This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record.
1. Trial at a Glance
NOAH was a double-blind, randomized, parallel-group phase 3 trial evaluating edoxaban versus ASA or placebo in patients with atrial high rate episodes. The primary endpoint was a time-to-event composite of stroke, systemic embolism, or cardiovascular death over 28 months.
| Feature | NOAH |
|---|---|
| Phase | Phase 3 |
| Condition | Atrial High Rate Episodes |
| Design | Randomized, double-blind, parallel-group |
| Allocation | Randomized |
| Primary purpose | Prevention |
| Enrollment | 2608 |
| Arms | 2 |
| Interventions | Edoxaban; ASA |
| Status | Terminated |
| Start | 2016-02 |
| Primary completion | 2022-12-31 |
| Lead sponsor | Atrial Fibrillation Network |
| ClinicalTrials.gov | NCT02618577 |
2. Clinical Question
The central question was whether edoxaban would improve the time to first occurrence of stroke, systemic embolism, or cardiovascular death compared with ASA or placebo in patients with atrial high rate episodes.
Population
Patients with atrial high rate episodes who met the trial's qualifying criteria and were randomized in the phase 3 NOAH trial.
Intervention
Edoxaban.
Comparator
ASA or placebo.
Primary question
Does edoxaban reduce the hazard of the composite of stroke, systemic embolism, or cardiovascular death relative to ASA or placebo?
3. Trial Design
Edoxaban
- Edoxaban was the study drug in the intervention group.
- Primary and secondary time-to-event outcomes were compared with the ASA or placebo group.
- Serious adverse events affected 498 of 1306 patients in this group.
ASA or placebo
- ASA or placebo was the comparator intervention.
- Primary and secondary outcomes were evaluated against the edoxaban group.
- Serious adverse events affected 467 of 1302 patients in this group.
The randomized parallel-group structure is important statistically because treatment assignment creates the basis for a comparative efficacy analysis. Double blinding further reduces the opportunity for knowledge of treatment assignment to influence outcome assessment or participant behavior.
4. Endpoints
| Role | Endpoint | Time frame | Endpoint type |
|---|---|---|---|
| Primary | Composite of Stroke, Systemic Embolism, or Cardiovascular Death | 28 months | Time-to-event |
| Secondary | Components of the Primary Outcome, Stroke | 28 months | Time-to-event |
| Secondary | Components of the Primary Outcome, Systemic Embolism | 28 months | Time-to-event |
| Secondary | Components of the Primary Outcome, Cardiovascular Death | 28 months | Time-to-event |
| Secondary | Major Adverse Cardiac Events (MACEs: Cardiac Death, Myocardial Infarction, Acute Coronary Syndrome (ACS) | 28 months | Time-to-event |
| Secondary | All-cause Death | 28 months | Time-to-event |
| Secondary | Major Bleeding Events | 28 months | Time-to-event |
| Secondary | Quality of Life Changes at 12 and 24 Months Compared to Baseline | Baseline, 12 months and 24 months | Continuous |
| Secondary | Patient Satisfaction at 12 and 24 Months Compared to Baseline | Baseline, 12 months and 24 months | Binary in the registry analysis classification |
The primary endpoint was defined as the time from randomisation to the first occurrence of stroke, systemic embolism, or cardiovascular death, with incidence of the first occurrence of the outcome measure.
5. Statistical Methodology
Primary analysis population
The primary analysis used a modified intention-to-treat population, consisting of all randomized patients with a qualifying atrial high rate episode and intake of at least one dose of study drug.
This population retains the randomized treatment comparison while requiring both a qualifying episode and exposure to at least one dose. The distinction is important: modified intention-to-treat is not identical to analyzing every randomized patient regardless of subsequent treatment exposure.
Cause-specific Cox proportional-hazards model
The primary endpoint was analyzed using a cause-specific Cox proportional-hazards model. The reported effect measure was an adjusted cause-specific hazard ratio comparing edoxaban with ASA or placebo.
The hazard ratio compares the modeled instantaneous event rate between the two randomized groups at a given point in follow-up, conditional on the model and its assumptions.
Effect measures
The registry reports two principal effect-measure families across the posted analyses: hazard ratios for time-to-event outcomes and mean differences for continuous quality-of-life and satisfaction measures.
Superiority framework
The primary and secondary analyses were identified as superiority hypotheses. The primary analysis therefore asks whether the observed time-to-event experience differs in favor of edoxaban rather than whether edoxaban satisfies a non-inferiority margin.
Time-to-event analysis
Time-to-event endpoints incorporate both whether an event occurred and when it occurred. Patients who remain event-free through their available observation period can contribute information through censoring rather than being treated as if they experienced the event.
6. Primary Result: Stroke, Systemic Embolism, or Cardiovascular Death
The primary endpoint was analyzed over a 28-month time frame using an adjusted cause-specific hazard ratio in the modified intention-to-treat population.
Adjusted cause-specific hazard ratio
95% CI: 0.6–1.08 · P = 0.15
Edoxaban vs ASA or placebo
| Primary endpoint | Edoxaban vs ASA or placebo | Interpretation framework |
|---|---|---|
| Composite of stroke, systemic embolism, or cardiovascular death | HR 0.81 (95% CI 0.6–1.08); P = 0.15 | Cause-specific Cox proportional-hazards analysis; superiority hypothesis |
An adjusted hazard ratio of 0.81 means that the fitted model estimated an instantaneous rate of the primary composite endpoint approximately 19% lower with edoxaban than with ASA or placebo, because 1 − 0.81 = 0.19.
The hazard ratio does not mean that 19% fewer patients experienced the endpoint, nor does it describe an absolute reduction in the probability of the composite outcome. It is a relative time-to-event measure.
The two-sided 95% confidence interval of 0.6–1.08 describes uncertainty around the estimated hazard ratio. Because the interval includes 1, the compatible effects include both a lower and a higher estimated hazard under the model.
The P = 0.15 value addresses statistical evidence against the null hypothesis in the specified superiority framework. It does not measure the size of the treatment effect, and it should not be interpreted as the probability that edoxaban is effective or ineffective.
Because the analysis uses a Cox proportional-hazards model, interpretation of a single hazard ratio also depends on the model's proportional-hazards framework. The reported result is additionally tied to the modified intention-to-treat population and the cause-specific analysis specified in the registry.
7. Secondary Time-to-Event Results
The registry contains posted statistical analyses for several secondary time-to-event endpoints. These analyses use the same general hazard-ratio framework, although a formal analysis method was not reported for every secondary endpoint.
| Secondary endpoint | Hazard ratio | 95% CI | P-value |
|---|---|---|---|
| Stroke | 0.79 | 0.45–1.39 | Not reported |
| Systemic Embolism | 0.51 | 0.27–0.96 | Not reported |
| Cardiovascular Death | 0.90 | 0.62–1.31 | Not reported |
| Major Adverse Cardiac Events | 0.89 | 0.67–1.18 | Not reported |
| All-cause Death | 1.16 | 0.88–1.53 | 0.28 |
| Major Bleeding Events | 2.1 | 1.3–3.38 | 0.002 |
Stroke
Adjusted cause-specific hazard ratio
95% CI: 0.45–1.39
Edoxaban vs ASA or placebo
The estimate of 0.79 corresponds to an estimated 21% lower hazard under the fitted model. The confidence interval extends from below 1 to above 1, indicating substantial uncertainty around the magnitude and direction of the relative effect.
Systemic Embolism
Adjusted cause-specific hazard ratio
95% CI: 0.27–0.96
Edoxaban vs ASA or placebo
A hazard ratio of 0.51 corresponds to an estimated 49% lower hazard under the fitted model. The 95% confidence interval of 0.27–0.96 remains below 1, but the interval is relatively broad, reflecting uncertainty around the effect estimate.
Cardiovascular Death
Adjusted cause-specific hazard ratio
95% CI: 0.62–1.31
Edoxaban vs ASA or placebo
The estimate of 0.90 corresponds to an approximately 10% lower estimated hazard under the model. The confidence interval includes 1 and extends in both directions around the null value.
Major Adverse Cardiac Events
Adjusted cause-specific hazard ratio
95% CI: 0.67–1.18
Edoxaban vs ASA or placebo
The estimated hazard was approximately 11% lower with edoxaban. The confidence interval includes 1, so the estimate should be interpreted together with its uncertainty rather than as a definitive reduction.
All-cause Death
Adjusted cause-specific hazard ratio
95% CI: 0.88–1.53 · P = 0.28
Edoxaban vs ASA or placebo
The point estimate corresponds to a 16% higher estimated hazard of death under the fitted model. The confidence interval includes 1, and the reported P-value is 0.28. The result therefore contains uncertainty in both directions around the null value.
Major Bleeding Events
Adjusted cause-specific hazard ratio
95% CI: 1.3–3.38 · P = 0.002
Edoxaban vs ASA or placebo
The reported hazard ratio of 2.1 indicates that the modeled instantaneous rate of major bleeding was estimated to be 2.1 times that in the ASA or placebo group. Expressed descriptively, this is an estimated 110% higher hazard under the fitted model.
The 95% confidence interval of 1.3–3.38 lies above 1, indicating that the interval of model-compatible relative effects is above the null value. The P-value of 0.002 quantifies statistical evidence under the reported superiority testing framework; it does not describe the clinical magnitude or absolute frequency of bleeding.
This endpoint also illustrates why efficacy and safety endpoints should be interpreted separately. A hazard ratio is not a single overall benefit-risk score, and the numerical result for major bleeding cannot by itself be combined algebraically with the primary composite endpoint.
8. Quality of Life and Patient Satisfaction
The registry also contains posted analyses of quality of life and patient satisfaction. These outcomes differ from the primary endpoint because they are continuous measures rather than time-to-first-event outcomes.
| Outcome | Measure | Estimate | 95% CI |
|---|---|---|---|
| Quality of Life Changes at 12 and 24 Months Compared to Baseline | EQ-5D-5L UK Index | Mean difference −0.01 | −0.02 to 0.01 |
| Quality of Life Changes at 12 and 24 Months Compared to Baseline | EQ-5D-5L VAS, FU 24 months | Mean difference −0.04 | −1.46 to 1.38 |
| Quality of Life Changes at 12 and 24 Months Compared to Baseline | Karnofsky score | Mean difference 0.27 | −0.56 to 1.09 |
| Patient Satisfaction at 12 and 24 Months Compared to Baseline | PACT-Q convenience | Mean difference −0.12 | −1.12 to 0.87 |
| Patient Satisfaction at 12 and 24 Months Compared to Baseline | PACT-Q satisfaction | Mean difference −1.04 | −2.60 to 0.52 |
The registry describes these estimates as baseline-adjusted trial-group-specific effect estimates. A mean difference compares average outcomes between the treatment groups on the specified measurement scale; it is not interpreted like a hazard ratio.
A mean difference of −0.01, for example, indicates that the adjusted mean outcome differed by −0.01 units between the groups on the corresponding EQ-5D-5L UK Index measure. The confidence interval of −0.02 to 0.01 expresses uncertainty around that estimated difference.
The same principle applies to the other reported continuous outcomes. The numerical size of a mean difference must be interpreted using the scale and clinical meaning of the instrument; a mean difference is not directly comparable in magnitude with a hazard ratio.
9. Safety Results
Serious adverse events were reported by arm in the registry. These counts provide a direct description of affected patients among those at risk.
| Safety measure | Edoxaban | ASA or placebo |
|---|---|---|
| Serious adverse events | 498 / 1306 | 467 / 1302 |
The serious-adverse-event counts should be distinguished from the major bleeding time-to-event analysis. The former describes affected patients among those at risk, whereas the latter is analyzed as a time-to-event endpoint using an adjusted cause-specific hazard ratio.
10. Statistical Methods Explained
Why was a Cox proportional-hazards model used?
The primary endpoint is defined by time from randomization to the first occurrence of stroke, systemic embolism, or cardiovascular death. A Cox model is designed for this type of censored time-to-event data and provides a relative hazard estimate while accounting for differing follow-up times.
What does a hazard ratio of 0.81 mean?
A hazard ratio of 0.81 means that the fitted model estimates the instantaneous event rate in the edoxaban group at about 81% of that in the ASA or placebo group. The corresponding relative reduction in the modeled hazard is 19%. It does not mean that 19% of patients avoided the event or that absolute risk was reduced by 19 percentage points.
Why is the confidence interval important?
The point estimate is only one representation of the treatment effect. The 95% confidence interval of 0.6–1.08 around the primary hazard ratio shows that the data are compatible with a range of relative effects. A wider interval indicates greater uncertainty than a narrower interval around the same point estimate.
Why does the P-value not measure effect size?
The P-value measures the degree of statistical evidence against a specified null hypothesis under the analysis framework. It is affected by the estimated effect, its variability, and the amount of information available. A P-value therefore cannot substitute for the hazard ratio and its confidence interval when describing the magnitude and precision of an effect.
What is special about a cause-specific hazard ratio?
The registry identifies the primary and several secondary time-to-event analyses as cause-specific Cox analyses. A cause-specific hazard describes the instantaneous rate of the particular event of interest in the presence of competing types of events. It should not automatically be interpreted as a direct comparison of cumulative incidence probabilities.
Why is the modified intention-to-treat population important?
The primary analysis includes randomized patients with a qualifying atrial high rate episode who took at least one dose of study drug. This preserves much of the randomized comparison while imposing the specified qualifying and exposure criteria. The exact analysis population therefore matters when interpreting what population the hazard ratio represents.
11. Understanding the Primary Endpoint Statistically
Composite endpoints combine multiple clinically distinct events into one analysis. Here, the first occurrence of stroke, systemic embolism, or cardiovascular death defines the primary endpoint.
Why use a composite?
A composite can capture several clinically important event types within one time-to-event endpoint. The statistical analysis then evaluates time to the first qualifying component.
Why the first event matters
The registered definition specifically uses the first occurrence of stroke, systemic embolism, or cardiovascular death. Later events do not redefine that patient's first-event time.
Why components need separate context
The individual components can have different clinical frequencies and effect estimates. Component analyses are therefore informative but should not automatically be treated as interchangeable with the composite endpoint.
Why time matters
A patient who experiences an event early and a patient who remains event-free for much longer are not equivalent observations. Survival analysis incorporates the timing of events and censoring.
12. Hazard Ratio, Absolute Risk, and Time-to-Event Interpretation
A hazard ratio is a relative model-based measure. Absolute event probabilities require information about the underlying event-time distribution and cannot be recovered from the hazard ratio alone.
This distinction is particularly important for the NOAH primary endpoint. The reported HR of 0.81 describes the relative event-rate comparison generated by the cause-specific Cox model. It does not establish the absolute number of events prevented, the number needed to treat, or an absolute percentage-point difference at 28 months.
Similarly, the major bleeding HR of 2.1 describes a relative time-to-event comparison. It should not be converted into an absolute bleeding risk without the corresponding underlying event probabilities or survival estimates.
The most complete reading of a time-to-event result combines the effect estimate, the confidence interval, the analysis population, the endpoint definition, and the time frame. Reading only the hazard ratio or only the P-value loses important information.
13. Secondary Endpoint Interpretation
The secondary results illustrate why individual endpoint estimates should be considered in their statistical context.
| Endpoint | Point estimate | 95% CI | What the estimate describes |
|---|---|---|---|
| Stroke | HR 0.79 | 0.45–1.39 | Relative cause-specific hazard |
| Systemic Embolism | HR 0.51 | 0.27–0.96 | Relative cause-specific hazard |
| Cardiovascular Death | HR 0.90 | 0.62–1.31 | Relative cause-specific hazard |
| Major Adverse Cardiac Events | HR 0.89 | 0.67–1.18 | Relative cause-specific hazard |
| All-cause Death | HR 1.16 | 0.88–1.53 | Relative cause-specific hazard |
| Major Bleeding Events | HR 2.1 | 1.3–3.38 | Relative cause-specific hazard |
These estimates span different clinical outcomes, so they should not be collapsed into a single numerical summary. In particular, efficacy endpoints and safety endpoints answer different questions.
14. Confidence Intervals and the Null Value
For hazard ratios, the conventional null value is 1. A hazard ratio of 1 represents equal modeled hazards between the comparison groups.
HR below 1
The estimated hazard is lower in the edoxaban group under the fitted model.
HR equal to 1
The estimated hazards are equal under the model's relative-effect scale.
HR above 1
The estimated hazard is higher in the edoxaban group under the fitted model.
CI crossing 1
The reported confidence interval includes the null value and therefore encompasses no relative difference as well as effects in both directions.
For the primary endpoint, the 95% confidence interval is 0.6–1.08. For major bleeding, the corresponding interval is 1.3–3.38. These intervals convey substantially more information about precision than the point estimates alone.
15. Multiplicity and Multiple Endpoints
NOAH contains one registered primary endpoint and multiple secondary endpoints. This creates a distinction between the primary confirmatory question and the collection of additional analyses.
| Endpoint group | Role | Statistical interpretation |
|---|---|---|
| Composite of stroke, systemic embolism, or cardiovascular death | Primary | Primary superiority comparison |
| Stroke, systemic embolism, cardiovascular death | Secondary components | Component-specific descriptive and inferential analyses |
| Major adverse cardiac events | Secondary | Additional cardiovascular time-to-event outcome |
| All-cause death | Secondary | Additional mortality outcome |
| Major bleeding events | Secondary | Safety-related time-to-event outcome |
| Quality of life and patient satisfaction | Secondary | Continuous outcome analyses |
When several hypotheses are tested, the probability of observing at least one statistically unusual result can increase if no multiplicity strategy is applied. The registry data identify the endpoints and posted analyses but do not provide a multiplicity-adjustment strategy in the information summarized here. Consequently, individual secondary P-values should be interpreted in the context of their secondary status rather than as automatically equivalent to the primary hypothesis test.
16. Censoring and Proportional-Hazards Considerations
Time-to-event analyses generally require appropriate handling of patients whose event status is not observed for the entire intended follow-up. Such patients may be censored at the end of their available observation period. Censoring is a statistical mechanism for incorporating incomplete event-time information; it does not mean that a patient is assumed to have remained event-free indefinitely.
The Cox proportional-hazards model also relies on a proportional-hazards framework for its usual single-HR interpretation. If relative hazards change materially over time, one hazard ratio can compress a more complicated pattern of treatment differences into a single summary.
17. Safety: Serious Adverse Events and Major Bleeding
Two different statistical representations of safety are available in the registry: serious adverse events are summarized as affected patients among those at risk, while major bleeding is analyzed as a time-to-event endpoint.
| Safety concept | Edoxaban | ASA or placebo | Statistical form |
|---|---|---|---|
| Serious adverse events | 498/1306 | 467/1302 | Affected patients / at risk |
| Major bleeding events | Compared with ASA or placebo | Comparator | HR 2.1 (95% CI 1.3–3.38); P = 0.002 |
These are not interchangeable summaries. A proportion of patients with a serious adverse event does not account for the timing of that event in the same way as a Cox model. Conversely, the hazard ratio for major bleeding does not directly provide the absolute percentage of patients who experienced bleeding.
18. Limitations
- Power for small effects: the registry states that the trial does not have sufficient power to detect or rule out a small beneficial effect of oral anticoagulation on the prevention of stroke.
- Generalizability across NOACs: the registry states that the generalizability of these findings with edoxaban to other NOACs is not known.
- Modified intention-to-treat population: the primary analysis is defined using randomized patients with a qualifying atrial high rate episode and at least one dose of study drug, rather than every randomized patient without qualification.
- Composite endpoint: the primary result combines stroke, systemic embolism, and cardiovascular death. Components can have different event rates and treatment effects.
- Cause-specific analysis: the primary effect estimate is a cause-specific hazard ratio, which should not automatically be interpreted as a cumulative-incidence ratio.
- Secondary analyses: several secondary outcomes are posted without a formal analysis method or P-value, limiting how fully their inferential framework can be characterized from the registry.
- Multiplicity: the registry information summarized here does not specify a multiplicity-adjustment strategy across the posted secondary analyses.
19. Why This Trial Matters Statistically
NOAH provides a useful teaching example because the registry contains a primary composite time-to-event endpoint, a cause-specific Cox analysis, a modified intention-to-treat population, multiple secondary survival endpoints, continuous patient-reported outcomes, and both affected-patient and time-to-event safety summaries.
| Concept | How it appears in NOAH |
|---|---|
| Randomization | 2608 patients allocated to two parallel groups |
| Double blinding | Participants and study personnel were blinded in the registered design |
| Modified intention-to-treat | Primary analysis population includes randomized patients with a qualifying AHRE and at least one dose of study drug |
| Time-to-event endpoint | Primary composite endpoint measured from randomization to first occurrence |
| Cox model | Cause-specific Cox proportional-hazards model used for the primary analysis |
| Hazard ratio | Primary effect estimate 0.81 with 95% CI 0.6–1.08 |
| Confidence interval | Quantifies uncertainty around hazard-ratio and mean-difference estimates |
| P-value | Primary P = 0.15; major bleeding P = 0.002; all-cause death P = 0.28 |
| Composite endpoint | Stroke, systemic embolism, or cardiovascular death |
| Safety analysis | Serious adverse events by arm and major bleeding as a time-to-event endpoint |
20. Clinical Biostats Interpretation of the Overall Statistical Pattern
The primary analysis produced an adjusted cause-specific hazard ratio of 0.81, with a two-sided 95% confidence interval of 0.6–1.08 and P = 0.15. The point estimate therefore lies below the null value, while the confidence interval extends across the null value.
The secondary analyses show heterogeneous point estimates across individual outcomes. The reported hazard ratio was 0.51 for systemic embolism, 0.79 for stroke, 0.90 for cardiovascular death, 0.89 for major adverse cardiac events, and 1.16 for all-cause death. Major bleeding had a hazard ratio of 2.1.
These results should be read as a collection of endpoint-specific estimates rather than as one aggregate effect. The primary composite endpoint has its own prespecified interpretation, while component endpoints, mortality, cardiovascular outcomes, quality of life, satisfaction, and safety each address different clinical and statistical questions.
The primary hazard ratio alone does not provide an absolute risk difference, number needed to treat, probability of individual patient benefit, or a direct comparison of cumulative event probabilities. Those quantities require additional information beyond the reported hazard ratio.
21. Statistical Methods in Plain Language
Randomization
Randomization creates the framework for comparing the two intervention groups while reducing systematic differences in baseline characteristics caused by treatment assignment.
Blinding
Double blinding reduces the opportunity for knowledge of treatment assignment to influence participant behavior, study conduct, or outcome assessment.
Kaplan-Meier estimation
Kaplan-Meier methods estimate event-time distributions while accommodating patients whose follow-up ends before an event occurs.
Cox regression
The Cox model estimates a relative hazard while using the timing of events and censoring information.
Hazard ratio
The hazard ratio expresses a relative instantaneous event-rate comparison. It is not the same as a relative risk or absolute risk difference.
Confidence interval
The confidence interval shows statistical uncertainty around an estimated treatment effect and should be interpreted alongside the point estimate.
22. Related Tutorials
Learn more about the methods used in this trial:
23. Related Calculators
24. Sources
- ClinicalTrials.gov: NCT02618577 — NOAH.
- PubMed: PMID 37622677.
Continue through the Clinical Biostats statistical library
Explore the survival-analysis methods and statistical tools that provide the foundation for interpreting randomized time-to-event trials.
25. Record Summary
NOAH provides a useful example of how a randomized phase 3 trial can combine a composite time-to-event endpoint with cause-specific Cox modeling, a modified intention-to-treat population, multiple secondary outcomes, continuous quality-of-life measures, and safety analyses. The primary adjusted cause-specific hazard ratio was 0.81 with a 95% confidence interval of 0.6–1.08 and P = 0.15. The secondary results included hazard ratios below 1 for stroke, systemic embolism, cardiovascular death, and major adverse cardiac events, while all-cause death had a hazard ratio of 1.16 and major bleeding had a hazard ratio of 2.1. The statistical interpretation depends on the endpoint definition, analysis population, model, confidence interval, and distinction between efficacy and safety outcomes.