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 limited to the ClinicalTrials.gov record.
1. Trial at a Glance
EMPULSE was a randomized, double-blind, parallel-group phase 3 trial evaluating empagliflozin versus placebo in patients hospitalized for acute heart failure. The primary endpoint was a composite clinical-benefit measure based on pairwise comparisons after 90 days of treatment.
| Feature | EMPULSE |
|---|---|
| Trial name | EMPULSE |
| NCT ID | NCT04157751 |
| Phase | Phase 3 |
| Condition | Heart Failure |
| Brief title | A Study to Test the Effect of Empagliflozin in Patients Who Are in Hospital for Acute Heart Failure |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Primary purpose | Treatment |
| Enrollment | 530 |
| Arms | 2 |
| Lead sponsor | Boehringer Ingelheim |
| Sponsor type | Industry |
| Start | May 18, 2020 |
| Primary completion | May 28, 2021 |
| Results posted | Yes |
2. Clinical Question
The trial asked whether empagliflozin produced better clinical outcomes than placebo in patients who were in hospital for acute heart failure. The primary statistical question was framed as a pairwise comparison of patients across treatment groups, incorporating death, heart failure events, time to the first heart failure event, and change from baseline in KCCQ-TSS after 90 days.
Population
Patients with heart failure who were in hospital for acute heart failure.
Intervention
10 mg empagliflozin.
Comparator
Placebo to empagliflozin.
Primary question
Does empagliflozin produce more pairwise wins of clinical benefit than placebo through 90 days of treatment?
3. Trial Design
Empagliflozin
- 10 mg empagliflozin
- Randomized treatment arm
- Included in the primary Randomised Set analysis
Placebo
- Placebo to empagliflozin
- Randomized comparator arm
- Included in the primary Randomised Set analysis
The trial used a randomized, parallel-group, double-masked design. The ClinicalTrials.gov record identifies 530 enrolled participants and two treatment arms but do not provide a randomization ratio or detailed allocation counts for the full trial in the ClinicalTrials.gov record.
4. Primary Endpoint
| Endpoint | Registry definition | Time frame | Primary analysis |
|---|---|---|---|
| Percentage of Pairwise Comparisons With Wins of Clinical Benefit | A composite of death, number of heart failure events (HFEs), time to the first HFE and ≥5-point difference in change from baseline in KCCQ-TSS after 90 days of treatment. | Up to 90 days. For KCCQ-TSS: at baseline and at day 90. | Asymptotic normal U statistics approach; stratified win ratio using weights analogous to a Mantel-Haenszel approach. |
The endpoint is unusual compared with a conventional single time-to-event endpoint. Rather than reducing the entire comparison to one event such as death, the analysis evaluates pairs of patients and determines which patient has the better clinical outcome according to a prespecified hierarchy.
How the pairwise hierarchy works
The registry analysis notes describe the hierarchy in terms of death, heart failure events, and KCCQ-TSS change. The listed ordering begins with death, followed by heart failure-event information and then the KCCQ-TSS comparison. A patient who achieves the better outcome under the hierarchy is counted as a win; the opposing patient contributes a loss.
The reported analysis applied weights analogous to a Mantel-Haenszel approach across strata. A win ratio above 1 indicates more favorable pairwise outcomes for the treatment group under the prespecified hierarchy.
5. Statistical Methodology
Stratified win-ratio analysis
The primary endpoint was analyzed using an asymptotic normal U statistics approach. The reported analysis calculated a stratified win ratio as the total number of wins in the empagliflozin group across all strata divided by the total number of losses, with weights applied analogously to a Mantel-Haenszel approach.
This is important because the win ratio is not simply an odds ratio or a conventional hazard ratio. It is a treatment-effect measure constructed from the ordering of pairwise outcomes. The resulting estimate describes the relative balance of favorable and unfavorable pairwise comparisons under the trial's endpoint hierarchy.
Stratified analysis
The registry analysis describes the primary calculation as stratified. Stratification is useful when comparisons are intended to account for clinically or statistically important strata rather than treating all pairwise comparisons as exchangeable without adjustment.
Cochran-Mantel-Haenszel framework
The registry describes the primary analysis as an asymptotic normal U-statistics approach, with weights applied analogously to a Mantel-Haenszel approach. This provides a useful conceptual connection to stratified categorical-data analysis, while the primary effect measure remains the stratified win ratio.
Logistic regression
The secondary KCCQ-TSS improvement endpoint used logistic regression. The model included baseline KCCQ-TSS, treatment, and heart failure status. The registry reports a Wald confidence interval for the odds ratio.
Mixed-effects model for repeated measures
Change from baseline in KCCQ-TSS was analyzed with a restricted maximum likelihood mixed-effect model for repeated measures. The model included discrete fixed effects for treatment group and heart failure status at each visit, together with continuous fixed effects for the baseline value at each visit.
ANCOVA
The change from baseline in log-transformed NT-proBNP area under the curve over 30 days was analyzed using ANCOVA. NT-proBNP was log-transformed because it was regarded as log-normally distributed, and the linear trapezoidal rule was used to calculate the AUC after the log transformation had been applied to each value.
Cox proportional-hazards model
The incidence rate of first cardiovascular death or heart failure event was analyzed using a Cox proportional-hazards model with terms for heart failure status and treatment. The resulting effect measure was a hazard ratio.
6. Primary Result
The primary analysis used the Randomised Set, including all randomized patients, and compared placebo with 10 mg empagliflozin. The reported effect measure was the stratified win ratio.
Stratified win ratio
95% CI: 1.09–1.68 · P = 0.0027
Endpoint: percentage of pairwise comparisons with wins of clinical benefit after 90 days.
A stratified win ratio of 1.36 means that, under the trial's prespecified pairwise hierarchy, the total number of favorable comparisons for the empagliflozin group was 1.36 times the total number of unfavorable comparisons represented in the win-ratio calculation. Equivalently, the reported estimate is above the neutral value of 1, favoring empagliflozin under this endpoint construction.
The win ratio does not mean that 36% more patients benefited, that an individual patient's risk was reduced by 36%, or that the probability of benefit for every patient was 1.36 times that under placebo. It is a population-level pairwise effect measure defined by the endpoint hierarchy.
The 95% confidence interval of 1.09–1.68 describes statistical uncertainty around the estimated win ratio under the reported analysis. It does not describe the range of individual patient responses.
The P-value of 0.0027 quantifies evidence against the null framework used for the statistical comparison; it does not measure the magnitude or clinical importance of the treatment effect. The effect magnitude is conveyed by the win ratio and its confidence interval.
Because this is a composite pairwise endpoint, interpretation also depends on the ordering of death, heart failure events, time to first heart failure event, and KCCQ-TSS change. A win-ratio result therefore should not be translated directly into a conventional mortality hazard ratio.
7. Secondary Endpoint Results
Improvement of at Least 10 Points in KCCQ-TSS
The registry reports the number of participants with improvement of at least 10 points in KCCQ-TSS after 90 days. Logistic regression included baseline KCCQ-TSS, treatment, and heart failure status.
Odds ratio
95% CI: 0.927–2.501 · P = 0.0970
The odds ratio of 1.522 is the estimated ratio of the odds of achieving at least a 10-point improvement in KCCQ-TSS for empagliflozin relative to placebo after adjustment for baseline KCCQ-TSS, treatment, and heart failure status.
An odds ratio is not the same as a risk ratio. In particular, an odds ratio of 1.522 should not be described as meaning that the probability of improvement was 52.2% higher.
The 95% CI of 0.927–2.501 is relatively broad and crosses the neutral value of 1.00. The P-value of 0.0970 provides the reported statistical evidence for this particular comparison, but it does not establish the size of any clinical effect by itself.
Change From Baseline in KCCQ-TSS
Difference of adjusted mean
95% CI: 0.32–8.59 · P = 0.0347
Assessment at baseline, day 15, day 30, and day 90.
The estimated difference of adjusted means was 4.45 points, comparing empagliflozin with placebo under the reported mixed-effects model for repeated measures.
The 95% CI of 0.32–8.59 represents uncertainty around the adjusted treatment difference. It is an interval for the model-based population comparison, not a prediction interval for an individual patient's KCCQ-TSS response.
The P-value of 0.0347 describes the statistical evidence for the model-based comparison. It should not be interpreted as a measure of how large or clinically important the difference is.
The analysis used observed-case data including data after treatment discontinuation. Missing-data handling is therefore an important part of interpretation, particularly because longitudinal models rely on assumptions about the information contributed by incomplete observations.
Change From Baseline in Log-transformed NT-proBNP AUC
Adjusted geometric mean ratio
95% CI: 0.82–0.98 · P = 0.0176
Log-transformed NT-proBNP AUC from baseline to day 30.
The adjusted geometric mean ratio of 0.90 means that the adjusted geometric mean for the empagliflozin group was estimated at 90% of the corresponding value for placebo on the multiplicative scale used for the log-transformed analysis.
This does not mean that every patient's NT-proBNP changed by exactly 10%, nor does it represent a 10-percentage-point difference. It is a ratio of adjusted geometric means.
The 95% CI of 0.82–0.98 describes uncertainty around that ratio. Because the interval lies below the neutral ratio of 1.00, the reported analysis estimates a lower adjusted geometric mean in the empagliflozin group.
The P-value of 0.0176 is evidence associated with the statistical comparison; it is not a direct measure of effect magnitude.
First Cardiovascular Death or Heart Failure Event
Hazard ratio
95% CI: 0.46–1.10 · P = 0.1241
Incidence rate of first cardiovascular death or heart failure event through 127 days.
The hazard ratio of 0.71 means that the fitted Cox model estimated an instantaneous event rate approximately 29% lower in the empagliflozin group relative to placebo over the analyzed period. This is a model-based relative hazard interpretation, not a statement that 29% of patients avoided an event.
The 95% CI of 0.46–1.10 indicates substantial uncertainty around the estimate and includes the neutral value of 1.00.
The P-value of 0.1241 is the reported statistical comparison. It should not be treated as a measure of the magnitude of the observed hazard ratio.
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 ClinicalTrials.gov record does not report a separate assessment of that assumption.
8. Secondary Results Summary
| Endpoint | Method | Effect measure | Estimate | 95% CI | P-value |
|---|---|---|---|---|---|
| At least 10-point KCCQ-TSS improvement after 90 days | Logistic regression | Odds ratio | 1.522 | 0.927–2.501 | 0.0970 |
| Change from baseline in KCCQ-TSS through day 90 | Mixed-effects model | Difference of adjusted mean | 4.45 | 0.32–8.59 | 0.0347 |
| Change from baseline in log-transformed NT-proBNP AUC through day 30 | ANCOVA | Adjusted geometric mean ratio | 0.90 | 0.82–0.98 | 0.0176 |
| First cardiovascular death or HFE through 127 days | Cox proportional-hazards model | Hazard ratio | 0.71 | 0.46–1.10 | 0.1241 |
The ClinicalTrials.gov record contains five posted statistical analyses: one primary analysis and four secondary analyses. This makes it possible to examine the trial as a compact example of how different endpoint types require different statistical models rather than applying a single method to every outcome.
9. Statistical Methods Explained
Why was a win ratio used for the primary endpoint?
The primary endpoint combines several dimensions of clinical benefit: death, heart failure events, time to the first heart failure event, and KCCQ-TSS change. A win-ratio framework allows these components to be ordered and compared pairwise rather than collapsing them into a single conventional binary or time-to-event outcome.
What does a win ratio of 1.36 mean?
A win ratio of 1.36 indicates that the total number of favorable pairwise comparisons for empagliflozin was 1.36 times the total number of unfavorable comparisons under the reported hierarchy and stratified calculation. The value 1.00 represents the neutral reference point.
Why is a win ratio not a hazard ratio?
A hazard ratio compares modeled instantaneous event rates for a time-to-event endpoint. A win ratio instead compares pairs of patients according to a hierarchical clinical outcome. Although both are relative effect measures, their numerical interpretations are different.
Why was logistic regression used for the KCCQ-TSS improvement endpoint?
The endpoint classified patients according to whether they achieved at least a 10-point improvement. That creates a binary outcome, making logistic regression a natural model for estimating an adjusted odds ratio while incorporating baseline KCCQ-TSS, treatment, and heart failure status.
Why was a mixed-effects model used for KCCQ-TSS change?
KCCQ-TSS was measured repeatedly at baseline, day 15, day 30, and day 90. A mixed-effects model for repeated measures can use the longitudinal structure of these observations and estimate adjusted treatment differences while accounting for within-patient correlation across visits.
Why was NT-proBNP log-transformed before ANCOVA?
The registry analysis states that NT-proBNP was regarded as log-normally distributed. Log transformation makes a multiplicative scale more appropriate for the analysis, after which ANCOVA was used to evaluate the AUC-based endpoint.
How should the Cox hazard ratio of 0.71 be interpreted?
The estimate indicates an approximately 29% lower estimated instantaneous rate of the composite event under the fitted Cox model. It does not mean a 29% absolute reduction in event probability, and the confidence interval must be considered alongside the point estimate.
10. Analysis Populations and Missing Data
| Endpoint | Analysis population | Missing-data information reported |
|---|---|---|
| Primary clinical-benefit win ratio | Randomised Set, including all randomized patients | Primary analysis uses the randomized population; detailed imputation method is not reported. |
| At least 10-point KCCQ-TSS improvement | Randomised Set, including all randomized patients | Baseline KCCQ-TSS was included in logistic regression. |
| KCCQ-TSS change | Patients in the Randomised Set with non-missing data for the endpoint; observed case including data after treatment discontinuation | Missing data caused by patient withdrawal or other reasons were handled implicitly by the MMRM approach; an unstructured covariance structure was used. |
| NT-proBNP AUC | Randomised Set with non-missing data for the endpoint | Not described in the ClinicalTrials.gov record |
| CV death or HFE | Randomised Set, including all randomized patients | No additional imputation procedure is reported. |
11. Safety Results
The ClinicalTrials.gov record reports serious adverse events by treatment arm. These are counts of participants affected among those at risk, rather than an overall adverse-event incidence percentage.
| Safety measure | Placebo | 10 mg Empagliflozin |
|---|---|---|
| Serious adverse events | 115 / 264 | 84 / 260 |
The ClinicalTrials.gov record does not provide a formal statistical comparison, confidence interval, or P-value for serious adverse events. Therefore, these counts should be treated as descriptive safety information rather than as a formally tested treatment effect.
12. Design Features That Affect Statistical Interpretation
Randomization
Randomization is a central design feature because it establishes the treatment groups before outcomes are observed. The ClinicalTrials.gov record identifies the allocation as randomized and the design as parallel, supporting a direct between-group comparison.
Double masking
The trial is recorded as double masked. Masking can reduce the influence of treatment assignment on behavior, assessment, reporting, and other processes that might otherwise introduce bias.
Multiplicity
The ClinicalTrials.gov record identifies one registered primary endpoint and five posted statistical analyses in total. The ClinicalTrials.gov record does not state a multiplicity-adjustment procedure or a formal hypothesis hierarchy across the secondary endpoints.
Consequently, the individual secondary P-values should be interpreted as the reported P-values for their respective analyses. They should not automatically be treated as independent confirmatory evidence under a familywise type I error framework unless such a framework is documented elsewhere.
Interim analysis
The ClinicalTrials.gov record does not identify an interim efficacy analysis, alpha-spending plan, or stopping boundary. These design elements are therefore not described here.
Non-inferiority
The ClinicalTrials.gov record does not identify a non-inferiority hypothesis or margin. The primary result is therefore presented as a superiority-style win-ratio comparison rather than a non-inferiority analysis.
Crossover
The ClinicalTrials.gov record does not report treatment crossover. No crossover adjustment or interpretation is therefore presented.
Bayesian methods
No Bayesian method is reported in the registry-reported statistical methodology. The analyses are described using frequentist methods including the win-ratio/U-statistics approach, logistic regression, mixed-effects modeling, ANCOVA, and Cox regression.
13. Endpoint-by-Endpoint Statistical Map
| Endpoint type | Endpoint in EMPULSE | Method | Effect measure |
|---|---|---|---|
| Hierarchical pairwise clinical outcome | Clinical benefit after 90 days | Asymptotic normal U statistics approach with stratified weighting | Stratified win ratio |
| Binary | At least 10-point KCCQ-TSS improvement | Logistic regression | Odds ratio |
| Continuous longitudinal | Change from baseline in KCCQ-TSS | Mixed-effects model for repeated measures | Difference of adjusted mean |
| Continuous biomarker AUC | Change from baseline in log-transformed NT-proBNP AUC | ANCOVA | Adjusted geometric mean ratio |
| Time-to-event | First cardiovascular death or HFE | Cox proportional-hazards model | Hazard ratio |
This mapping illustrates an important statistical principle: the endpoint determines much of the appropriate analysis strategy. A binary improvement threshold, a repeated continuous measurement, a skewed biomarker AUC, a time-to-event outcome, and a hierarchical composite can all require different inferential tools.
14. Understanding the Primary Win-Ratio Result
The reported stratified win ratio of 1.36 indicates that the balance of pairwise wins and losses favored empagliflozin under the trial's hierarchy of clinical outcomes.
The result does not provide a conventional probability that an individual patient will benefit. It also does not establish that the effect was driven by death, heart failure events, or KCCQ-TSS specifically unless the component-specific contribution to the overall win ratio is separately reported.
The 95% CI of 1.09–1.68 gives a measure of uncertainty around the estimated win ratio. The lower and upper limits show that the point estimate is not being treated as exact. The interval is also important because the clinical meaning of a pairwise effect can differ substantially depending on where the true value lies within that range.
The P-value of 0.0027 summarizes statistical evidence under the specified comparison. It does not indicate that the treatment effect is "0.27%" or that the probability the null hypothesis is true is 0.27%. The win ratio and confidence interval are the appropriate quantities for describing the magnitude and precision of the reported effect.
15. Why the Secondary Analyses Matter
The secondary analyses provide several complementary perspectives on the same randomized comparison. They should not be collapsed into a single number because each measures a different aspect of the clinical course.
Patient-reported symptoms
KCCQ-TSS improvement and continuous KCCQ-TSS change address symptoms and health status from different statistical perspectives.
Biomarker response
NT-proBNP AUC provides a biomarker-based outcome analyzed on a logarithmic scale.
Clinical events
The CV death or HFE endpoint uses time-to-event methodology and therefore differs fundamentally from the KCCQ-based analyses.
Converging evidence
The endpoints provide different measurements of treatment effect and should be interpreted according to their own definitions and statistical models.
16. Limitations
- Composite hierarchy: the primary win-ratio endpoint combines several clinical components, so the overall estimate cannot be interpreted as a conventional effect on any single component.
- Component contribution: the ClinicalTrials.gov record does not provide enough component-level results to determine how much of the overall win ratio was attributable to death, heart failure events, time to first HFE, or KCCQ-TSS.
- Different effect measures: the secondary endpoints use odds ratios, mean differences, geometric mean ratios, and hazard ratios. These estimates are not directly interchangeable.
- Confidence intervals: some secondary confidence intervals are relatively wide, particularly for the binary KCCQ-TSS improvement endpoint and the cardiovascular death/HFE hazard ratio.
- Multiplicity: the ClinicalTrials.gov record does not identify a formal multiplicity-adjustment strategy across the secondary analyses.
- Missing data: the registry-reported analysis text does not contain the full missing-data procedures for all longitudinal and biomarker endpoints.
- Observed-case analysis: the KCCQ-TSS mixed-model endpoint is explicitly described as an observed-case analysis including data after treatment discontinuation.
- Safety inference: serious adverse-event counts are reported descriptively without a formal comparative analysis in the ClinicalTrials.gov record.
- Registry scope: the analysis presented here is limited to the numerical and methodological information from ClinicalTrials.gov and does not reconstruct additional analyses from external publications.
17. Why This Trial Matters Statistically
EMPULSE is a useful statistical teaching case because it places several modern clinical-trial methods in one randomized study. Most notably, the primary endpoint uses a hierarchical win-ratio framework rather than a conventional single-event endpoint, while the secondary analyses move across binary, longitudinal continuous, biomarker, and time-to-event outcomes.
| Concept | How it appears in EMPULSE |
|---|---|
| Randomization | Randomized, parallel-group phase 3 design |
| Blinding | Double-masked trial |
| Win ratio | Primary composite clinical-benefit endpoint |
| Stratified analysis | Primary win-ratio calculation uses stratified weighting |
| Mantel-Haenszel-type weighting | Stratum weights in the primary win-ratio analysis |
| Logistic regression | Binary KCCQ-TSS improvement endpoint |
| Mixed-effects model | Repeated KCCQ-TSS measurements |
| ANCOVA | Log-transformed NT-proBNP AUC |
| Geometric mean ratio | Effect measure for the log-transformed biomarker analysis |
| Cox model | First cardiovascular death or HFE |
| Hazard ratio | Relative time-to-event effect measure |
| Confidence intervals | Reported for the primary and secondary effect estimates |
| Missing data | Relevant to the longitudinal KCCQ-TSS and NT-proBNP analyses |
18. A Deeper Look at the Effect Measures
Win ratio: 1.36
The win ratio is centered at 1.00 rather than 0.00. Values above 1 favor the treatment group because there are more wins than losses in the pairwise framework. Its interpretation depends directly on the hierarchy used to decide which patient in a pair has the better outcome.
Odds ratio: 1.522
The odds ratio compares odds rather than probabilities. An odds ratio of 1.522 indicates higher estimated odds of achieving the binary KCCQ-TSS improvement endpoint under the fitted logistic model, but it should not be described as a 52.2% increase in probability.
Mean difference: 4.45
The mean difference is an additive treatment contrast on the KCCQ-TSS scale used by the mixed-effects model. It directly describes the model-estimated difference in adjusted means rather than a relative ratio.
Geometric mean ratio: 0.90
The geometric mean ratio is multiplicative. A value below 1 indicates a lower geometric mean in the treatment group on the analyzed scale. Because the underlying biomarker was log-transformed, the ratio is naturally interpreted multiplicatively.
Hazard ratio: 0.71
The hazard ratio compares modeled instantaneous event rates. It is particularly appropriate for time-to-event endpoints because it accounts for event timing and censoring within the survival-analysis framework.
19. Time Frames and Follow-up
| Outcome | Registry time frame |
|---|---|
| Primary clinical-benefit win ratio | Up to 90 days; KCCQ-TSS at baseline and day 90 |
| KCCQ-TSS improvement of at least 10 points | Baseline and day 90 |
| Change from baseline in KCCQ-TSS | Baseline, day 15, day 30, and day 90 |
| NT-proBNP AUC | Baseline to day 30 |
| CV death or HFE | Up to 127 days |
The different follow-up windows are statistically important. A 90-day KCCQ outcome and a 127-day time-to-event outcome do not represent the same observation period. Effect estimates should therefore always be interpreted together with the endpoint definition and time frame.
20. Clinical Interpretation vs Statistical Interpretation
Statistical interpretation
The primary randomized comparison produced a stratified win ratio of 1.36 with a 95% CI of 1.09–1.68 and a P-value of 0.0027. Secondary analyses used distinct models appropriate to their endpoint structures.
Clinical interpretation
The trial's statistical evidence addresses several dimensions of clinical benefit, including the hierarchical composite endpoint, KCCQ-TSS, NT-proBNP, and cardiovascular death or heart failure events. Each should be considered according to its own endpoint definition.
The distinction is important: statistical evidence describes the strength and uncertainty of an estimated comparison under a specified model, whereas clinical interpretation asks what that estimate means for patients and clinical outcomes. The ClinicalTrials.gov record supports the former directly and provide several components for the latter, but they do not justify collapsing every endpoint into one overall clinical conclusion.
21. Related Tutorials
Learn more about the methods used in this trial:
22. Related Calculators
23. Sources
- ClinicalTrials.gov: EMPULSE — NCT04157751.
- PubMed: PMID 41793401.
- PubMed: PMID 40526444.
- PubMed: PMID 37540060.
- PubMed: PMID 35377706.
- PubMed: PMID 35228754.
Continue through the Clinical Biostats statistical tutorials
Explore the statistical methods and calculators that correspond to the endpoints and models used in randomized clinical trials.
24. Record Summary
EMPULSE provides a useful example of how modern clinical-trial statistics can combine a hierarchical pairwise primary endpoint with several conventional secondary analyses. The primary result was a stratified win ratio of 1.36 with a 95% CI of 1.09–1.68 and P = 0.0027. The secondary analyses then used logistic regression for a binary KCCQ-TSS improvement endpoint, a mixed-effects model for repeated KCCQ-TSS measurements, ANCOVA for log-transformed NT-proBNP AUC, and a Cox proportional-hazards model for cardiovascular death or heart failure events.
The most important statistical lesson is that these effect measures answer different questions. The win ratio describes the balance of hierarchical pairwise clinical outcomes; the odds ratio describes relative odds of a binary outcome; the adjusted mean difference describes an additive longitudinal treatment contrast; the geometric mean ratio describes a multiplicative biomarker contrast; and the hazard ratio describes relative instantaneous event rates in a time-to-event model.