mg529 of 9152
Rivaroxaban 5mg + Aspirin Placebo566 of 9117
Rivaroxaban Placebo + Aspirin 100mg566 of 9126
LTOLE Rivaroxaban Rivaroxaban 2.5mg + Aspirin 100mg283 of 12964

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0.1% reporting threshold.

ArmParticipants affected of at risk
Rivaroxaban 2.5mg + Aspirin 100mg557 of 9134
Rivaroxaban 5mg + Aspirin Placebo529 of 9109
Rivaroxaban Placebo + Aspirin 100mg501 of 9107
LTOLE Rivaroxaban Rivaroxaban 2.5mg + Aspirin 100mg49 of 12903

Most frequent serious adverse event terms

Event termOrgan systemRivaroxaban 2.5mg + Aspirin 100mgRivaroxaban 5mg + Aspirin PlaceboRivaroxaban Placebo + Aspirin 100mgLTOLE Rivaroxaban Rivaroxaban 2.5mg + Aspirin 100mg
Acute kidney injuryRenal and urinary disorders29 of 913422 of 910920 of 91078 of 12903
PneumoniaInfections and infestations15 of 913421 of 910922 of 910717 of 12903
SepsisInfections and infestations18 of 913418 of 910917 of 91076 of 12903
Lung neoplasm malignantNeoplasms benign, malignant and unspecified (incl cysts and polyps)17 of 913414 of 910911 of 91078 of 12903
Urinary tract infectionInfections and infestations17 of 913414 of 91099 of 91077 of 12903
CataractEye disorders17 of 913411 of 91097 of 91070 of 12903
Large intestine polypGastrointestinal disorders8 of 913414 of 91099 of 91071 of 12903
CholecystitisHepatobiliary disorders10 of 91349 of 910912 of 91070 of 12903
CellulitisInfections and infestations9 of 913411 of 91098 of 91073 of 12903
AngiocardiogramInvestigations10 of 91349 of 910912 of 91070 of 12903

Most frequent non-serious adverse event terms

Event termOrgan systemRivaroxaban 2.5mg + Aspirin 100mgRivaroxaban 5mg + Aspirin PlaceboRivaroxaban Placebo + Aspirin 100mgLTOLE Rivaroxaban Rivaroxaban 2.5mg + Aspirin 100mg
NasopharyngitisInfections and infestations188 of 9134181 of 9109195 of 91070 of 12903
DiarrhoeaGastrointestinal disorders48 of 913458 of 910926 of 91075 of 12903
EpistaxisRespiratory, thoracic and mediastinal disorders38 of 913429 of 910924 of 91071 of 12903
ContusionInjury, poisoning and procedural complications37 of 913422 of 910927 of 91072 of 12903
Back painMusculoskeletal and connective tissue disorders25 of 913437 of 910925 of 91070 of 12903
DizzinessNervous system disorders25 of 913425 of 910935 of 91072 of 12903
ArthralgiaMusculoskeletal and connective tissue disorders28 of 913426 of 910930 of 91070 of 12903
Haemorrhage subcutaneousSkin and subcutaneous tissue disorders49 of 913418 of 910917 of 91070 of 12903
Abdominal pain upperGastrointestinal disorders28 of 913418 of 910921 of 91075 of 12903
Diabetes mellitusMetabolism and nutrition disorders26 of 913416 of 910928 of 91070 of 12903

Serious events with the highest arm-level rate: acute kidney injury (0.3%), pneumonia (0.2%), sepsis (0.2%), cataract (0.2%), urinary tract infection (0.2%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The adverse-event record lists serious adverse events for the three main antithrombotic groups as affected participants and participants at risk. The listed figures are 692 of 9134 for rivaroxaban 2.5 mg plus aspirin, 664 of 9109 for rivaroxaban 5 mg plus aspirin placebo, and 630 of 9107 for rivaroxaban placebo plus aspirin. These are event-section counts, not the primary efficacy outcome. The record also lists other adverse events and deaths separately; these categories should not be combined or treated as interchangeable.

The most frequently listed serious-event terms include acute kidney injury at 0.3%, and pneumonia, sepsis, cataract, urinary tract infection, and lung neoplasm malignant at 0.2% each. A separately labeled LTOLE group is also listed, with 292 of 12903 affected for serious adverse events. Its label distinguishes it from the three main groups, so it should not be combined with them without further information.

These figures describe what the registry reports, but do not by themselves establish causality or comparative safety. The record does not provide sufficient detail about event definitions, exposure-adjusted rates, event timing, severity grading, or how the separately listed group relates to the main analysis period. Counts and percentages should therefore be read as descriptive registry summaries rather than as a complete benefit-harm assessment.

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

The primary results describe comparisons between randomized groups for a composite of myocardial infarction, stroke, or cardiovascular death during the recorded follow-up. The sponsor-reported time-to-event analysis estimates a lower event hazard for rivaroxaban 2.5 mg plus aspirin relative to the aspirin-based control, with a confidence interval below the hazard-ratio null value. For rivaroxaban 5 mg twice daily versus control, the reported confidence interval includes the null value. These statements describe the posted statistical results; they do not predict an individual participant's outcome.

A hazard ratio is a relative time-to-event measure, not an absolute probability or a count of events prevented. The unadjusted risk-difference recalculations offer an absolute comparison of participant event proportions, but the registry flags a discrepancy and the sponsor's own analysis takes precedence. The composite endpoint also combines distinct outcomes. Its overall result does not show which component contributed most, and component-specific primary results are not reported in the registry record.

The registry findings do not establish what would happen in populations outside those enrolled, or under different treatment regimens and follow-up conditions. Detailed eligibility criteria and the complete statistical analysis plan are not reported in the registry record. The results also do not by themselves resolve how to weigh efficacy outcomes against adverse events: the posted safety summaries do not provide a complete comparative assessment of timing, exposure, or causality.

General statistical explanation: a statistically notable estimate is not necessarily large or important in every clinical context, and uncertainty remains even when a confidence interval excludes a null value. The purpose of this interpretation is to describe the analyses and their precision, not to make treatment recommendations. Clinical decisions require evidence and considerations beyond these registry summaries.

18. Why This Trial Matters Statistically

COMPASS is statistically informative because it reports randomized, parallel-group comparisons of multiple antithrombotic regimens and includes both participant event counts and time-to-event analyses. The primary endpoint is a clinically interpretable composite, and the sponsor's log-rank results quantify relative event timing through hazard ratios. The registry also gives confidence intervals, which help readers assess uncertainty rather than relying on a single point estimate or p-value.

The record illustrates why effect measures and analysis methods matter. A simple risk difference based on event counts addresses a different question from a hazard ratio based on event timing. Follow-up is reported as a mean of 702 days to the stated outcome cut-off date, and the time-to-event method can use information about when events occurred. The discrepancy flag makes it especially important to distinguish the sponsor's inferential analysis from unadjusted recalculations based on summary counts.

The multiple primary comparisons and posted secondary outcomes also make multiplicity a meaningful interpretive issue. The registry does not report an adjustment or testing hierarchy, so secondary p-values cannot be assumed to have confirmatory error control. The sample-size planning illustration further shows how power targets depend on the effect assumed: planning for smaller fractions of the observed effect requires larger per-arm samples for binary outcomes. These features make the record useful for statistical education about estimands, confidence intervals, multiplicity, and the limits of registry reporting.

19. Limitations

The primary outcome combines myocardial infarction, stroke, and cardiovascular death, but component-specific primary results are not reported in the registry record. That limits understanding of which events contribute to the composite estimates. Detailed participant eligibility criteria and baseline characteristics are also not reported in the information summarized for this analysis, constraining assessment of generalizability and possible effect variation across participant groups.

The reported mean follow-up is 702 days to the outcomes cut-off date, but the distribution of follow-up and the detailed censoring rules are not reported. Counts of participants with events do not incorporate event timing, while the sponsor's time-to-event analysis cannot be independently reconstructed from the summary counts. The registry flags a discrepancy between sponsor analyses and recalculations; this requires keeping the sponsor analysis primary for inference and treating the recalculated count-based measures as supplementary.

Important analysis-plan details are absent, including the original sample-size justification, multiplicity procedures, interim-analysis plans, missing-outcome handling, and full model specifications. The registry's intention-to-treat population description is useful, but does not answer every question about exclusions or missing data. Safety reporting is also limited: the adverse-event counts and listed terms do not establish causality, account for exposure duration, or provide a complete comparative benefit-harm analysis. These limitations concern what can be learned from the registry record; they do not establish that the underlying trial lacked these procedures or data.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

Continue through the Clinical Biostats statistical pathway

Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.

23. Record Summary

The registry record describes a completed phase 3 randomized, quadruple-masked, parallel-group trial enrolling 27395 participants. The antithrombotic groups were rivaroxaban 2.5 mg twice daily plus aspirin, rivaroxaban 5 mg twice daily with aspirin placebo, and rivaroxaban placebo with aspirin. The primary outcome was the first occurrence of myocardial infarction, stroke, or cardiovascular death, with a mean follow-up of 702 days to the outcomes cut-off date.

The sponsor reported log-rank hazard ratios for both primary comparisons. The 2.5 mg rivaroxaban plus aspirin comparison had a hazard ratio of 0.76, with a 95% confidence interval from 0.66 to 0.86; the 5 mg rivaroxaban comparison had a hazard ratio of 0.90, with a 95% confidence interval from 0.79 to 1.03. The registry flags a discrepancy with unadjusted count-based recalculations, so the sponsor's own analysis takes precedence. Details on multiplicity, missing-data handling, interim analyses, and the original sample-size justification are not reported in the registry record.

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