Heart Rate Reduction in Heart Failure: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Heart Rate Reduction in Heart Failure (NCT01178528), a randomized phase 3 study. The primary outcome is Exercise Tolerance Assessed by 6 Minute Walking Test.

2. Clinical Question

3. Trial Design

This was a phase 3, randomized, double-masked, parallel-group trial with an enrollment of 121. The registry lists three treatment groups: ivabradine, carvedilol, and carvedilol with ivabradine. The primary outcome was assessed at 3 months. The listed arm counts for the primary outcome are 41 for ivabradine, 38 for carvedilol, and 42 for the combination. The registry record does not say whether those counts represent everyone randomized, everyone treated, or participants with outcome data available at the assessment.

The study start is recorded as 2009-09, primary completion as 2010-06, and status as completed. IRCCS San Raffaele is listed as sponsor. The record describes an aim to evaluate the effect of heart-rate reduction with the three regimens in patients with heart failure of ischemic origin. It also notes the study context of exercise tolerance and the 6-minute walking test.

The registry record does not report the method used to generate the random sequence, how treatment allocation was concealed, or the roles that were masked. It does not describe the planned treatment duration beyond the outcome timeframe, the details of follow-up, or the protocol for managing changes in treatment. Further eligibility criteria, sites, and participant characteristics are not reported in the registry record. Although the design is listed as double-masked, the people or procedures covered by masking are not specified. These omissions limit what can be inferred about the trial's conduct from the record alone.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Exercise Tolerance Assessed by 6 Minute Walking Test, measured over 3 months.

The primary endpoint is exercise tolerance assessed by distance walked during a 6-minute walking test, recorded in meters at 3 months. Participants were asked to walk at their own maximal pace along a 100 m hospital corridor. The test was supervised by a physical therapist, and a standard phrase of encouragement was given at the beginning of the last (6th) minute. Participants could stop if signs or symptoms of significant distress occurred and were instructed to resume walking as soon as possible.

The record says that testing followed a standardized procedure. Measurements were taken at baseline, before inclusion at least 1 week after baseline evaluation, and at the end of the study. Patients who had not completed at least two tests in the past underwent two practice 6-minute walking tests at least 3 days apart. These procedures aim to make the walking assessment more consistent across participants and occasions.

As a general statistical point, a measured walking distance provides a continuous outcome: each participant's result can take a range of values, and group means can be compared. It is used in this trial as an operational measure of exercise tolerance. It does not by itself capture every aspect of heart failure or quality of life, and the registry record does not report a threshold for interpreting a particular distance as clinically important.

7. Results Posted in the Registry

• Carvedilol: mean 435.70 versus 474.80 on control; difference -39.10 (95% CI -93.92 to 15.72), standardized effect d = -0.31; z-test p = 0.162.
• Carvedilol and Ivabradine: mean 453.10 versus 474.80 on control; difference -21.70 (95% CI -68.79 to 25.39), standardized effect d = -0.20; z-test p = 0.366.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Quality of Life

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Carvedilol: mean 4.10 versus 6.70 on control; difference -2.60 (95% CI -2.94 to -2.26), standardized effect d = -3.37; z-test p = <0.001.
  • Carvedilol and Ivabradine: mean 6.10 versus 6.70 on control; difference -0.60 (95% CI -0.93 to -0.27), standardized effect d = -0.79; z-test p = <0.001.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Carvedilol than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Carvedilol and Ivabradine than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

New York Heart Association (NYHA) Class

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Carvedilol: 13.2% (5/38) versus 73.2% (30/41) on control; risk difference -60.0 percentage points (95% CI -77.3 to -42.7), risk ratio 0.18 (0.08–0.42); unadjusted two-proportion z-test p = <0.001.
  • Carvedilol and Ivabradine: 47.6% (20/42) versus 73.2% (30/41) on control; risk difference -25.6 percentage points (95% CI -45.9 to -5.3), risk ratio 0.65 (0.45–0.94); unadjusted two-proportion z-test p = 0.017.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the proportion with the event is statistically lower for Carvedilol than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
  • The 95% confidence interval excludes no difference, so the proportion with the event is statistically lower for Carvedilol and Ivabradine than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The registry lists two secondary outcomes at 3 months: quality of life and New York Heart Association (NYHA) Class. The posted comparisons show nominal differences between the reference group and the other groups on these secondary measures, while the primary walking-distance comparisons are less conclusive. This means the secondary findings and the primary result do not form a uniformly consistent statistical pattern. Different outcomes can capture different aspects of participants' experience and status, so their results need not move together.

The interpretation of these secondary outcomes is limited by what the record says about their measurement. Quality of life is reported in units on a scale, but the scale name, range, direction, and meaningful change threshold are not reported in the registry record. The NYHA outcome is presented as numbers of participants, but the exact category or event represented by those counts is not specified. Without those details, the direction and practical meaning of the group contrasts cannot be fully interpreted.

The secondary comparison calculations are unadjusted and the registry record lists no reported analyses. When multiple outcomes and group comparisons are examined, the chance of seeing a nominally unusual result can increase. Whether an adjustment was planned or applied is not reported in the registry record. The secondary results therefore carry less weight than a clearly specified primary analysis and should be treated as exploratory evidence rather than definitive confirmation of the primary finding.

The secondary outcomes may add useful context, but they do not resolve the uncertainty in the primary endpoint. Their different scales and incomplete measurement descriptions make it especially important to avoid treating one nominal result as a substitute for the overall evidence or as a basis for a claim about treatment effectiveness.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Quality of Life
• New York Heart Association (NYHA) Class

9. Statistical Interpretation

10. Statistical Methods Explained

The primary endpoint is continuous, because it is a distance measured in meters. The registry reports an arithmetic mean and standard deviation for each arm. A mean describes the center of the observed group values. A standard deviation describes how spread out individual values are around that mean; it is not itself a confidence interval and does not directly describe the precision of the mean.

What does a mean difference express?

The posted comparisons use ivabradine as the reference. A mean difference is the mean in the comparison group minus the mean in the reference group. A negative estimate therefore means that the comparison group's observed mean distance was lower than the ivabradine mean; a positive estimate would mean it was higher. This description is about the direction of the posted estimates and does not establish a treatment effect.

The confidence interval around a mean difference reflects uncertainty in the estimated contrast. As a general statistical explanation, a confidence interval is constructed by a method that, under its assumptions, would cover the underlying parameter at the stated rate across repeated samples. It is not a probability statement that the particular interval has a specified chance of containing the true effect. An interval that crosses zero includes both no difference and nonzero differences in either direction.

What do the p-values tell the reader?

A p-value measures how incompatible the observed data are with a specified null hypothesis, under the statistical model used. Smaller values indicate greater incompatibility with that null hypothesis, but a p-value does not measure the size or importance of an effect and does not give the probability that the null hypothesis is true. The values posted for the primary comparisons are unadjusted. The registry record does not identify the test used, its model assumptions, or a prespecified significance threshold for the primary analysis.

The comparison estimates, intervals, and p-values are simple unadjusted recalculations from the posted summary statistics. They are not described as an analysis reported by the trial investigators; the registry record lists no reported analyses. The calculations use the available means, standard deviations, and group counts. They do not account for any covariates, repeated measurements, or other design features that are not represented in those summaries.

How should standard deviations and standardized effects be understood?

The pooled standard deviation is a combined measure of variation used in the standardized effect calculation. The reported standardized effect, d, expresses the mean difference in units of pooled standard deviation, rather than in meters. This can help compare effect sizes measured on different scales, but it does not preserve the direct interpretation of a distance difference. The registry record does not report a clinical interpretation threshold for either the raw or standardized primary effect.

As a general point, over-dispersion matters particularly for count outcomes: if the variability is greater than a model expects, standard errors and inference from that model can be misleading. That issue is distinct from the primary continuous endpoint, whose variability is described with standard deviations. The registry record does not report an over-dispersion assessment or a model for the secondary count-based outcome.

What do the planning calculations represent?

The planning illustrations use the observed effect, a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Their rows consider the full observed effect and smaller fractions of that observed effect. For outcomes other than time-to-event outcomes, the figures are participants per arm. The registry's own original design assumptions and sample-size justification are not reported in the registry record, so these calculations should not be confused with the trial's original plan.

As a general statistical principle, a smaller effect is harder to distinguish from random variation when other assumptions are held constant, and therefore requires more participants for a given target power. A planning estimate is conditional on its assumptions, including the effect size used. It cannot repair missing information about the original trial protocol, and it does not establish that an observed comparison is reliable or clinically important.

11. Confidence Intervals and Precision

The primary comparisons have broad confidence intervals relative to their point estimates. For carvedilol versus ivabradine, the estimated mean difference is -39.1 meters and the 95% confidence interval runs from -93.92 to 15.72. For carvedilol and ivabradine versus ivabradine, the estimated mean difference is -21.7 meters and the 95% confidence interval runs from -68.79 to 25.39. Each interval includes zero and allows for values on either side of no difference.

A confidence interval is useful because it presents a range of effect estimates compatible with the data under the calculation's assumptions. It conveys more about precision than a point estimate alone. It does not mean that every value in the interval is equally plausible, nor does it establish a clinically meaningful range. The registry record does not report a threshold for a meaningful difference in walking distance, so the importance of the interval's endpoints cannot be judged against a stated clinical benchmark.

The reported arm counts are 41 for ivabradine, 38 for carvedilol, and 42 for the combination. The standard deviations are 127.3, 121.3, and 87.4 meters, respectively. These group summaries help describe the amount of variation in observed walking distances, but they do not reveal whether the groups differed at baseline or whether the comparison was adjusted for baseline distance. Baseline outcome summaries and an adjusted analysis are not reported in the registry record.

The confidence intervals and p-values are unadjusted recalculations from posted summary data. Their precision should be read in that context: no reported model, missing-data method, or analysis population is available to assess. The intervals quantify sampling uncertainty under the calculation, but they cannot account for unreported sources of bias or differences in trial conduct.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures describe participants per arm for outcomes that are not time-to-event outcomes, including the continuous walking-distance measure. They are not total event counts. Each planning row is tied to a fraction of the observed effect: the full observed effect, 75% of that effect, or 50% of that effect. For instance, planning for the full observed carvedilol contrast gives 160 participants per arm for 80% power and 213 participants per arm for 90% power. For the full observed combination contrast, the corresponding figures are 396 and 530 participants per arm.

The assumptions listed for these illustrations are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. The trial's original sample-size assumptions and justification are not reported in the registry record. These figures are planning illustrations based on the posted observed effects, not a description of the trial's original design.

In plain terms, 80% power is the probability targeted by a design calculation of detecting an effect of the specified size if that effect is present and the assumptions hold. The 90% column uses a higher target probability of detection. A higher target generally requires more participants under the same assumptions. Smaller target effects also require more participants, because they are harder to distinguish from random variation. The posted rows reflect this pattern.

These numbers are planning estimates, not observed power. They do not measure the chance that the trial's result is correct, and they do not change the uncertainty in the primary confidence intervals. Because the calculations depend on observed effects, they should be interpreted cautiously, especially when the original design inputs are unavailable.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -39.100; pooled standard deviation σ = 124.453.
2. n = 2 × (1.96 + 0.842)² × 124.453² / -39.100² = 159.0, rounded up to 160 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -39.1                      # observed difference in means
sigma <- 124.452991699104                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(1178528)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 160 (80% power), 213 (90% power)
 75% of observed effect: n per arm = 283 (80% power), 379 (90% power)
 50% of observed effect: n per arm = 637 (80% power), 852 (90% power)
power.t.test: 160 
Simulated power at n = 160 per arm: 0.796 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

14. Multiplicity, Missing Data and Analysis Populations

The record identifies a primary endpoint and two secondary outcomes, but it does not report a statistical analysis plan describing how the different outcomes or pairwise comparisons were handled. The posted comparison p-values are unadjusted. A multiplicity strategy, such as a prespecified hierarchy or adjustment across comparisons, is not reported in the registry record. Without that information, nominal secondary findings should be interpreted cautiously because examining multiple outcomes can increase the chance of false-positive results.

There are no reported analyses listed in the registry record. It does not state which analysis population was intended, such as all randomized participants or participants with available outcome data. No intention-to-treat, per-protocol, or other population definition is reported. The record also does not describe how participants who discontinued, missed visits, or lacked an endpoint measurement were handled.

Missing-data methods are not reported in the registry record. There is no description of imputation, sensitivity analyses, or assumptions about why measurements might be missing. The posted arm counts give the number associated with each outcome, but do not establish whether any data were missing or how missing observations were treated. A reader therefore cannot determine whether the displayed summaries represent all randomized participants or a subset with recorded measurements.

The registry record also does not report an interim-analysis plan, stopping rules, or a prespecified model for the repeated assessments described for the walking test. These details should not be inferred from the trial's randomized, double-masked, parallel design. Their absence limits evaluation of whether the posted comparisons correspond to the original analysis plan, and it prevents a fuller assessment of multiplicity, attrition, and analysis-population choices.

15. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

The serious adverse event figures report zero affected participants among 41 at risk in the ivabradine group, 38 in the carvedilol group, and 42 in the combination group. The registry also reports zero participants with other, non-serious adverse events in each of those groups. No serious adverse event terms are listed. These are the posted counts for the recorded groups; they do not establish that no adverse events occurred beyond what was captured or entered in the registry.

Deaths are not reported in the registry record: the death counts are listed as unavailable rather than as zero. The record does not provide event descriptions, timing, severity details beyond the serious/non-serious grouping, or information about how events were collected and attributed. The small group counts and absence of further safety detail limit interpretation. Zero recorded events in these groups should not be treated as proof of no risk or as a comparison establishing that one regimen is safer than another.

16. What the Result Does, and Does Not, Mean

The posted primary results describe mean 6-minute walking distances for three randomized groups at 3 months. The observed mean was highest in the ivabradine group, with lower means in the carvedilol and combination groups. However, the unadjusted comparison intervals include zero, and the p-values do not provide clear statistical evidence of a difference from ivabradine. The estimates remain compatible with a range of possible differences in either direction.

This does not establish that the treatments are equivalent or that there is no difference. Equivalence requires an appropriate prespecified margin and analysis, neither of which is reported in the registry record. Nor do the observed means establish that a particular regimen improves or worsens health. They are summaries of one measured outcome in a trial with an enrollment of 121, and the registry does not report a threshold for a clinically important change in walking distance.

The trial's stated aim concerns heart-rate reduction and exercise tolerance in patients with heart failure of ischemic origin. The posted endpoint reflects performance on a standardized walking test; it does not measure every aspect of disease status, daily activity, or quality of life. The secondary results add context, but their measurement details and multiplicity handling are not reported, limiting their interpretability.

The registry record is also incomplete about analysis populations, missing data, baseline outcome values, and the prespecified statistical plan. Those gaps matter because they affect how the comparisons should be understood and how well they represent the randomized groups. The most defensible reading is therefore focused: the posted summary data show no clear statistical separation between ivabradine and either comparator on the primary walking-distance measure, while leaving meaningful uncertainty about the size and direction of any difference. This is a description of the recorded evidence, not medical advice or a recommendation about treatment.

17. Why This Trial Matters Statistically

This trial illustrates why the point estimate, uncertainty interval, and analysis context need to be read together. The observed mean distances differ across the three groups, but the primary comparison intervals cross zero. Looking only at the group means could suggest a simple ordering; the intervals show that the comparative estimates are not precise enough to support a firm conclusion about differences.

It also demonstrates the value of defining the outcome in concrete terms. The primary endpoint is a distance measured during a standardized 6-minute walking test, with specified instructions and supervision. That makes the statistical quantity interpretable as a difference in mean distance, while still leaving open how large a difference would matter clinically. The registry record does not report such a threshold.

The trial has two secondary outcomes that provide different kinds of information, but their measurement descriptions are incomplete and no multiplicity strategy is reported. This highlights a general issue in clinical statistics: nominal evidence across several outcomes can be difficult to weigh when the analysis plan and adjustment approach are unknown. Secondary outcomes can inform interpretation, but they should not automatically outweigh an uncertain primary result.

Finally, the planning illustrations make clear that sample-size calculations depend on an assumed effect size and design assumptions. Estimates based on the observed effect are not the same as the original trial's design justification, which is not reported in the registry record. For researchers, the distinction between planned and observed quantities is essential when interpreting power, precision, and the limits of a completed study.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

Several limitations specific to this record constrain interpretation. The trial enrolled 121 participants across three groups, and the primary outcome counts are 41, 38, and 42. These counts are modest for estimating differences precisely, as reflected in the confidence intervals. The registry record does not report whether the outcome counts include every randomized participant or how any missing measurements were handled.

The record describes a standardized walking assessment but does not provide baseline group means or a baseline-adjusted comparison. It also does not give participant characteristics that would help assess how similar the groups were or how broadly the results might apply. Eligibility criteria beyond the general description of heart failure of ischemic origin are not reported in the registry record.

The statistical analysis plan is not available in the registry record. The analysis model, test, analysis population, multiplicity approach, interim-analysis plans, and missing-data methods are not reported. The comparison calculations are unadjusted recalculations from posted summaries, so they cannot account for unreported covariates or other analysis choices.

The secondary outcomes have incomplete measurement descriptions: the quality-of-life scale is not identified, and the NYHA participant counts are not defined in more detail. Safety reporting lists zero serious and other adverse events, but deaths are not reported and further event details are absent. The original sample-size rationale is also not reported. These gaps mean the posted summaries support a limited statistical reading, rather than a complete evaluation of the trial's methods or outcomes.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Heart Rate Reduction in Heart Failure — NCT01178528.
• Registry record last updated 2014-09-30; status last verified 2014-09.
• Results first posted 2014-09-30.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

NCT01178528, titled “Heart Rate Reduction in Heart Failure,” is recorded as a completed phase 3 randomized, double-masked, parallel-group trial sponsored by IRCCS San Raffaele. Enrollment was 121. The trial compared ivabradine, carvedilol, and their combination in patients with heart failure of ischemic origin.

The primary endpoint was mean distance on the 6-minute walking test at 3 months. The unadjusted comparisons with ivabradine have confidence intervals that include zero, so the posted primary results do not clearly distinguish either comparator from the reference group. Quality of life and NYHA Class were listed as secondary outcomes. Further analysis-plan, missing-data, and multiplicity details are not reported in the registry record.