This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical results on this page are restricted to the registry-reported FOURIER trial data. Statistical interpretation is presented separately from the reported registry results.
1. Trial at a Glance
FOURIER was a completed phase 3 randomized, parallel-group, quadruple-masked treatment trial in subjects with dyslipidemia and elevated risk. The registry reports two intervention groups: evolocumab and placebo.
| Feature | FOURIER |
|---|---|
| Trial name | Further Cardiovascular Outcomes Research With PCSK9 Inhibition in Subjects With Elevated Risk |
| NCT identifier | NCT01764633 |
| Therapeutic area | Cardiology |
| Condition | Dyslipidemia |
| Phase | 3 |
| Status | COMPLETED |
| Allocation | RANDOMIZED |
| Design model | PARALLEL |
| Masking | QUADRUPLE |
| Primary purpose | TREATMENT |
| Enrollment | 27,564 |
| Interventions | Evolocumab (biological); Placebo (drug) |
| Lead sponsor | Amgen |
| Sponsor type | INDUSTRY |
| Start | 2013-02-08 |
| Primary completion | 2016-11-11 |
2. Clinical Question
The statistical question is whether the time to the registered cardiovascular composite endpoint differs between randomized participants assigned to evolocumab and those assigned to placebo.
Population
The registry identifies the condition as dyslipidemia and the brief trial title describes subjects with elevated risk.
Intervention
Evolocumab, identified in the registry data as a biological intervention.
Comparator
Placebo, identified in the registry data as a drug intervention.
Primary question
Does randomized assignment to evolocumab change the time to cardiovascular death, myocardial infarction, hospitalization for unstable angina, stroke, or coronary revascularization compared with placebo?
3. Trial Design
Evolocumab
- Intervention type: biological
- Compared with placebo
- Included in the randomized efficacy comparison
Placebo
- Intervention type: drug
- Comparator group
- Included in the randomized efficacy comparison
4. Randomization, Masking, Stratification, and Analysis Population
The registry identifies the allocation as RANDOMIZED and the masking as QUADRUPLE. The primary endpoint analysis used all randomized participants. The analysis text also states that the number of participants entered at each time point represents the number of participants at risk.
| Feature | Registry-supported description |
|---|---|
| Allocation | RANDOMIZED |
| Masking | QUADRUPLE |
| Analysis population | All randomized participants |
| At-risk counts | The number entered at each time point represents the number at risk. |
| Stratification | Final screening LDL-C level and region |
| Primary comparison | Placebo vs Evolocumab |
Stratification is important here because the reported log-rank comparison was not simply an unstratified comparison of event-time distributions. The registry specifies a two-sided log-rank test stratified by the randomization stratification factors: final screening LDL-C level and region. The corresponding hazard-ratio analysis was based on a Cox model stratified by those same factors.
5. Primary Endpoint
| Endpoint | Registry definition / time frame | Analysis |
|---|---|---|
| Time to Cardiovascular Death, Myocardial Infarction, Hospitalization for Unstable Angina, Stroke, or Coronary Revascularization | Events that occurred from randomization to the last confirmed survival status date. | Two-sided stratified log-rank test; stratified Cox model for hazard ratio. |
The registry extract states that all deaths and potential endpoint events were adjudicated by an independent external Clinical Events Committee led by the Thrombolysis in Myocardial Infarction (TIMI) Study Group, using standardized definitions. This is statistically important because the composite endpoint depends on consistent determination of whether individual component events occurred.
The primary endpoint was compared between treatment groups at a significance level of 0.05. The reported hypothesis type was superiority.
6. Primary Result
Primary cardiovascular composite endpoint
95% CI: 0.79–0.92 · P < 0.0001
Two-sided stratified log-rank test; hazard ratio based on a stratified Cox model.
The primary analysis compared placebo with evolocumab using all randomized participants. The estimated hazard ratio was 0.85, with a two-sided 95% confidence interval of 0.79 to 0.92 and a reported P-value of < 0.0001.
What the estimate means: An HR of 0.85 corresponds to an estimated instantaneous event rate that is approximately 15% lower in the evolocumab group relative to placebo under the fitted Cox model.
What it does not mean: It does not mean that exactly 15% of participants avoided an event, that absolute event risk was reduced by 15 percentage points, or that every participant experienced the same reduction.
What the confidence interval says: The 95% CI of 0.79–0.92 describes uncertainty around the estimated hazard ratio under the model and sampling framework. It does not describe the range of individual treatment effects.
Why the P-value is different: The P-value addresses the evidence against the null hypothesis under the prespecified test. It is not a measure of the size of the treatment effect. The effect size is conveyed by the HR and its confidence interval.
Important modeling caution: The HR is a model-based relative measure. Its interpretation as a single summary of relative event rate is most straightforward when the proportional-hazards representation is reasonable over the analyzed follow-up. The registry extract does not provide a formal test or diagnostic for that assumption.
Censoring also matters: Time-to-event analysis uses the available event and follow-up information rather than treating every participant as having the same observation time. The registry specifically identifies the last confirmed survival status date as the endpoint's follow-up boundary and provides numbers at risk over time.
7. Secondary Endpoint Results
The registry contains eight secondary statistical analyses in addition to the primary analysis. All use time-to-event methodology, compare placebo with evolocumab, and report hazard ratios from stratified survival analyses. The following table reproduces the posted estimates and uncertainty measures.
| Secondary endpoint | HR | 95% CI | P-value |
|---|---|---|---|
| Time to Cardiovascular Death, Myocardial Infarction, or Stroke | 0.80 | 0.73–0.88 | < 0.0001 |
| Time to Cardiovascular Death | 1.05 | 0.88–1.25 | 0.6188 |
| Time to All Cause Death | 1.04 | 0.91–1.19 | 0.5368 |
| Time to First Myocardial Infarction | 0.73 | 0.65–0.82 | < 0.0001 |
| Time to First Stroke | 0.79 | 0.66–0.95 | 0.0101 |
| Time to First Coronary Revascularization | 0.78 | 0.71–0.86 | < 0.0001 |
| Time to Cardiovascular Death or First Hospitalization for Worsening Heart Failure | 0.98 | 0.86–1.13 | 0.8179 |
| Time to First Ischemic Fatal or Non-Fatal Stroke or Transient Ischemic Attack | 0.77 | 0.65–0.92 | 0.0035 |
Reading the secondary hazard ratios
HR below 1
For example, an HR of 0.73 corresponds to an estimated instantaneous event rate approximately 27% lower in the evolocumab group under the Cox model.
HR near 1
An HR of 0.98 is close to the null value of 1.00. Its 95% CI of 0.86–1.13 also spans 1.
HR above 1
An HR of 1.05 corresponds to an estimated instantaneous event rate approximately 5% higher under the model, but its 95% CI of 0.88–1.25 includes 1.
Precision matters
The confidence interval must be interpreted alongside the point estimate. A P-value alone does not communicate the magnitude or precision of an effect.
8. Key Secondary Endpoint: Cardiovascular Death, Myocardial Infarction, or Stroke
Key secondary composite
95% CI: 0.73–0.88 · P < 0.0001
The key secondary endpoint combined cardiovascular death, myocardial infarction, or stroke. Its analysis used the same all-randomized analysis population and the same stratification factors as the primary endpoint.
An HR of 0.80 means that the fitted model estimated approximately a 20% lower instantaneous event rate in the evolocumab group relative to placebo. The 95% CI of 0.73–0.88 gives the corresponding uncertainty interval for the hazard-ratio estimate.
The key distinction is between a composite endpoint and any individual component. A composite HR summarizes the time to the first qualifying component event; it does not imply that the same relative effect occurred for cardiovascular death, myocardial infarction, and stroke individually.
The registry specifies a conditional testing sequence: if the primary endpoint reached statistical significance at the 0.05 level, the key secondary endpoint was tested at a significance level of 0.05. This is part of the trial's multiplicity structure rather than an after-the-fact choice of threshold.
9. Cardiovascular Death and All-Cause Death
| Endpoint | HR | 95% CI | P-value | Interpretive point |
|---|---|---|---|---|
| Time to Cardiovascular Death | 1.05 | 0.88–1.25 | 0.6188 | The interval includes 1. |
| Time to All Cause Death | 1.04 | 0.91–1.19 | 0.5368 | The interval includes 1. |
These two endpoints illustrate why a primary composite and individual components can tell different statistical stories. The primary endpoint contains several types of cardiovascular events, whereas cardiovascular death and all-cause death isolate mortality outcomes.
The cardiovascular-death estimate of 1.05 should not be translated into a conclusion that evolocumab caused a 5% increase in cardiovascular mortality. The confidence interval of 0.88–1.25 spans values below and above 1, and the reported P-value is 0.6188.
Likewise, the all-cause-death HR of 1.04 has a 95% CI of 0.91–1.19 and a P-value of 0.5368. The statistical result is an estimate with uncertainty, not proof that the two groups have identical underlying hazards.
This distinction is especially important for readers who equate a P-value above 0.05 with evidence that there is no treatment effect. A nonsignificant result means that the prespecified data and test did not provide sufficient statistical evidence for the tested alternative at that threshold; it does not establish exact equality.
10. Myocardial Infarction, Stroke, and Revascularization
| Endpoint | HR | 95% CI | P-value |
|---|---|---|---|
| Time to First Myocardial Infarction | 0.73 | 0.65–0.82 | < 0.0001 |
| Time to First Stroke | 0.79 | 0.66–0.95 | 0.0101 |
| Time to First Coronary Revascularization | 0.78 | 0.71–0.86 | < 0.0001 |
Each of these analyses used the same general survival-analysis framework: all randomized participants, placebo versus evolocumab, a two-sided log-rank test, and a stratified Cox model. The differences between the endpoints are therefore primarily clinical definitions rather than fundamentally different statistical estimators.
The myocardial-infarction HR of 0.73 corresponds to an estimated instantaneous event rate approximately 27% lower under the fitted model. The coronary-revascularization HR of 0.78 corresponds to an estimated instantaneous event rate approximately 22% lower. The stroke HR of 0.79 corresponds to an estimated instantaneous event rate approximately 21% lower. These are relative hazard interpretations, not absolute risk reductions.
11. Heart Failure and Ischemic Stroke/TIA Endpoints
| Endpoint | HR | 95% CI | P-value |
|---|---|---|---|
| Time to Cardiovascular Death or First Hospitalization for Worsening Heart Failure | 0.98 | 0.86–1.13 | 0.8179 |
| Time to First Ischemic Fatal or Non-Fatal Stroke or Transient Ischemic Attack | 0.77 | 0.65–0.92 | 0.0035 |
The heart-failure composite has an HR very close to 1, with a confidence interval spanning both sides of the null value. By contrast, the ischemic stroke/TIA composite has an HR of 0.77 with a 95% CI of 0.65–0.92.
These endpoints demonstrate why statistical analysis should be performed endpoint by endpoint. A trial can produce different hazard-ratio estimates for distinct event definitions even when the same participants, randomization, and statistical framework are used.
The ischemic stroke/TIA estimate should be read in the context of the prespecified multiplicity procedure. Its P-value of 0.0035 is not, by itself, the complete inferential statement because the registry specifies a multiple-testing framework for the remaining secondary endpoints.
12. Statistical Methodology
Kaplan-Meier estimation
The trial's endpoints are time-to-event outcomes. A Kaplan-Meier estimator is a natural descriptive tool for displaying the estimated event-free survival function over time. It accommodates participants whose event status is not observed for the entire follow-up period by incorporating their information up to censoring.
Here, di is the number of events at event time ti and ni is the number at risk immediately before that time.
The ClinicalTrials.gov record does not provide numerical Kaplan-Meier estimates at specific time points. Accordingly, this page does not construct a survival curve or invent time-specific event probabilities.
Stratified log-rank test
The reported primary analysis used a two-sided log-rank test stratified by the randomization stratification factors: final screening LDL-C level and region. The purpose of stratification is to account for the trial's prespecified randomization strata when comparing event-time distributions.
The log-rank test is a hypothesis test for differences in survival experience between randomized groups. Conceptually, it compares observed and expected event counts across event times while accounting for the number of participants at risk.
Cox proportional-hazards model
The registry states that the primary hazard ratio was based on a Cox model stratified by the randomization stratification factors. The Cox model converts the time-to-event comparison into a relative hazard measure.
The hazard ratio is a relative, model-based measure. It is not an absolute risk difference, relative risk, odds ratio, or percentage of participants who benefit.
Analysis population
All randomized participants formed the analysis population specified for the posted efficacy analyses. This is an important feature of randomized clinical-trial analysis because it retains the original treatment assignment when estimating the randomized treatment comparison.
Composite endpoints
The primary endpoint combines cardiovascular death, myocardial infarction, hospitalization for unstable angina, stroke, and coronary revascularization. A participant enters the time-to-first-event analysis when the first qualifying component occurs.
A composite can increase the number of observed events and therefore provide statistical information across several clinically relevant event types. But the interpretation remains tied to the precise composite definition. A composite hazard ratio should not be treated as though it were automatically the hazard ratio for every component.
13. Multiplicity and Endpoint Hierarchy
FOURIER's registry analysis provides unusually explicit information about the multiple-testing structure. The primary endpoint was tested at a significance level of 0.05. If the primary endpoint reached statistical significance at 0.05, the key secondary composite of cardiovascular death, myocardial infarction, and stroke was tested at 0.05.
The registry then specifies that, if the primary endpoint, key secondary endpoint, and cardiovascular-death endpoint reached statistical significance at 0.05, all-cause death was tested at 0.04 and the remaining secondary endpoints at an overall significance level of 0.01 using the Hochberg method.
| Stage | Endpoint / family | Registry-specified significance level | Method detail |
|---|---|---|---|
| Primary | Primary cardiovascular composite | 0.05 | Two-sided stratified log-rank |
| Key secondary | Cardiovascular death, myocardial infarction, or stroke | 0.05 if primary endpoint significant | Two-sided stratified log-rank |
| Next endpoint | Cardiovascular death | 0.05 if preceding conditions met | Two-sided stratified log-rank |
| Next endpoint | All Cause Death | 0.04 if preceding conditions met | Multiplicity-adjusted sequence |
| Remaining secondary endpoints | Remaining secondary family | Overall significance level 0.01 | Hochberg method |
Multiplicity is not merely a technical footnote. If many hypotheses are tested independently at 0.05, the chance of at least one false-positive result increases. A prespecified hierarchy or multiplicity adjustment controls how the evidence should be interpreted across the endpoint family.
The FOURIER registry record explicitly identifies multiplicity adjustment for the later secondary endpoints. Consequently, reading each posted P-value as an independent test at 0.05 would discard an important part of the statistical design.
The Hochberg procedure is a step-up multiple-testing method. Its presence in the registry means the secondary endpoint family should be interpreted through the specified testing procedure rather than through isolated P-values alone.
14. Statistical Methods Explained
Why was a stratified log-rank test used?
The endpoint is time-to-event, so a log-rank test is appropriate for comparing event-time distributions between randomized groups. The registry specifies stratification by final screening LDL-C level and region because these were the randomization stratification factors. The resulting comparison therefore respects the structure of the randomized design.
What does an HR of 0.85 mean?
An HR of 0.85 means that the fitted model estimates the instantaneous event rate in the evolocumab group to be approximately 15% lower than in the placebo group. It does not mean that 15% fewer participants necessarily experienced an event, because the hazard ratio is not an absolute risk measure.
Why is the confidence interval important?
The estimate 0.85 is only one point on a range of plausible values under the statistical model. The 95% CI of 0.79–0.92 conveys the uncertainty around that estimate. It also shows that the interval lies below 1, which is consistent with the direction of the primary hazard-ratio estimate.
Why doesn't the P-value measure effect size?
The P-value describes the compatibility of the observed data with the null hypothesis under the specified statistical test. It depends on both the magnitude of an observed effect and the amount of statistical information. A very small P-value therefore cannot be interpreted as meaning that an effect is necessarily large.
Why does the analysis population matter?
The posted analysis population is all randomized participants. This anchors the primary efficacy comparison to treatment assignment rather than selectively analyzing participants according to what happened after randomization. That distinction is fundamental to interpreting a randomized treatment effect.
Why does multiplicity change how secondary P-values are read?
The registry specifies a testing sequence and the Hochberg method for remaining secondary endpoints. Therefore, each secondary P-value should be interpreted in the context of that prespecified error-control strategy. A nominal P-value is not automatically equivalent to a standalone confirmatory test at 0.05.
15. Primary Result in Statistical Context
| Component | Primary analysis | What it tells the reader |
|---|---|---|
| Effect estimate | HR 0.85 | Estimated relative event-rate difference under the Cox model |
| 95% CI | 0.79–0.92 | Uncertainty around the hazard-ratio estimate |
| P-value | < 0.0001 | Evidence against the null under the specified test |
| Test | Two-sided stratified log-rank | Comparison of time-to-event experience |
| Model | Stratified Cox model | Hazard-ratio estimation |
| Population | All randomized participants | Preserves randomized treatment assignment |
| Hypothesis | Superiority | Tests whether the treatment groups differ rather than demonstrating non-inferiority |
The most informative way to read the primary result is therefore as a chain: the trial randomized participants; follow-up generated time-to-event information; the stratified log-rank test compared the treatment groups; the stratified Cox model summarized the relative difference as an HR; the confidence interval quantified precision; and the P-value quantified evidence against the null hypothesis under the prespecified test.
16. Safety
The ClinicalTrials.gov record reports serious adverse events by randomized arm using affected participants over participants at risk:
| Arm | Serious adverse events |
|---|---|
| Placebo | 3404 / 13756 affected / at risk |
| Evolocumab | 3410 / 13769 affected / at risk |
These figures describe serious adverse events rather than the primary efficacy endpoint. They should therefore be interpreted separately from the hazard ratio for the cardiovascular composite.
The serious-adverse-event counts provide a safety comparison by randomized arm, but they are not themselves a time-to-event efficacy estimate. The numerator describes participants affected and the denominator describes participants at risk as reported in the ClinicalTrials.gov record.
The ClinicalTrials.gov record does not provide enough information here to reconstruct event timing, exposure duration, severity distributions, or cause-specific safety analyses. Those quantities should not be inferred from the affected/at-risk counts.
17. What the Hazard Ratio Does — and Does Not — Mean
The primary HR of 0.85 represents a model-based relative comparison of the instantaneous event rate between randomized treatment groups. Expressed descriptively, it corresponds to an estimated hazard approximately 15% lower with evolocumab than with placebo.
An HR of 0.85 cannot be converted directly into an absolute percentage-point reduction in the probability of an event. Absolute risk depends on the underlying event rate and the time horizon.
The HR does not mean that a particular percentage of individuals benefited, nor does it imply that every individual participant experienced the same relative change in event risk.
The 95% CI of 0.79–0.92 expresses uncertainty about the estimated hazard ratio under the model and sampling framework. It is not a prediction interval for individual participants.
The reported P-value of < 0.0001 provides evidence against the null hypothesis under the prespecified two-sided test. It does not measure clinical importance, treatment magnitude, or probability that the hypothesis is true.
18. Limitations and Interpretation Issues
- Composite endpoint interpretation: the primary endpoint combines cardiovascular death, myocardial infarction, hospitalization for unstable angina, stroke, and coronary revascularization. Its HR summarizes the first qualifying event in the composite rather than each component separately.
- Hazard-ratio interpretation: the Cox HR is model-based and summarizes relative instantaneous event rates. It should not be treated as an absolute risk difference or individual-level treatment effect.
- Proportional-hazards assumption: the ClinicalTrials.gov record does not report a formal diagnostic of proportional hazards. A single HR is therefore best understood as the model's summary measure rather than a guarantee that the relative hazard was identical at every point in follow-up.
- Censoring: the time frame ends at the last confirmed survival status date. Interpretation of survival analyses depends on appropriate handling and assumptions concerning censored observations.
- Multiplicity: the secondary endpoint family was explicitly subject to a hierarchical significance framework and Hochberg adjustment. Individual P-values should not be read as independent 0.05 tests.
- Component interpretation: a statistically different composite does not automatically imply the same effect for every component. Individual component analyses must be examined separately.
- Safety denominator: the reported serious-adverse-event figures are affected/at-risk counts. The ClinicalTrials.gov record does not provide sufficient information to derive additional time-adjusted safety measures.
- Incomplete follow-up wording in the registry extract: the time-frame field ends with the phrase “the median duration of follow-up was” without a numerical value. This page therefore does not supply or infer a median follow-up duration.
- External validity: the ClinicalTrials.gov record identifies dyslipidemia and subjects with elevated risk, but do not provide a detailed eligibility or baseline-characteristics table. Broader claims about representativeness should therefore not be inferred from this record alone.
19. Why This Trial Matters Statistically
FOURIER provides a useful teaching example because its registry record connects several major principles of modern time-to-event analysis in a single randomized phase 3 trial.
| Statistical concept | How it appears in FOURIER |
|---|---|
| Randomization | Participants were assigned in a randomized parallel-group design. |
| Blinding | The registry identifies quadruple masking. |
| Time-to-event analysis | The primary endpoint and all posted statistical analyses are time-to-event outcomes. |
| Kaplan-Meier estimation | Provides the standard descriptive framework for event-free survival over time. |
| Log-rank testing | The posted primary and secondary analyses use log-rank testing. |
| Stratified analysis | Tests and Cox models are stratified by final screening LDL-C level and region. |
| Hazard ratio | The principal effect measure for the posted analyses. |
| Confidence interval | Every posted formal analysis includes a 95% two-sided confidence interval. |
| Superiority testing | The primary and secondary hypotheses are identified as superiority hypotheses. |
| Multiplicity | The registry specifies conditional testing levels and the Hochberg method. |
| Safety analysis | Serious adverse events are reported by randomized arm. |
The educational value is not simply that the primary P-value is small. The deeper lesson is how the entire statistical architecture works together: randomization defines the comparison, stratification reflects the design, survival methods account for event timing and censoring, the Cox model produces a relative effect estimate, confidence intervals describe uncertainty, and multiplicity determines how a family of endpoint claims should be interpreted.
20. Reading the FOURIER Results as a Statistical Story
Step 1 · Define the event
The primary endpoint is a composite time-to-first-event measure with five specified cardiovascular components.
Step 2 · Preserve randomization
The efficacy analysis uses all randomized participants and compares placebo with evolocumab.
Step 3 · Compare event times
The stratified log-rank test compares the time-to-event experience between groups.
Step 4 · Quantify the effect
The stratified Cox model summarizes the comparison with a hazard ratio and 95% confidence interval.
Step 5 · Account for multiplicity
Secondary endpoints are interpreted through the prespecified testing sequence and Hochberg adjustment.
Step 6 · Separate efficacy and safety
Serious adverse events are considered independently from the time-to-event efficacy results.
This framework helps prevent several common statistical errors: treating a hazard ratio as an absolute risk reduction, treating a P-value as an effect-size measure, ignoring confidence intervals, reading each secondary endpoint as an independent hypothesis test, or assuming that a composite endpoint represents every component equally.
21. Related Tutorials
Learn more about the methods used in this trial:
22. Related Calculators
Use statistical calculators to explore the quantitative methods underlying this analysis:
23. Sources
- ClinicalTrials.gov: FOURIER, NCT01764633.
- Linked publication: PubMed record, PMID 41178569.
- Linked publication: PubMed record, PMID 40255182.
- Linked publication: PubMed record, PMID 36779348.
- Linked publication: PubMed record, PMID 36585131.
- Linked publication: PubMed record, PMID 36007987.
Continue through the Clinical Biostats statistical pathway
FOURIER connects randomized trial design with survival analysis, hazard ratios, confidence intervals, stratified testing, and multiplicity. Explore the underlying methods through the Clinical Biostats tutorial and calculator collections.
24. Record Summary
FOURIER is a phase 3 randomized, parallel, quadruple-masked trial with 27,564 enrolled participants and a time-to-event primary endpoint. The primary analysis compared evolocumab with placebo using a two-sided stratified log-rank test and a stratified Cox model, with final screening LDL-C level and region as the randomization stratification factors. The reported primary hazard ratio was 0.85 with a 95% CI of 0.79–0.92 and P < 0.0001.
The secondary analyses demonstrate why clinical-trial interpretation requires more than reading one P-value. Hazard ratios ranged across individual cardiovascular endpoints, with different confidence intervals and P-values, while the registry specified a hierarchical multiplicity framework and Hochberg adjustment for remaining secondary endpoints. Serious adverse events were also reported separately by randomized arm.
Statistically, the central lesson is the integration of randomization, time-to-event methodology, stratified log-rank testing, Cox hazard ratios, confidence intervals, and multiplicity control. The primary HR of 0.85 is a relative, model-based estimate; it should be interpreted alongside its confidence interval, P-value, endpoint definition, analysis population, censoring framework, and prespecified testing structure.