This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. The ClinicalTrials.gov record contains posted outcome measures but does not provide formal statistical-analysis results for the registered primary endpoint. Accordingly, this page distinguishes what the registry reports from how an endpoint of this type would ordinarily be analyzed.
1. Trial at a Glance
RELAX was a completed, randomized phase 3 trial evaluating sildenafil versus placebo in people with diastolic heart failure. The registry describes a parallel-group design with triple masking and a primary endpoint measuring change in exercise capacity, as determined by peak oxygen uptake, from baseline to Week 24.
| Feature | RELAX |
|---|---|
| Trial name | RELAX |
| Brief title | Evaluating the Effectiveness of Sildenafil at Improving Health Outcomes and Exercise Ability in People With Diastolic Heart Failure (The RELAX Study) |
| Phase | Phase 3 |
| Condition | Heart Failure |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Triple |
| Primary purpose | Treatment |
| Enrollment | 216 |
| Arms | 2 |
| Interventions | Placebo (drug); Sildenafil (drug) |
| Lead sponsor | Duke University |
| Sponsor type | OTHER |
| Start | 2008-09 |
| Primary completion | 2012-09 |
| Status | COMPLETED |
| ClinicalTrials.gov | NCT00763867 |
2. Clinical Question
The trial addresses whether sildenafil affects exercise capacity in people with diastolic heart failure. The registry's primary endpoint focuses specifically on change from baseline to Week 24 in exercise capacity as determined by peak oxygen uptake.
Population
People with diastolic heart failure, with the registry condition listed as Heart Failure.
Intervention
Sildenafil.
Comparator
Placebo.
Primary question
What is the difference between randomized groups in change in exercise capacity, as determined by peak oxygen uptake, from baseline to Week 24?
This framing is important statistically. The primary question is not simply whether peak oxygen uptake at Week 24 is different between groups. The registered endpoint is explicitly a change-from-baseline endpoint. The analysis therefore needs to account for both the baseline measurement and the Week 24 measurement.
3. Trial Design
Placebo
- Placebo (drug)
- Randomized comparator arm
- Primary endpoint assessed at Week 24
Sildenafil
- Sildenafil (drug)
- Randomized intervention arm
- Primary endpoint assessed at Week 24
The available registry data do not provide a randomized allocation ratio or arm-level enrollment counts for the primary efficacy endpoint. 0.
4. Registered Primary Endpoint
| Endpoint | Registry definition | Time frame | Results posted? |
|---|---|---|---|
| Exercise Capacity, as Determined by Peak Oxygen Uptake | Exercise Capacity, as Determined by Peak Oxygen Uptake | Change from Baseline to Week 24 | Yes |
The registry identifies 1 registered primary endpoint and classifies its endpoint type as Other / unclear. The outcome measure is nevertheless specific enough to establish the statistical structure of the primary question: a continuous physiologic measure is assessed in terms of its change from baseline over a prespecified 24-week interval.
5. Results Availability
The RELAX ClinicalTrials.gov record reports 45 outcome measures and indicates that results have been posted. However, no entries are reported in the statistical-analysis section for the registered primary endpoint. That means there are no omitted formal analyses that need to be reconstructed from the ClinicalTrials.gov record.
6. Planned Analysis
Because the registry supplies the primary endpoint definition but no formal statistical-analysis result, this section describes the analysis appropriate for an endpoint of this type rather than reporting an outcome.
Change from baseline as the estimand
The primary outcome is defined as the change in peak oxygen uptake between baseline and Week 24. Conceptually, for each participant:
The treatment comparison would then focus on the difference in the average change between the randomized sildenafil and placebo groups, subject to the prespecified analysis model.
ANCOVA as a conventional approach
For a randomized two-arm trial with a continuous baseline measurement and a continuous follow-up measurement, a common primary analysis is an analysis of covariance (ANCOVA) model with Week 24 peak oxygen uptake as the outcome, treatment group as the main comparison, and baseline peak oxygen uptake as a covariate.
Here, β₁ represents the adjusted difference between randomized treatment groups at Week 24 after accounting for the baseline measurement. This is an educational description of a conventional analysis, not a claim that this exact model was used in the RELAX registry.
Why not simply compare Week 24 means?
A comparison of Week 24 means alone can ignore useful information contained in the baseline measurement. Adjusting for baseline can improve precision when baseline values are related to follow-up values. Because randomization balances prognostic factors in expectation rather than making every observed baseline measurement identical, baseline adjustment can also account for chance baseline differences.
Change-score analysis versus ANCOVA
A direct comparison of change scores is another recognizable approach. It asks whether the mean improvement or decline differs between randomized groups. ANCOVA instead models the Week 24 value while adjusting for baseline. These methods answer closely related treatment questions, but their statistical efficiency and assumptions can differ.
The ClinicalTrials.gov record does not specify which of these models was used. Therefore, the methodology should be presented as the appropriate analytical framework for the registered endpoint, not as a documented RELAX statistical-analysis result.
7. Statistical Methods Explained
Why is a baseline measurement important?
The primary endpoint is a change from baseline, so every participant's baseline peak oxygen uptake is part of the definition of the outcome. A participant with a high baseline value and a participant with a low baseline value cannot be interpreted solely from their Week 24 measurements without considering where each started.
Why might ANCOVA be preferred to a simple change-score comparison?
ANCOVA can use the baseline measurement directly as a covariate rather than first converting each participant's observations into a change score. When baseline and follow-up measurements are correlated, this can provide a more precise treatment comparison. The exact choice remains a protocol or statistical-analysis-plan question, and the ClinicalTrials.gov record does not identify the model used.
What would the treatment estimate mean?
For this endpoint, the most natural treatment estimate would describe the difference between randomized groups in peak oxygen uptake at Week 24 after accounting for baseline, or equivalently a prespecified difference in change depending on the chosen model. A positive or negative estimate would need to be interpreted according to the direction in which peak oxygen uptake represents greater exercise capacity.
What would a confidence interval add?
A confidence interval would describe statistical uncertainty around the estimated between-group treatment difference. A narrow interval would indicate greater precision than a wide interval. It would not describe the range of responses expected for individual participants.
What would a p-value tell us?
A p-value would quantify how compatible the observed data are with a specified null hypothesis under the statistical model. It would not measure the magnitude or clinical importance of the treatment effect. A small p-value and a large treatment effect are different concepts, just as a large p-value does not by itself establish that the treatment groups are clinically equivalent.
Why does randomization matter for the analysis?
Randomization creates the basis for a causal comparison between the assigned treatment groups, subject to the usual assumptions of randomized-trial inference. The primary analysis should therefore preserve the randomized comparison rather than selectively comparing only participants who completed treatment or follow-up.
8. Analysis Population and Missing Week 24 Measurements
The ClinicalTrials.gov record does not specify the exact analysis population used for the primary endpoint, nor do they provide a missing-data or imputation strategy. Those details matter because a change-from-baseline endpoint requires information at baseline and at Week 24, and participants may not always have complete measurements at both time points.
Complete cases
A simple analysis could restrict the comparison to participants with both baseline and Week 24 measurements, but this can reduce precision and can introduce bias if missingness is related to prognosis or treatment.
Model-based handling
Longitudinal or ANCOVA-based approaches can incorporate available measurements under explicit assumptions about the missing-data mechanism. The actual RELAX strategy is not specified in the ClinicalTrials.gov record.
Multiple imputation
Multiple imputation is another possible strategy when appropriate auxiliary information is available. It requires assumptions that should be prespecified and evaluated.
Sensitivity analysis
Sensitivity analyses can examine how conclusions change under alternative assumptions about missing Week 24 measurements. No such analysis is reported in the ClinicalTrials.gov record.
9. Blinding and Randomization
Two design features are especially important for interpreting a subjective or effort-dependent physiologic endpoint such as exercise capacity: randomization and masking.
Masking is particularly relevant when an endpoint involves exercise testing or participant effort. Knowledge of treatment assignment could potentially affect expectations, behavior, encouragement, or assessment. Triple masking is therefore a design feature that should be considered when evaluating the internal validity of the trial, although the ClinicalTrials.gov record does not specify which three groups of individuals were masked.
10. Safety Results
The ClinicalTrials.gov record provides serious adverse-event counts by randomized arm. The reported figures are shown exactly as provided:
| Safety measure | Placebo | Sildenafil |
|---|---|---|
| Serious adverse events, affected / at risk | 16 / 103 | 25 / 113 |
The denominators differ between the two reported safety groups: 103 for placebo and 113 for sildenafil. Consequently, the affected-participant counts alone should not be interpreted as exposure-adjusted rates. The ClinicalTrials.gov record does not provide exposure duration, definitions of individual serious adverse events, severity categories, relatedness assessments, or a formal statistical comparison of serious adverse events.
11. Statistical Interpretation of the Primary Endpoint
The registered endpoint measures change in exercise capacity as determined by peak oxygen uptake from baseline to Week 24. It therefore captures within-participant change over a fixed period and then compares that change between randomized treatment groups.
It is not a direct measure of survival, hospitalization, mortality, or every aspect of health status. The registry wording reported here identifies exercise capacity as the primary endpoint; broader clinical outcomes should not be substituted for it.
A formal treatment estimate would quantify the between-group difference attributable to randomized assignment under the specified analysis model. Without that estimate, the available data establish the trial design and endpoint but do not establish the magnitude of the primary treatment effect.
Even if a formal p-value were available, it would not communicate how large the treatment difference was or how precisely it was estimated. A complete statistical interpretation would pair the treatment estimate with its confidence interval and explain the analysis population and missing-data assumptions.
12. What a Complete Primary Analysis Would Report
For a randomized two-arm trial with this registered endpoint, a complete statistical results presentation would ideally include several linked quantities rather than a single significance test.
| Quantity | Purpose |
|---|---|
| Baseline peak oxygen uptake | Describes the starting value used to define change or as a covariate in an adjusted analysis. |
| Week 24 peak oxygen uptake | Describes the endpoint measurement at the registered assessment time. |
| Mean change by arm | Describes within-group change from baseline to Week 24. |
| Between-group treatment difference | Quantifies the randomized comparison in the primary endpoint. |
| 95% confidence interval | Describes statistical precision around the treatment estimate. |
| P-value | Tests the prespecified null hypothesis under the chosen statistical model. |
| Analysis population | Clarifies which randomized participants contributed to the primary analysis. |
| Missing-data strategy | Shows how participants without complete Week 24 measurements were handled. |
The registry-reported RELAX data do not contain these formal primary-analysis estimates. Listing the components here is therefore a methodological guide rather than a substitute for the missing numerical results.
13. Multiplicity and Multiple Endpoints
The registry reports 45 outcome measures, while only one registered primary endpoint is reported in the ClinicalTrials.gov record. This distinction is statistically important.
Primary endpoint
The registered primary endpoint is exercise capacity as determined by peak oxygen uptake, measured as change from baseline to Week 24.
Other outcomes
The registry reports 45 outcome measures overall, but the ClinicalTrials.gov record does not identify the full set of secondary or exploratory endpoints.
Type I error
When many hypotheses are tested, the probability of at least one false-positive finding can increase unless multiplicity is addressed.
What cannot be inferred
The ClinicalTrials.gov record does not state an alpha hierarchy, multiplicity-adjustment procedure, gatekeeping strategy, or testing sequence for the 45 posted outcomes.
A formal statistical analysis plan would be the appropriate source for determining which hypotheses were confirmatory, which were secondary or exploratory, and how familywise type I error was controlled. Those details are not present in the ClinicalTrials.gov record.
14. No Non-Inferiority or Equivalence Framework Is Identified
The ClinicalTrials.gov record describes a randomized phase 3 treatment trial comparing sildenafil with placebo. It does not identify a non-inferiority margin, an equivalence margin, or a non-inferiority hypothesis for the primary endpoint.
That distinction matters because a superiority analysis and a non-inferiority analysis use different inferential logic. A conventional superiority test asks whether the data support a difference between groups, whereas a non-inferiority design asks whether the experimental treatment is not worse than the comparator by more than a prespecified margin. No such margin is posted on ClinicalTrials.gov for RELAX, so a non-inferiority interpretation should not be imposed on the trial.
15. No Factorial or Crossover Design Is Identified
The registry identifies the design model as PARALLEL and the allocation as RANDOMIZED. The registry-reported intervention list contains placebo and sildenafil. There is no registry information in the ClinicalTrials.gov recordset identifying a factorial treatment structure or a treatment crossover.
| Design feature | RELAX registry information reported |
|---|---|
| Randomized | Yes |
| Parallel | Yes |
| Triple masked | Yes |
| Factorial design | Not identified in the ClinicalTrials.gov record |
| Crossover design | Not identified in the ClinicalTrials.gov record |
| Non-inferiority margin | Not identified in the ClinicalTrials.gov record |
| Bayesian primary analysis | Not identified in the ClinicalTrials.gov record |
16. Interim Analysis and Bayesian Methods
The ClinicalTrials.gov record does not identify an interim efficacy analysis, stopping boundary, alpha-spending procedure, or Bayesian primary analysis. Those methods therefore should not be attributed to RELAX on the basis of the ClinicalTrials.gov record.
In general, an interim analysis would require prespecified control of the overall type I error if repeated looks at accumulating efficacy data were used for confirmatory inference. A Bayesian analysis would instead require explicit specification of a prior distribution and a posterior decision rule. Neither framework is documented in the ClinicalTrials.gov record.
17. Serious Adverse Events and Denominator Interpretation
The serious-adverse-event data provide an instructive example of why denominators matter in clinical-trial statistics. The registry reports 16/103 for placebo and 25/113 for sildenafil.
The numerator is the number of affected participants and the denominator is the corresponding number at risk reported in the ClinicalTrials.gov record.
A comparison of raw numerators would ignore the different denominators. A formal safety comparison would also need to specify the analysis population, event definition, observation period, and statistical method. For recurrent events or differing exposure durations, a simple participant-level proportion may not fully capture the relevant safety experience.
The ClinicalTrials.gov recordset does not provide enough detail to determine whether a formal between-arm hypothesis test for serious adverse events was prespecified or performed.
18. Trial Timeline
Trial start
The registry lists September 2008 as the study start.
Randomized parallel trial
The study is classified as a phase 3 randomized, parallel-group, triple-masked treatment trial with two interventions.
Primary completion
The registry lists September 2012 as the primary completion date.
Results posted
The registry record is marked completed and indicates that results have been posted, including 45 outcome measures.
19. Limitations
- No formal statistical-analysis estimates reported: the statistical-analysis section provided for this page is empty, so no treatment-effect estimate, confidence interval, or p-value can be reported for the primary endpoint from the ClinicalTrials.gov record.
- Primary endpoint results are not reproduced: although the registry indicates that results are posted for the primary endpoint, the numerical result itself is not included in the ClinicalTrials.gov record.
- Analysis model unspecified: the ClinicalTrials.gov record does not identify whether the primary endpoint was analyzed with ANCOVA, a change-score model, a repeated-measures model, or another prespecified approach.
- Missing-data strategy unspecified: the ClinicalTrials.gov record does not identify the method used to handle participants without a Week 24 measurement.
- Analysis population unspecified: the ClinicalTrials.gov record does not state the exact population used for the primary efficacy analysis.
- Multiplicity unspecified: 45 outcome measures are posted, but the ClinicalTrials.gov record does not identify the statistical hierarchy or multiplicity-control strategy.
- Limited safety detail: serious adverse events are reported by arm, but detailed event definitions, exposure time, and formal statistical comparisons are not reported.
- Registry-versus-publication distinction: the registry facts reported here should not be supplemented with remembered results from publications when those numerical results are not included in the trial dataset used for this page.
20. Why This Trial Matters Statistically
RELAX is useful as a teaching example because its primary endpoint illustrates a different statistical structure from a conventional survival endpoint. Instead of asking how long participants remain alive or free of an event, the primary question concerns a continuous physiologic measurement and its change over time.
| Concept | How it appears in RELAX |
|---|---|
| Randomization | The trial used randomized allocation between sildenafil and placebo. |
| Parallel-group design | The registry identifies the design model as parallel. |
| Triple masking | The registry identifies the trial as triple masked. |
| Continuous endpoint | The primary endpoint is exercise capacity as determined by peak oxygen uptake. |
| Change from baseline | The registered time frame is change from baseline to Week 24. |
| Baseline adjustment | ANCOVA is a conventional framework for a continuous follow-up endpoint with a baseline measurement. |
| Confidence intervals | A complete treatment analysis would use an interval estimate to quantify uncertainty around the between-group effect. |
| Missing data | Participants without complete baseline and Week 24 measurements require an explicit analysis strategy. |
| Multiplicity | The registry reports 45 outcome measures, while one registered primary endpoint is reported here. |
| Safety denominators | Serious adverse events are reported as affected participants divided by participants at risk. |
21. A Statistical Walkthrough of the Primary Question
Step 1: Preserve the randomized comparison
The first principle is to compare participants according to randomized treatment assignment. The trial is randomized and parallel, so the primary efficacy question is naturally framed as a between-group comparison rather than as a within-sildenafil comparison alone.
Step 2: Define the outcome precisely
The registered endpoint is not simply "peak oxygen uptake." It is Exercise Capacity, as Determined by Peak Oxygen Uptake, with the time frame Change from Baseline to Week 24. The exact endpoint definition determines what the analysis should estimate.
Step 3: Quantify treatment effect
A continuous treatment effect could be expressed as an adjusted or unadjusted between-group difference. The sign of the estimate must be interpreted according to the direction of peak oxygen uptake and the prespecified coding of treatment.
Step 4: Quantify uncertainty
The treatment estimate should be accompanied by a confidence interval. This distinguishes a precise estimate from one that is highly uncertain even if the point estimate appears substantial.
Step 5: Evaluate the statistical hypothesis
A prespecified hypothesis test can provide a p-value for the treatment comparison. The p-value should be interpreted alongside the effect estimate and confidence interval rather than treated as a measure of treatment magnitude.
Step 6: Examine assumptions
For ANCOVA, important considerations include the relationship between baseline and follow-up outcome and the adequacy of the model specification. For a change-score analysis, assumptions concern the distribution and variance of the change measurements. For either approach, missing data can materially affect interpretation.
22. What the Registry Data Allow Us to Conclude
Established from the ClinicalTrials.gov record
RELAX was a completed phase 3 randomized parallel trial with triple masking, two intervention arms, and 216.0 enrolled participants.
Primary endpoint established
The registered primary endpoint was exercise capacity as determined by peak oxygen uptake, measured as change from baseline to Week 24.
Results availability
The registry indicates that results were posted and reports 45 outcome measures.
Formal comparison unavailable here
The registry-reported statistical-analysis section contains no formal primary-endpoint analysis, so a numerical treatment effect cannot be responsibly reported from the registry record.
This distinction is central to evidence-based statistical reporting. A trial can have a completed status and posted outcomes while the specific numerical analysis needed to support a particular claim is not present in the data posted on ClinicalTrials.gov for a secondary educational summary.
23. Related Tutorials
Learn more about the methods used in this trial:
24. Related Statistical Calculators
25. Sources
- ClinicalTrials.gov: RELAX, NCT00763867.
- Linked publication: PubMed PMID 23478662.
- Linked publication: PubMed PMID 38533961.
- Linked publication: PubMed PMID 35358904.
- Linked publication: PubMed PMID 32150314.
- Linked publication: PubMed PMID 31805424.
Continue through the Clinical Biostats statistical methods
Explore the broader statistical concepts behind randomized trials, continuous endpoints, baseline adjustment, masking, and analysis of clinical-trial outcomes.
26. Record Summary
RELAX provides a useful statistical example of a randomized phase 3 trial centered on a continuous physiologic endpoint rather than a time-to-event outcome. The registry identifies a randomized, parallel, triple-masked comparison of sildenafil and placebo in people with diastolic heart failure, with 216.0 enrolled participants and a primary endpoint of change in exercise capacity as determined by peak oxygen uptake from baseline to Week 24.
The central statistical task is to estimate the between-group treatment difference while appropriately incorporating the baseline measurement, the Week 24 outcome, the randomized design, and any missing-data assumptions. ANCOVA is a conventional framework for this type of endpoint, although the ClinicalTrials.gov record does not establish that it was the actual prespecified RELAX model.
The registry data also report serious adverse events as 16/103 in the placebo group and 25/113 in the sildenafil group. These safety figures require separate interpretation from the primary efficacy endpoint and should not be converted into a broader benefit-risk conclusion without the additional information normally contained in a full statistical analysis and safety report.