1. Trial at a Glance
ARISTOTLE was a randomized, double-masked, parallel-group phase 3 prevention trial enrolling 20,976 participants. The registered comparison was apixaban versus warfarin, and the posted primary analysis used an intention-to-treat population and a Cox proportional-hazards model.
2. Clinical Question
Population
The trial enrolled participants with atrial fibrillation or atrial flutter. The registry reports an enrollment of 20,976 participants.
Intervention
The intervention was apixaban.
Comparator
The comparator was warfarin.
Primary statistical question
The principal registered efficacy question concerned the time to the first event of ischemic/unspecified stroke, hemorrhagic stroke, or systemic embolism during the intended treatment period, together with the corresponding rate of adjudicated stroke or systemic embolism.
Statistically, the posted primary comparison estimated the relative hazard of the adjudicated stroke or systemic embolism rate for apixaban versus warfarin.
3. Trial Design
ARISTOTLE used a randomized, double-masked, parallel design. Its primary purpose was prevention. The registry reports two intervention arms and 20,976 enrolled participants.
Apixaban
- Drug intervention
- Compared with warfarin
- Included in the intention-to-treat primary efficacy analysis
Warfarin
- Drug comparator
- Compared with apixaban
- Included in the intention-to-treat primary efficacy analysis
Trial timeline
Trial start
The registry reports the study start date as December 31, 2006.
Primary completion
The registry reports primary completion on May 25, 2011.
4. Endpoints
Primary endpoint 1: first efficacy event
Number of Participants With First Event of Ischemic/Unspecified Stroke, Hemorrhagic Stroke, or Systemic Embolism (SE) During the Intended Treatment Period
Time frame: Time to first event in "Intended Treatment Period": started on day of randomization, ended at efficacy cut-off date.
The registry states that all suspected efficacy events were adjudicated by the Central Events Committee (CEC). Its stroke definition is a nontraumatic focal neurological deficit lasting at least 24 hours and includes ischemic stroke, hemorrhagic stroke, ischemic stroke with hemorrhagic conversion, stroke of uncertain type, and retinal ischemic event (embolism, infarction). The registry defines systemic embolism using a clinical history consistent with an acute loss of blood flow to an arterial site.
Primary endpoint 2: event rate
Rate of Adjudicated Stroke or Systemic Embolism (SE) During the Intended Treatment Period
Time frame: "Intended Treatment Period" started on the day of randomization and ended at the efficacy cut-off date.
Unit: Number of adjudicated stroke or SE events per 100 patient years.
The registry therefore describes both an event-based formulation and a rate formulation of the principal efficacy outcome. The posted formal statistical analysis is for the rate of adjudicated stroke or systemic embolism and treats it as a time-to-event endpoint.
Secondary endpoints represented in the posted analyses
| Endpoint | Time frame | Population |
|---|---|---|
| Rate of Adjudicated Major (ISTH) Bleed Events During Treatment Period | Treatment Period; first dose of blinded study drug through 2 days after last dose | Treated participants |
| Rate of Adjudicated All-Cause Death During the Intended Treatment Period | Intended Treatment Period | Intention-to-treat analysis, randomized participants |
| Ischemic or unspecified stroke | Intended Treatment Period | Intention-to-treat analysis, randomized participants |
| Hemorrhagic stroke | Intended Treatment Period | Intention-to-treat analysis, randomized participants |
| Systemic embolism | Intended Treatment Period | Intention-to-treat analysis, randomized participants |
| Myocardial infarction | Intended Treatment Period | Intention-to-treat analysis, randomized participants |
| Composite stroke / systemic embolism / major bleeding in warfarin/VKA-naive participants | Intended Treatment Period | Intention-to-treat analysis, randomized participants |
| Major or clinically relevant non-major bleed | Treatment Period | Treated participants |
| All bleeding events | Treatment Period | Treated participants |
| GUSTO bleeding endpoints | Treatment Period | Treated participants |
| TIMI bleeding endpoints | Treatment Period | Treated participants |
| Net-clinical benefit | Treatment Period | Treated participants |
5. Statistical Methodology
Primary analysis
The posted primary analysis used a Cox proportional-hazards model for the rate of adjudicated stroke or systemic embolism during the intended treatment period. The analysis population was the intention-to-treat population of randomized participants.
The model compared apixaban versus warfarin and reported a hazard ratio (HR).
The posted estimate was 0.79, with a two-sided 95% confidence interval of .66 to .95 and P = 0.0114.
Covariate adjustment and stratification
The analysis text identifies covariate adjustment and stratified analysis as concepts in the primary analysis. For the posted major-bleeding analysis, the registry explicitly states that the model included treatment group as a covariate and was stratified by investigative site and prior warfarin/vitamin K antagonist status. The registry also identifies covariate adjustment and stratified analysis in the primary efficacy analysis.
Intention-to-treat analysis
The primary efficacy analysis was based on randomized participants. Participants who did not experience an efficacy endpoint event were censored according to the registry's stated censoring rules, including the earlier of death date when death was not part of the endpoint, last contact, or the applicable efficacy cut-off.
This distinction matters because an intention-to-treat analysis preserves the randomized comparison. Censoring, meanwhile, determines which portions of follow-up contribute information to the time-to-event model.
Analysis of bleeding endpoints
The registry used the same general survival-analysis framework for several bleeding outcomes. The major ISTH bleeding analysis used treated participants and censored participants without a bleeding endpoint at the earlier of 2 days after discontinuation of study drug, death date, or last-contact date, according to the registry description.
Multiplicity and hierarchical testing
The important statistical point is that the subsequent superiority P-values should not be interpreted in isolation from the prespecified testing sequence. The registry explicitly describes a hierarchical closed-testing framework.
6. Primary Result: Stroke or Systemic Embolism
Apixaban vs Warfarin
Two-sided 95% CI: .66–.95 · P = 0.0114
Analysis: Cox proportional-hazards model · Population: intention-to-treat randomized participants
The primary posted analysis estimated a hazard ratio of 0.79 for adjudicated stroke or systemic embolism for apixaban relative to warfarin. In relative terms, an HR of 0.79 corresponds to a 21% lower estimated hazard under the fitted model, because 1 − 0.79 = 0.21.
The HR of 0.79 describes a relative difference in the instantaneous rate of the modeled time-to-event outcome. It does not mean that 21% of participants avoided an event, that every individual had exactly a 21% reduction in risk, or that cumulative event probability was reduced by exactly 21% at every time point.
The two-sided 95% CI of .66–.95 describes statistical uncertainty around the estimated hazard ratio under the model and analysis framework. It does not describe the range of treatment effects experienced by individual participants.
The P-value of 0.0114 is evidence against the relevant null hypothesis within the prespecified testing framework; it is not a measure of effect size. The magnitude of the estimated relative effect is communicated by the HR, while the confidence interval communicates its precision.
Because this is a Cox proportional-hazards analysis, interpretation of a single HR also depends on the proportional-hazards model being an appropriate summary of the relative event hazards over follow-up. The registry's use of censoring means that participants contribute information only until the specified censoring time or event.
7. Secondary Results: Major Bleeding
Adjudicated Major (ISTH) Bleed Events
Two-sided 95% CI: 0.60–0.80 · P < .0001
Analysis: Cox proportional-hazards model · Population: treated participants
The posted analysis estimated a hazard ratio of 0.69 for adjudicated major ISTH bleed events during the treatment period, comparing apixaban with warfarin. The corresponding two-sided 95% CI was 0.60–0.80, with P < .0001.
An HR of 0.69 corresponds to a 31% lower estimated hazard of the analyzed major-bleeding endpoint under the fitted model. This is a relative hazard interpretation, not a statement that 31% of patients avoided bleeding or that absolute bleeding probability changed by 31 percentage points.
The 95% CI of 0.60–0.80 gives the statistical uncertainty around the estimated HR. The interval is narrower than the primary efficacy interval in absolute HR units, but precision should always be considered in relation to the endpoint, follow-up, and analysis population.
The P-value of < .0001 does not itself quantify the magnitude of the difference. The HR and confidence interval provide that information. This endpoint was analyzed among treated participants rather than the randomized ITT population, which is an important distinction when comparing the statistical analyses across endpoints.
8. Secondary Results: All-Cause Death
All-Cause Death
Two-sided 95% CI: 0.80–1.00 · P = 0.0465
Analysis: Cox proportional-hazards model · Population: intention-to-treat randomized participants
The estimated hazard ratio for adjudicated all-cause death during the intended treatment period was 0.89. The two-sided 95% CI was 0.80–1.00, and the posted P-value was 0.0465.
The HR of 0.89 corresponds to an estimated 11% lower hazard under the fitted model. The confidence interval reaches 1.00, illustrating why the exact interval should be considered alongside the point estimate rather than focusing only on the P-value.
The P-value of 0.0465 is a hypothesis-testing quantity. It does not say that there is a 4.65% probability that the treatment effect is due to chance, nor does it measure clinical importance. The HR and its confidence interval remain the primary descriptive measures of the estimated relative effect.
This endpoint was analyzed within the same broad intended-treatment time-to-event framework as the primary efficacy analysis, but it was a secondary endpoint. The registry also describes a closed-testing sequence for the key objectives, so the multiplicity framework matters when interpreting secondary superiority results.
9. Additional Secondary Efficacy Results
The registry contains several additional time-to-event analyses. The estimates below are reported exactly as posted and should be interpreted as hazard ratios for apixaban versus warfarin.
| Outcome | HR | 95% CI | P-value |
|---|---|---|---|
| Ischemic or unspecified stroke | 0.92 | 0.74–1.13 | 0.4220 |
| Hemorrhagic stroke | 0.51 | 0.35–0.75 | 0.0006 |
| Systemic embolism | 0.87 | 0.44–1.75 | 0.7020 |
| Myocardial infarction | 0.88 | 0.66–1.17 | 0.3720 |
| Stroke / systemic embolism / major bleeding | 0.77 | 0.69–0.86 | < .0001 |
| Stroke / systemic embolism / all-cause death | 0.89 | 0.81–0.98 | 0.0192 |
| Stroke / systemic embolism / major bleeding / all-cause death | 0.85 | 0.78–0.92 | 0.0002 |
| Stroke / systemic embolism / MI / all-cause death | 0.88 | 0.80–0.97 | 0.0107 |
| Ischemic or unspecified stroke / all-cause death | 0.90 | 0.82–1.00 | 0.0432 |
| Hemorrhagic stroke / all-cause death | 0.88 | 0.79–0.98 | 0.0167 |
| Systemic embolism / all-cause death | 0.89 | 0.80–1.00 | 0.0464 |
| Myocardial infarction / all-cause death | 0.89 | 0.80–0.99 | 0.0253 |
| Stroke / systemic embolism / major bleeding in warfarin/VKA-naive participants | 0.80 | 0.67–0.95 | 0.0098 |
These estimates are not interchangeable. Each HR refers to a different endpoint, and several endpoints are composites containing different clinical events. An HR of 0.51 for hemorrhagic stroke, for example, describes a different outcome from an HR of 0.92 for ischemic or unspecified stroke.
The width of the confidence interval also varies substantially. The systemic-embolism estimate of 0.87 has a 95% CI of 0.44–1.75, illustrating considerably greater uncertainty than some of the composite estimates. A wide interval can occur when relatively fewer events contribute information to the analysis.
Because multiple secondary outcomes were evaluated, the individual P-values should not automatically be treated as though each were an isolated primary hypothesis test. The registry specifically documents a closed testing procedure for four key objectives.
10. Bleeding and Net-Clinical-Benefit Analyses
| Endpoint | HR | 95% CI | P-value |
|---|---|---|---|
| Major or clinically relevant non-major (CRNM) bleed | 0.68 | 0.61–0.75 | < .0001 |
| All bleeding events | 0.71 | 0.68–0.75 | < .0001 |
| Severe GUSTO bleeding events | 0.46 | 0.35–0.60 | < .0001 |
| Severe or moderate GUSTO bleeding events | 0.60 | 0.50–0.71 | < .0001 |
| Major TIMI bleeding event | 0.57 | 0.46–0.70 | < .0001 |
| Major or minor TIMI bleeding criteria | 0.63 | 0.54–0.75 | < .0001 |
| Net-clinical benefit | 0.74 | 0.65–0.83 | < .0001 |
The registry identifies these analyses as time-to-event analyses using Cox proportional-hazards models. The GUSTO and TIMI outcomes are separately defined bleeding classifications, so their HRs should be interpreted within their respective endpoint definitions.
The net-clinical-benefit analysis is likewise a composite endpoint rather than a generic measure of overall benefit. Its HR of 0.74 summarizes the specific events included in the registry's definition; it should not be interpreted as a universal treatment-effect measure across all clinical outcomes.
11. Safety: Serious Adverse Events
| Arm | Affected | At risk |
|---|---|---|
| Warfarin | 3182 | 9088 |
| Apixaban | 3302 | 9052 |
The registry reports serious adverse events by arm as 3182/9088 for warfarin and 3302/9052 for apixaban. These are affected-participant counts and at-risk denominators as reported in the ClinicalTrials.gov record.
12. Statistical Methods Explained
Why was a Cox proportional-hazards model used?
The registered outcomes are time-to-event endpoints. Rather than reducing follow-up to a simple yes/no event indicator, a survival model uses information about when events occur and accounts for censoring. The Cox model expresses the treatment comparison through a hazard ratio.
What does an HR of 0.79 mean?
An HR of 0.79 means that the fitted model estimates the instantaneous event hazard under apixaban at 79% of the corresponding hazard under warfarin, giving a relative hazard reduction of 21%. It does not mean a 21% absolute reduction in the probability of stroke or systemic embolism.
Why is the confidence interval important?
The 95% CI of .66–.95 shows the statistical uncertainty surrounding the primary HR estimate. The point estimate alone can make an effect appear more precise than the data justify. The interval gives readers a range of values compatible with the statistical estimation framework used for the analysis.
Why does the P-value not measure effect size?
A P-value addresses compatibility with a null hypothesis under the specified statistical framework. It is affected by the amount of information in the study as well as by the magnitude of the observed effect. The HR communicates relative effect size; the confidence interval communicates both the estimate and its precision.
Why does intention-to-treat analysis matter?
The primary efficacy analysis included randomized participants. Maintaining participants in their randomized groups preserves the treatment comparison established by randomization. This is particularly important in a randomized trial because changing the analysis population based on post-randomization events can compromise the comparability created at randomization.
Why are censoring rules important?
A participant who does not experience the endpoint does not necessarily contribute follow-up indefinitely. The registry specifies censoring rules for the primary and bleeding analyses. Cox models rely on these observed follow-up intervals, so the definition of when observation ends is part of the statistical analysis rather than an administrative detail.
Why does multiplicity matter?
ARISTOTLE's registry analysis notes describe a closed testing procedure for four key objectives, beginning with non-inferiority for the primary efficacy endpoint and then proceeding conditionally to superiority testing. This means the sequence of hypotheses is part of the inferential design. A collection of P-values should therefore not be read as though every endpoint had been designated an independent primary test.
13. Understanding the Non-Inferiority Logic
The primary analysis notes state that, with 448 subjects with confirmed strokes or systemic emboli, the study would have at least 90% power to meet both regulatory definitions of non-inferiority described in the registry.
The first stated non-inferiority criterion was that the upper bound of the two-sided 95% CI for relative risk be less than 1.38. The registry then describes superiority testing as a subsequent step after non-inferiority is demonstrated.
The non-inferiority margin is not the same as the null value of 1.00. The margin specifies how much relative loss of efficacy could be accepted for the non-inferiority claim, under the prespecified framework.
This distinction is central to reading the statistical design correctly. A treatment can be evaluated first against a non-inferiority margin and subsequently against the conventional superiority null. Those are different hypotheses and should not be collapsed into one generic "significant/not significant" decision.
14. What the Hazard Ratio Does—and Does Not—Tell You
What it tells you
The HR summarizes the relative event hazard estimated by the Cox model. Values below 1 indicate a lower modeled hazard for apixaban than for warfarin.
What it does not tell you
The HR is not an absolute risk difference, does not give the probability that an individual will experience an event, and does not mean the relative difference is identical at every time point.
Why the CI matters
The confidence interval indicates uncertainty around the estimated relative hazard and should be considered alongside the point estimate.
Why the P-value matters differently
The P-value addresses the statistical test; it is not a scale for clinical magnitude and should not replace examination of the HR and CI.
15. Analysis Populations: A Crucial Detail
One of the most important features of the ARISTOTLE registry results is that the analysis population is not identical for every endpoint.
| Analysis type | Population reported |
|---|---|
| Primary efficacy | Intention-to-treat analysis, randomized participants |
| All-cause death | Intention-to-treat analysis, randomized participants |
| Individual stroke, systemic embolism and MI analyses | Intention-to-treat analysis, randomized participants |
| Composite efficacy analyses | Intention-to-treat analysis, randomized participants |
| Major ISTH bleeding | Treated participants |
| Major or CRNM bleeding | Treated participants |
| All bleeding events | Treated participants |
| GUSTO and TIMI bleeding analyses | Treated participants |
| Net-clinical benefit | Treated participants |
This difference is statistically consequential. An ITT analysis is anchored to randomization, whereas a treated-participant analysis conditions on receiving study treatment. The two approaches can answer related but not identical questions.
16. Intended Treatment Period vs Treatment Period
The registry uses two distinct time-frame labels. The Intended Treatment Period begins on the day of randomization and ends at the efficacy cut-off date. The Treatment Period begins with the first dose of blinded study drug and ends 2 days after the last dose of blinded study drug.
This distinction is important because efficacy and bleeding analyses are not necessarily observing the same time window. The primary efficacy endpoint uses the intended treatment period, whereas the bleeding endpoints reported here use the treatment period.
17. Interpreting Composite Endpoints
Several secondary analyses combine multiple events into composite endpoints. Examples in the registry include stroke/systemic embolism/major bleeding, stroke/systemic embolism/all-cause death, and stroke/systemic embolism/MI/all-cause death.
A composite HR summarizes the time to the first qualifying component of the composite. It should therefore be interpreted as an effect on the combined endpoint as defined, not as though the same HR separately describes every component.
The component results illustrate why this distinction matters. The individual endpoint estimates reported by the registry range from 0.51 for hemorrhagic stroke to 0.92 for ischemic or unspecified stroke, with different confidence intervals and P-values. The composite results therefore cannot be used as substitutes for the individual-event analyses.
18. A Statistical Reading of the Results
| Statistical feature | Interpretation |
|---|---|
| Randomized comparison | The principal efficacy comparison is anchored to randomized treatment assignment. |
| Time-to-event endpoint | Timing of events and censoring contribute to the analysis. |
| Cox proportional-hazards model | The treatment effect is summarized using a hazard ratio. |
| Primary HR 0.79 | The fitted model estimates a 21% lower hazard for the primary event under apixaban relative to warfarin. |
| 95% CI .66–.95 | Quantifies statistical uncertainty around the primary HR. |
| P = 0.0114 | Provides the reported hypothesis-test result and does not measure effect magnitude. |
| Closed testing | Controls the interpretation of the sequence of key objectives. |
| Different analysis populations | Efficacy and bleeding analyses should not be treated as though they used identical populations. |
| Composite endpoints | Each composite HR applies to its specified combination of events. |
19. Limitations and Interpretation Issues
- Hazard-ratio assumptions: The Cox proportional-hazards model produces a single HR summary. Interpretation therefore depends on the model being an appropriate representation of the relative hazards over the analyzed follow-up.
- Censoring: Time-to-event analyses depend on prespecified rules for when participants leave the risk set. Different censoring rules can change the estimand being analyzed.
- Different analysis populations: The primary efficacy analyses use randomized participants, whereas bleeding analyses use treated participants. Direct comparison of HRs across these analyses should account for that distinction.
- Multiplicity: Numerous secondary and other pre-specified endpoints were analyzed. The registry explicitly documents a closed testing procedure for four key objectives, so individual P-values should not automatically be treated as independent confirmatory tests.
- Composite endpoints: A composite HR does not necessarily represent the treatment effect for every individual component. Component-specific results should be examined separately.
- Registry detail: The ClinicalTrials.gov record does not provide a full baseline characteristics table, subgroup forest plots, or detailed event-time summaries. Those sections are therefore not reconstructed here.
- Safety counts: Serious adverse-event counts and at-risk denominators are reported descriptively here. They should not be conflated with the separate time-to-event bleeding analyses.
20. Why This Trial Matters Statistically
ARISTOTLE is a useful statistical teaching case because it combines randomized treatment assignment with large-scale time-to-event analysis, adjudicated clinical endpoints, Cox modeling, intention-to-treat analysis, stratification, non-inferiority logic, hierarchical testing, and multiple safety and efficacy outcomes.
| Concept | How it appears in ARISTOTLE |
|---|---|
| Randomization | 20,976 participants were enrolled in a randomized two-arm parallel design. |
| Blinding | The registered design is double-masked. |
| Intention-to-treat analysis | The primary efficacy analysis used randomized participants. |
| Time-to-event endpoint | The primary rate outcome is analyzed as time to adjudicated stroke or systemic embolism. |
| Cox model | The primary analysis and multiple secondary analyses use Cox proportional-hazards models. |
| Hazard ratio | The primary estimate is HR 0.79 for apixaban versus warfarin. |
| Confidence interval | The primary two-sided 95% CI is .66–.95. |
| P-value | The primary reported P-value is 0.0114. |
| Covariate adjustment | The registry identifies covariate adjustment as part of the analysis methodology. |
| Stratified analysis | The registry identifies stratified analysis; the major-bleeding analysis specifies stratification by investigative site and prior warfarin/VKA status. |
| Non-inferiority | The analysis notes specify a relative-risk upper-bound criterion of 1.38 for one regulatory definition. |
| Closed testing | Four key objectives were tested using a closed testing procedure. |
| Composite endpoints | Multiple secondary analyses combine stroke, systemic embolism, bleeding, MI and/or all-cause death. |
| Safety analysis | Serious adverse events are reported by treatment arm, alongside multiple time-to-event bleeding outcomes. |
21. Related Tutorials
Learn more about the methods used in this trial:
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: NCT00412984 — ARISTOTLE.
- PubMed: PMID 37506747.
- PubMed: PMID 36990261.
- PubMed: PMID 35570249.
- PubMed: PMID 34358298.
- PubMed: PMID 33741689.
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24. Record Summary
ARISTOTLE provides a detailed example of randomized time-to-event analysis. The trial used a randomized, double-masked, parallel design with 20,976 participants and compared apixaban with warfarin. Its primary posted statistical analysis used an intention-to-treat population and a Cox proportional-hazards model, producing an HR of 0.79 with a two-sided 95% CI of .66–.95 and P = 0.0114. The registry also reports a non-inferiority framework followed by conditional superiority testing, multiple secondary efficacy and safety analyses, and distinct analysis populations for efficacy and bleeding endpoints.
The most important statistical lesson is that the headline HR is only one part of the analysis. Proper interpretation requires attention to the endpoint definition, observation period, censoring rules, analysis population, model, confidence interval, testing sequence, and distinction between individual and composite outcomes.