Beta-Blockers in Heart Failure: Pharmacy-level Intervention Comparison: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Beta-Blockers in Heart Failure: Pharmacy-level Intervention Comparison (NCT01002456), a randomized na study. The primary outcome is Rate of Adherence to Guideline Prescription.

2. Clinical Question

3. Trial Design

This was a completed, randomized, parallel-group pilot study, with allocation described as randomized and masking listed as none. The registry record describes randomization by site in the study summary. The intervention target was the pharmacy, and the two approaches differed in the specificity of information about nonadherence: Level 1 was site-specific, while Level 2 was site- and patient-specific.

The study’s overall objective was to begin evaluating methods for promoting adherence to guideline beta-blocker therapy in heart failure. Its summary describes site-level baseline measurement, feedback, remeasurement after six months, and randomized comparison samples. The primary outcome timeframe is also listed as 6 months. The record gives an enrollment of 220 and arm counts of 98 for Level 1 and 122 for Level 2.

The registry lists the study as starting in 2009-10, with primary completion in 2011-06 and status completed. Phase is listed as NA. The sponsor is the US Department of Veterans Affairs. The record does not report the number of sites, how sites were assigned, whether any clustering was accounted for in the analysis, or whether participants and staff received any masking beyond the listed none.

Because the unit of randomization is described as the site, interpretation of the participant-level counts depends in part on the analysis accounting for the site-level design. The registry record does not report the statistical method used for the sponsor’s analysis or explain how site clustering was handled. It also does not report the original protocol’s sample-size rationale or the number of sites contributing data.

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 Rate of Adherence to Guideline Prescription, measured over 6 months.

The primary endpoint is the rate of adherence to guideline prescription, defined in the registry description as full adherence to the guideline medication and dose. Its unit is patients, and the posted measure is a count of patients meeting that definition at 6 months. It therefore represents whether a patient was fully adherent according to the specified prescription criterion, rather than a continuous measure of how much medication was taken or a measure of a clinical event.

Adherence is relevant to the stated purpose of the pilot because the interventions were intended to promote adherence to guideline beta-blocker therapy. A count-based endpoint can describe how many participants in each arm met the stated criterion. Comparing the arms can then estimate how the two information approaches differed on that outcome in the enrolled study population.

The endpoint’s interpretation depends on the exact assessment process: how prescriptions and adherence were determined, how missing or incomplete information was handled, and whether assessment was consistent across sites. Those details are not reported in the registry record. The endpoint also does not, by itself, establish that a patient experienced a particular health benefit or that any change in adherence was caused only by the intervention.

7. Results Posted in the Registry

• Level 2: 4.9% (6/122) versus 4.1% (4/98) on control; risk difference 0.8 percentage points (95% CI -4.6 to 6.3), risk ratio 1.20 (0.35–4.15); unadjusted two-proportion z-test p = 0.767.

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.

Progress Toward Adherence to Guideline Prescription

• 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:
  • Level 2:Provide Site- and Patient-specific Information: 18.0% (22/122) versus 10.2% (10/98) on control; risk difference 7.8 percentage points (95% CI -1.3 to 16.9), risk ratio 1.77 (0.88–3.55); unadjusted two-proportion z-test p = 0.102.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Level 2:Provide Site- and Patient-specific Information and the control. The interval gives the range of effects that remain compatible with the data.

The registry posts one secondary endpoint, progress toward adherence to guideline prescription. The numerical direction favors Level 2 over Level 1, but the unadjusted comparison remains uncertain because its interval includes no difference. The secondary endpoint is related to the primary adherence question but is not the same outcome: the primary endpoint requires full adherence to the guideline medication and dose, whereas the secondary endpoint describes progress toward adherence.

Considering both outcomes, the posted pattern is numerically more favorable for Level 2, but it does not provide a clear, consistent inferential basis for concluding that the approaches differ. The primary endpoint is the main stated outcome, and the secondary result should not replace it or be used to resolve the uncertainty in its comparison. The registry record does not report whether the secondary outcome was prespecified in the protocol or how it was assessed.

Unadjusted secondary results generally carry less weight when multiple outcomes are examined because the chance of at least one apparently notable result can increase as more comparisons are considered. This is a general statistical concern, not evidence that a particular result in this study is spurious. The registry reports two outcome measures and one posted secondary endpoint, but does not report a multiplicity strategy or adjustment. Accordingly, the secondary finding is best treated as supportive descriptive context rather than independent confirmation of the primary result.

The registry record also does not report whether these endpoints were analyzed in the same population, whether site clustering was accounted for, or how missing observations were handled. Those details affect how much confidence can be placed in comparisons across outcomes. The overall interpretation remains exploratory: the two endpoint patterns do not eliminate the uncertainty in the primary estimate or establish a causal explanation for any observed differences.

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

• Progress Toward Adherence to Guideline Prescription

9. Statistical Interpretation

10. Statistical Methods Explained

What does a risk difference describe?

A risk difference compares the proportion of participants with the binary outcome in one arm with the proportion in the other. In this trial, the outcome is full adherence to the guideline medication and dose by 6 months. A positive difference for Level 2 relative to Level 1 indicates a higher observed event proportion in Level 2; a negative difference indicates a lower observed proportion. A value near zero indicates little observed separation on this scale. The recalculated risk difference is an unadjusted comparison based on the posted arm counts, not necessarily the sponsor’s chosen analysis.

Why use an interval as well as a point estimate?

A point estimate gives one value for the contrast, but it does not show how uncertain that estimate is. A confidence interval gives a range of values compatible with the data and the method used, under the method’s assumptions. If an interval for a risk difference includes zero, the data do not clearly distinguish a positive difference from no difference or a negative difference at the interval’s stated confidence level. An interval should not be interpreted as assigning a probability to the true value after the data are observed.

How do odds ratios differ?

An odds ratio compares odds rather than proportions. It is not the same quantity as a risk difference, and the numerical values cannot be compared directly across those scales. Its interpretation also depends on which arm is in the numerator and how the outcome is coded. The registry reports an odds ratio for the two groups, but does not report the method or coding details. The reported estimate and interval should therefore be interpreted as the sponsor’s analysis, not assumed to be a direct restatement of the recalculated risk difference.

What does the p-value contribute?

A p-value describes how compatible the observed data are with a specified null hypothesis under a statistical model. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of a difference. The unadjusted p-value from the posted primary counts is 0.767. It does not, by itself, establish equivalence between the approaches. A conclusion of equivalence would require a prespecified margin and an analysis designed for that question; neither is reported in the registry record.

Why can event counts affect inference?

For a binary endpoint, the number of events and the number of participants in each group both affect precision. When only a small number of participants meet the endpoint, each observation can have a relatively large influence on the estimated contrast. This can lead to wide intervals and unstable estimates. It also makes the exact statistical method more consequential, especially if the randomization unit differs from the unit at which the outcome is counted.

Here the study summary describes randomization by site, while the primary outcome is recorded as a patient count. In a site-randomized design, participants within the same site may share features. If that similarity is present, treating every participant as statistically independent can understate uncertainty. A site-adjusted or cluster-aware analysis may be appropriate in general, but the method used by the sponsor and any allowance for site clustering are not reported in the registry record. The recalculated comparison is explicitly a simple unadjusted calculation from the posted summary counts and should not be mistaken for a reconstruction of the sponsor’s analysis.

The registry’s sponsor-reported odds ratio has a 95% confidence interval, but the statistical model, covariates, site handling, and analysis population are not described. Without those details, it is not possible to determine whether its difference from the recalculated result arises from adjustment, the handling of clustering, a different population, or another analytical choice. Those are possible general sources of variation between analyses, not claims about what this study did.

Finally, a pilot outcome comparison is best understood as descriptive and exploratory when its planning and analysis details are unavailable. The registry record does not report an interim-analysis plan, a full statistical analysis plan, or a sample-size justification for the original study. The posted results still describe what was observed, but the design and reporting limitations matter when judging inferential strength.

11. Confidence Intervals and Precision

The recalculated primary risk-difference interval extends from a negative value to a positive value, so it includes no difference as well as effects in either direction. Its breadth indicates that the posted counts do not pin down the primary contrast precisely. The unadjusted p-value is 0.767, which is consistent with the absence of a clear separation under that calculation. Neither result proves that the approaches are equivalent; the interval also allows a range of potentially different effects.

The sponsor-reported odds ratio is 1.9, with a 95% confidence interval from 1.1 to 3.2. That interval is reported on the odds-ratio scale and should not be read as if it were the interval for the risk difference. The registry record does not state the analysis method or the direction in which the odds ratio was formed. The reported interval and the interval recalculated from counts therefore need to remain distinct unless further analytical details are available.

Precision is affected by the number of observed endpoint events, the arm sizes, and the design. The primary counts include few participants meeting the endpoint. Also, the study summary says sites were randomized, which can affect uncertainty if participants within a site are correlated. The registry record does not say whether the sponsor’s analysis accounted for this design feature.

Confidence intervals describe uncertainty under their respective analysis methods; they do not capture every source of uncertainty. In particular, they do not resolve concerns about outcome measurement, missing data, analysis populations, or whether the reported model reflects the randomized design. The registry record does not report those details. The safest reading is therefore to recognize both the imprecision of the unadjusted count-based contrast and the limits on interpreting the sponsor’s model-based result.

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 are expressed as participants per arm for this binary outcome, not as a total number of events. They are illustrations based on the observed effect and use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is varied as 100%, 75%, or 50% of the observed effect. These are planning assumptions for the illustration, not reported assumptions for the original trial design.

The 80% power column gives the estimated participants per arm under those assumptions for a design with an 80% chance of detecting the specified effect if that effect is the true one and the model assumptions hold. The 90% power column gives the corresponding requirement for a higher chance of detection under the same assumptions. Power is a design property calculated before observing study results; it is not a measure of whether the study result is true.

For the primary outcome, the displayed requirements increase as the target effect is reduced from the full observed effect to smaller fractions. The same pattern applies to the secondary endpoint. Smaller effects are harder to distinguish from random variation, so more participants are needed to detect them at the same nominal power and significance level. The estimates also assume equal allocation, even though the posted arm sizes differ.

These calculations are planning illustrations, not observed power. The registry record does not report the original sample-size justification, its assumptions, or a prospective target for the trial. The illustration should therefore not be used to claim that the completed study was adequately or inadequately powered according to its original plan.

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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.041; treatment proportion p₁ = 0.049; average p̄ = 0.045.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.2932 = 0.5746.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.2931 = 0.2467.
4. n = (0.5746 + 0.2467)² / (0.0084)² = 9,641.8, rounded up to 9,642 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
p0 <- 0.0408163265306122                          # control proportion
p1 <- 0.0491803278688525                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(1002456)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 9,642 (80% power), 12,908 (90% power)
 75% of observed effect: n per arm = 16,762 (80% power), 22,439 (90% power)
 50% of observed effect: n per arm = 36,859 (80% power), 49,343 (90% power)
power.prop.test: 9641.8 
Simulated power at n = 9,642 per arm: 0.802 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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. Analyses Reported by the Sponsor

The registry reports the sponsor’s primary analysis as an odds ratio of 1.9, with a 95% confidence interval from 1.1 to 3.2. The registry record does not give a p-value for that analysis or state its statistical method. It also does not specify the direction of the odds-ratio coding, adjustment variables, analysis population, or how the site-randomized design was handled.

The simple recalculation from the posted primary counts is an unadjusted risk-difference analysis. Its interval includes zero, and its unadjusted p-value is 0.767. This is not the same estimand or scale as an odds ratio, and the recalculation does not reproduce a model-based sponsor analysis. The two summaries therefore should not be treated as interchangeable.

The registry record does not flag a discrepancy. Even so, the available methods information is insufficient to explain why the sponsor-reported estimate and the simple count-based recalculation give different statistical impressions. If an explicit discrepancy between sponsor and recalculated results were identified, the sponsor’s own analysis would take precedence. Any interpretation of the sponsor result should remain conditional on the missing model and coding details, while the unadjusted recalculation should be understood as a transparent comparison based only on the posted counts.

15. Multiplicity, Missing Data and Analysis Populations

The registry identifies a primary endpoint and posts one secondary endpoint. Testing more than one outcome can increase the chance of at least one result appearing notable by chance. Statistical plans sometimes address this through a hierarchy of outcomes, adjusted significance thresholds, or other prespecified procedures. The registry record does not report whether any such multiplicity approach was planned or used. The unadjusted secondary comparison should therefore be interpreted cautiously, and the absence of a reported adjustment should not be taken to mean that none was used.

The registry record does not describe missing-data handling for either endpoint. It does not state whether every randomized participant contributed an outcome, how unavailable adherence information was classified, or whether any imputation or sensitivity analyses were performed. The posted arm counts and event counts alone do not establish how missing observations were treated.

The analysis populations are also not reported in sufficient detail. The record does not specify whether the results follow an intention-to-treat population, a per-protocol population, or another defined group. Without that information, it is difficult to assess whether the analysis preserves the randomized comparison or how exclusions may have affected the estimate.

Randomization is described as occurring by site, but the sponsor’s statistical method and its handling of site-level clustering are not reported. That is an important design feature because the endpoint is counted for patients. In general, clustered data can require methods that account for similarities within sites to obtain appropriate uncertainty estimates. The record also does not report a full statistical analysis plan, interim analyses, or the original sample-size justification. These unreported items limit evaluation of whether the posted analyses followed prespecified procedures.

16. 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 0% reporting threshold.

The registry lists 98 participants at risk for serious adverse events in Level 1 and 122 in Level 2. It records 0 affected in each group. For other adverse events, the same at-risk counts are listed, with 0 affected in both groups. These entries describe what the registry record reports for the specified groups.

Deaths are not reported in the record. The zero entries should be read as zero events recorded in these fields, not as proof that no adverse experiences occurred or that the interventions are free of risk. The registry does not provide a list of adverse-event terms or additional safety detail, and no serious-event terms are listed.

Because this is a pilot focused on adherence, the adverse-event entries do not provide a broad safety evaluation of beta-blocker therapy or of the information interventions. They are limited to the registry’s reported counts and do not establish whether event collection was complete or how events were assessed.

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

The posted data describe a pilot comparison of two pharmacy-directed information approaches for promoting adherence to guideline beta-blocker prescriptions in heart failure. The primary outcome is full adherence to the guideline medication and dose at 6 months. The primary count-based recalculation gives an uncertain comparison, with an interval spanning no difference and an unadjusted p-value of 0.767.

The registry also reports a sponsor odds ratio with a confidence interval that does not include the null value for an odds ratio. However, the statistical method, coding direction, and handling of site randomization are not reported. That result should be distinguished from the simple unadjusted recalculation rather than combined with it as though both analyses estimated the same quantity by the same method.

The results do not establish that the two approaches are equivalent. Nor do they establish that either approach changes clinical outcomes, improves health, or is effective across other settings. The trial’s stated outcome concerns adherence, and the registry record does not report clinical event results as the primary question. The study is described as a pilot intended to begin evaluation of adherence-promotion methods, which is a limited basis for broad conclusions.

The secondary endpoint’s numerical direction is consistent with the primary comparison’s general pattern, but its uncertainty and the unreported multiplicity plan mean it should not be treated as definitive confirmation. Missing-data handling, analysis populations, site-adjusted methods, and the original design assumptions are also not reported. These limits make the record useful for understanding the observed comparison while leaving important questions about precision and analysis unresolved.

18. Why This Trial Matters Statistically

Statistically, this trial highlights the distinction between a randomized design and the details needed to interpret its estimates. The study summary describes randomization by site, while outcomes are reported as patient counts. Whether the analysis accounts for the site-level assignment can influence uncertainty, but the registry record does not report the sponsor’s method or its treatment of clustering.

It also illustrates why an endpoint definition matters. Full adherence to a guideline medication and dose is a specific binary outcome, distinct from progress toward adherence and from clinical outcomes. The primary count-based comparison is imprecise, while the sponsor’s reported odds ratio carries limited method detail. Readers must keep outcome scale, analysis method, and uncertainty together rather than relying on a single estimate.

The pilot framing is also important. A pilot can contribute information about how an intervention comparison is organized and what outcomes are recorded, but the registry’s original sample-size rationale and analysis plan are not reported. Planning illustrations based on observed effects cannot substitute for those original design details.

Finally, the record shows how incomplete reporting affects reproducibility. Details on missing observations, analysis populations, multiplicity, and site handling would help readers evaluate the primary and secondary comparisons. Their absence does not erase the posted data, but it limits how confidently those data can be interpreted beyond the descriptive comparison.

19. 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.

The most consequential trial-specific limitation is the combination of site-level randomization and patient-level outcome counts without a reported statistical method. If the analysis did not account for similarities among participants within sites, uncertainty could be misrepresented; the registry record does not say whether such adjustment was made. The number of sites is also not reported, limiting assessment of the design.

The primary event counts are small, which contributes to uncertainty and makes the estimate sensitive to individual observations. The unadjusted recalculation does not incorporate covariates or site structure. The sponsor’s odds-ratio analysis has a reported estimate and interval, but its method, coding direction, adjustment, and analysis population are not described, so it cannot be fully reproduced from the registry entry.

Outcome assessment details are limited. The registry defines full adherence but does not explain how adherence was measured, who assessed it, or how inconsistent or unavailable records were handled. Missing-data procedures and analysis populations are not reported. The record also does not describe whether the secondary endpoint or the analysis strategy was prespecified.

The study is identified as a pilot, and the record does not report its original sample-size justification or statistical analysis plan. The posted planning illustrations use observed effects and should not be interpreted as evidence about the study’s original design adequacy. The trial also lists no masking. The potential for assessment or implementation differences is difficult to evaluate because the operational details of the interventions and outcome measurement are not reported.

These limitations restrict precision, reproducibility, and generalization. They do not mean the observed counts are invalid, but they require cautious interpretation of the contrast and its statistical strength.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Beta-Blockers in Heart Failure: Pharmacy-level Intervention Comparison — NCT01002456.
• Registry record last updated 2015-04-28; status last verified 2014-09.
• Results first posted 2014-10-15.
• 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.

23. Record Summary

The registry record describes a completed randomized, parallel pilot study sponsored by the US Department of Veterans Affairs. It compared site-specific information about nonadherence with site- and patient-specific information, with the intervention directed at pharmacies in a VA setting. The primary endpoint was the number of patients fully adherent to the guideline medication and dose at 6 months.

The posted primary counts support an imprecise unadjusted comparison, while the registry also reports a sponsor odds ratio whose method is not described. One secondary endpoint concerns progress toward adherence. The record lists zero serious and other adverse events in both groups, while deaths are not reported.

Important details about the analysis plan, missing data, analysis populations, multiplicity, and handling of site-level randomization are not reported in the registry record. The findings are best read as pilot evidence describing the recorded adherence comparison, with substantial limits on reconstructing and generalizing the analyses.