Comparison of Nebivolol and Metoprolol With Exercise and Angiotensin II in Hypertensive Patients: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Comparison of Nebivolol and Metoprolol With Exercise and Angiotensin II in Hypertensive Patients (NCT01502787), a randomized phase 4 study. The primary outcome is Forearm Blood Flow.

2. Clinical Question

The trial's stated rationale concerned potential differences in vasoconstriction responses, oxidative stress, and sympathetic activity. Those are proposed physiological pathways, not outcomes that can be treated as established findings from the primary endpoint. The posted results focus on forearm blood flow and blood pressure. They do not report a direct outcome for oxidative stress, nor do they report a clinical event outcome. Accordingly, the clinical question answered by these results is narrow: how the recorded physiological measures compare after the medication periods, and how uncertain those comparisons are.

3. Trial Design

The registry describes a completed randomized, unmasked, phase 4 crossover study of nebivolol and metoprolol in hypertensive patients. Enrollment was 46. In a crossover design, participants receive more than one intervention in different periods, so each participant may contribute measurements under both treatments. This structure can support within-participant comparisons, but correct analysis depends on details such as treatment sequence, period effects, and the association between measurements from the same person.

The arm descriptions say that participants began treatment with metoprolol succinate or nebivolol and continued the specified medication for 12 weeks before study procedures. The posted primary outcome labels describe a first intervention with metoprolol at 12 weeks and a second intervention with nebivolol at 24 weeks. The record does not report enough detail to reconstruct treatment sequences, washout periods, or the timing and handling of all measurements. Those details are not reported in the registry record.

Procedures listed include forearm blood flow measurement, microneurography, rhythmic handgrip exercise, lower body negative pressure, and angiotensin II administration. The secondary outcomes listed are blood pressure during exercise and blood pressure during angiotensin II infusion. The primary endpoint is forearm blood flow. The record identifies no masking, so participants and investigators were not reported as blinded.

The registry lists mean results for the outcome groups and comparison estimates, but no reported analyses for the secondary outcomes. The analysis population, handling of missing measurements, statistical model for the crossover, and any adjustment for treatment period or sequence are not reported in the registry record. The original sample-size justification and the trial's planned statistical analysis are also not reported. Therefore, the posted group summaries can be described, but the degree to which they represent a planned crossover analysis cannot be confirmed from the record.

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 Forearm Blood Flow, measured over 12 weeks after each specified medication.

Forearm blood flow is a continuous physiological measure, recorded in ml/min. The primary endpoint is listed as the mean measurement at 12 weeks after each specified medication. Blood flow provides a quantitative way to assess vascular responses in the forearm during the study procedures. In this trial's stated rationale, the investigators were interested in how the medications might relate to vasoconstriction during exercise and during angiotensin II exposure.

Using a continuous outcome preserves more information about the measured response than reducing it to categories such as high or low. Reporting a mean describes the average value in each intervention group, while a measure of dispersion describes variability among observations. The registry identifies standard deviation as the dispersion measure for the primary outcome. Mean differences are interpretable in the original measurement unit, so the estimate can be read as a difference in ml/min between the two labeled intervention results.

The endpoint is a physiological surrogate, not a direct measure of symptoms, functional ability, or clinical events. It can address the recorded blood-flow response but does not, by itself, establish effects on broader health outcomes. The posted summaries also do not explain how repeated measurements from the crossover were analyzed. That matters because the statistical precision of a within-person treatment comparison can depend on how strongly paired measurements are related. This relationship is not reported in the registry record.

7. Results Posted in the Registry

• Second Intervention Nebivolol: 24 Weeks: mean 105.00 versus 96.00 on control; difference 9.00 (95% CI 3.42 to 14.58), standardized effect d = 0.98; z-test p = 0.002.

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.

Blood Pressure During Exercise

• 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 errors.
• Result:
  • Initial Treatment With Nebivolol: mean 103.00 versus 101.00 on control; difference 2.00 (95% CI -6.32 to 10.32), standardized effect d = 0.15; z-test p = 0.637.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Initial Treatment With Nebivolol and the control. The interval gives the range of effects that remain compatible with the data.

Blood Pressure During Angiotensin II Infusion

• 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 errors.
• Result:
  • Nebivolol: mean 113.00 versus 114.00 on control; difference -1.00 (95% CI -9.32 to 7.32), standardized effect d = -0.07; z-test p = 0.814.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Nebivolol and the control. The interval gives the range of effects that remain compatible with the data.

The secondary outcomes concern blood pressure during exercise and during angiotensin II infusion. Across these outcomes, the posted mean differences are small relative to their uncertainty, and both confidence intervals include zero. The corresponding unadjusted p-values do not indicate a clear difference in the posted comparisons. This pattern does not provide an obvious blood-pressure counterpart to the positive primary forearm blood-flow estimate.

Blood pressure and forearm blood flow are related physiological measures but are not interchangeable endpoints. A result for one does not require a matching result for the other, and the secondary comparisons do not directly confirm or refute the primary blood-flow estimate. They address different responses under different conditions. The registry record does not report a combined analysis linking the blood-pressure outcomes to the primary endpoint.

The secondary outcomes carry less inferential weight because the record does not report whether they were prespecified as confirmatory tests, how multiplicity was handled, or the analysis population and model. The listed secondary analyses are not accompanied by reported analyses in the registry record. Their summary comparisons should therefore be treated as descriptive and exploratory. A confidence interval that includes zero does not demonstrate that the treatments are equivalent; no equivalence margin or equivalence design is reported.

There are two posted secondary outcome categories, but the registry record does not say whether additional analyses were conducted or whether results were withheld. Without a stated hierarchy of hypotheses, a multiplicity procedure, and details of the crossover model, the secondary results cannot establish a broad pattern of treatment effects. They provide context for the primary result, while remaining limited by uncertainty about precision and analysis choices.

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

• Blood Pressure During Exercise
• Blood Pressure During Angiotensin II Infusion

9. Statistical Interpretation

10. Statistical Methods Explained

What does a mean difference represent?

A mean is the arithmetic average of the recorded measurements in a group. A mean difference expresses the contrast between two group means in the original measurement unit. For the primary outcome, that unit is ml/min. The posted estimate is 9.0 ml/min in the direction of the nebivolol-labeled intervention relative to the metoprolol-labeled intervention. The estimate describes the observed summaries; its causal interpretation depends on the design and analysis being appropriate.

For a crossover study, a treatment contrast is usually based on each participant's measurements under both treatments, rather than on unrelated groups. The advantage is that stable differences between participants can be controlled through within-participant comparison. The analysis then needs to account for the pairing and may also need to consider period and sequence. The registry record identifies a crossover design but does not report the model or the analysis details. No paired estimates or participant-level data are reported.

What does the confidence interval communicate?

In general, a confidence interval describes the range of estimates reasonably compatible with the observed data under a specified statistical procedure and its assumptions. It communicates precision as well as direction: a narrower interval indicates greater precision than a wider interval, all else equal. A confidence interval does not assign a probability that the true effect lies inside the particular interval after it has been calculated. Its interpretation relies on the method used to construct it.

The primary 95% confidence interval runs from 3.423 to 14.58 ml/min. It lies on the positive side of zero for the stated direction of comparison. The posted interval is unadjusted. Since the record does not specify how the crossover was modeled, readers cannot verify whether its calculation accounts for within-participant dependence, treatment period, or sequence. The interval should therefore be interpreted alongside that limitation.

How should the p-value be understood?

In general, a p-value measures how incompatible the observed data, or more extreme data, are with a specified null hypothesis under the statistical model. It is not the probability that the null hypothesis is true, and it is not a measure of clinical importance. The primary comparison has an unadjusted p-value of 0.002. The registry record does not report a planned testing hierarchy, multiplicity adjustment, or a complete analysis plan, so this p-value should not be treated as evidence that all design and analysis choices were prespecified.

The secondary p-values are also unadjusted. When several outcomes are examined, the chance of at least one apparently unusual result can increase if each is tested separately without accounting for the set of tests. This is one reason secondary outcomes without a reported multiplicity approach warrant less weight than a clearly prespecified primary analysis. The record does not report whether other outcomes or analyses were considered but not posted.

Why does variability matter?

Dispersion describes how spread out measurements are around the group mean. The primary outcome identifies standard deviation as its dispersion measure, while the secondary blood-pressure outcomes identify standard error. Standard deviation describes variability among individual observations. Standard error describes uncertainty in an estimated mean and depends on both variability and the number of observations. They are not interchangeable, so the reported spread should be interpreted according to the measure named for each outcome.

In general, a standard error is useful for describing how precisely a sample mean estimates a population mean, whereas standard deviation helps describe the observed distribution of participant measurements. A standard error is not a direct description of how different participants' measurements are from one another. The record does not provide distributions, missingness details, or participant-level observations that would allow further checks of the means or their assumptions.

What is not established by recalculation?

Simple unadjusted calculations from posted summary statistics can describe a contrast and support planning illustrations, but they cannot recreate a trial's intended analysis when important design details are absent. The registry record does not report the original statistical model, the crossover pairing, or the treatment-period structure needed to evaluate a paired treatment effect. It also does not report an original sample-size justification, interim analyses, or a statistical analysis plan. Those details are not reported in the registry record.

In general, an analysis can be affected by missing measurements, departures from distributional assumptions, and period or sequence effects. These considerations are particularly relevant in crossover designs. No specific issue should be assumed to have occurred, but the record does not describe how these possibilities were handled. The reported comparison is therefore informative as a summary of the posted values, while its design-based inferential interpretation remains limited by missing analysis details.

11. Confidence Intervals and Precision

The primary mean difference is 9.0 ml/min, and its 95% confidence interval extends from 3.423 to 14.58 ml/min. This interval expresses uncertainty around the estimated difference under the calculation used. It is entirely above zero, while its width indicates that the data remain compatible with a range of possible positive differences. A confidence interval does not show whether any difference within that range is clinically important; the registry record does not report a threshold for clinical importance.

Precision depends on both the amount of information and the analysis model. The primary outcome entries report 21 participants for each labeled intervention, but the record does not explain the crossover pairing or the number of complete paired measurements. In a crossover analysis, the correlation between each participant's measurements under the two treatments can materially affect the standard error. That correlation is not reported in the registry record. Therefore, the posted interval should not be assumed to capture the precision of a paired analysis unless the method is confirmed.

The p-value of 0.002 accompanies the posted primary comparison, but it is unadjusted. It does not replace the interval or resolve uncertainty about model choice, clinical relevance, or multiplicity. The secondary blood-pressure intervals are wider relative to their point estimates and include zero. Those estimates are correspondingly compatible with effects in either direction under the posted calculations. Their lack of precision is distinct from evidence of equivalence: the record does not report a prespecified equivalence margin or an equivalence analysis.

Overall, the primary result has a positive estimated difference and an interval excluding zero under the calculation reported, but the uncertainty in its analysis framework remains important. The record does not report the underlying participant-level data, the crossover-adjusted method, or the original statistical plan, so precision should be understood conditionally on the posted calculation rather than as a complete account of the trial's design-based uncertainty.

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 participants per arm, not total events. They are illustrations based on the observed effect, not the original trial design. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses the stated fraction of the observed effect as the effect to detect. The registry's original sample-size assumptions and justification are not reported in the registry record.

The 80% power column describes the number of participants per arm that the planning calculation estimates would give an 80% chance of detecting the specified effect under those assumptions, if that effect were the true one. The 90% power column gives the corresponding planning figure for a 90% chance. These are design-planning probabilities under a model, not probabilities that the trial result is correct. They are not observed power.

The rows for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect use progressively smaller effects as planning targets. Smaller effects are harder to distinguish from random variation, so the calculations require more participants per arm. These figures are not a retrospective statement about what the trial achieved and do not account for crossover pairing, period effects, missing outcomes, or any other factor not included in the stated planning assumptions. Interpret them as conditional illustrations rather than a recommendation for a future study.

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 = 9.000; pooled standard deviation σ = 9.220.
2. n = 2 × (1.96 + 0.842)² × 9.220² / 9.000² = 16.5, rounded up to 17 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 <- 9                      # observed difference in means
sigma <- 9.21954445729289                     # 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(1502787)
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 = 17 (80% power), 23 (90% power)
 75% of observed effect: n per arm = 30 (80% power), 40 (90% power)
 50% of observed effect: n per arm = 66 (80% power), 89 (90% power)
power.t.test: 17.5 
Simulated power at n = 17 per arm: 0.787 (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 registry record does not report a multiplicity plan describing how inference was to be handled across the primary and secondary outcomes, or across any additional comparisons. The primary comparison has an unadjusted p-value, and the secondary comparisons are also unadjusted. When many hypotheses are examined, interpreting each p-value separately can overstate the strength of evidence because chance findings become more likely across a collection of tests. Without a reported testing hierarchy or correction, the secondary results are best regarded as exploratory, and the primary p-value should not be read as if the wider set of analyses were irrelevant.

Missing-data handling is not reported in the registry record. The outcome summaries give group counts, but they do not explain whether all randomized participants contributed data, whether measurements were unavailable, or how missing measurements were handled. The analysis population is also not reported: the record does not identify whether analyses followed an intention-to-treat principle, included only participants who completed both periods, or used another population definition.

These omissions matter particularly for a crossover design. The record does not report how incomplete treatment sequences, treatment-period effects, sequence effects, or within-participant correlation were addressed. It also does not report a protocol-level statistical analysis plan, interim analyses, or the original sample-size justification. No particular missing-data problem or analytical departure can be inferred from these omissions; rather, the registry record does not provide the information needed to assess them.

As a result, the posted estimates remain useful descriptions, but their confirmatory status and robustness cannot be fully evaluated. The reported summary should be interpreted with the stated uncertainty about multiplicity, analysis populations, missingness, and crossover methods in mind.

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 0% reporting threshold.

The posted adverse-event figures list 21 participants at risk for serious adverse events in the metoprolol group and 21 in the nebivolol group. The serious adverse-event count is 0 in each group. The figures also list 21 participants at risk for other adverse events in each group, with 0 recorded in each group. These are the event counts reported in the registry record, not proof that no events occurred outside the recorded follow-up or reporting process.

Deaths are listed as null for both groups, so a death count is not reported in the registry record. No serious adverse-event terms are listed. The record does not provide further detail on event definitions, collection procedures, duration of safety observation, or completeness of reporting. The figures should therefore be read narrowly as the posted counts, not as a comprehensive estimate of risk or a comparison establishing that the interventions have equivalent safety.

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

The posted primary comparison reports higher mean forearm blood flow for the nebivolol-labeled intervention than for the metoprolol-labeled intervention, with a mean difference of 9.0 ml/min and a 95% confidence interval from 3.423 to 14.58. The interval and unadjusted p-value describe the result under the calculation used. They do not establish a clinically meaningful benefit, because the registry record does not report a threshold for meaningful change or a patient-centered outcome linked to this measure.

The study addresses physiological responses in hypertensive patients after specified medication periods. Its listed procedures and outcomes concern forearm blood flow and blood pressure during exercise or angiotensin II infusion. The result does not establish effects on symptoms, long-term health, cardiovascular events, or other outcomes not reported in the registry record. Nor does it prove the proposed mechanisms involving oxidative stress or sympathetic activity; those mechanisms appear in the study rationale, not as confirmed findings in the posted results.

The crossover design could allow direct within-person comparisons, but the registry record does not describe the analysis needed to verify that this was done or explain how treatment period and sequence were handled. The posted inferential result should therefore be interpreted cautiously. An interval excluding zero under the posted calculation is not a substitute for knowing whether the method matched the design.

The secondary blood-pressure comparisons do not show a clear difference under their unadjusted calculations, but they do not prove equivalence. The adverse-event entries show zero recorded serious and other adverse events in the listed groups, while death counts are not reported. These summaries are not sufficient to establish the absence of risk. Overall, the results describe a physiological comparison with limitations in analysis reporting; they do not warrant a broad conclusion about clinical effectiveness or safety.

17. Why This Trial Matters Statistically

This trial is statistically instructive because its registry identifies a randomized crossover design while presenting intervention-group summaries and comparison estimates without describing the crossover analysis. In crossover studies, the central statistical feature is the pairing of observations within participants. Accounting for that pairing can change uncertainty estimates, so the analysis method is essential to interpreting a confidence interval and p-value.

The posted primary comparison is also an example of why estimates should be read together with precision and design context. The mean difference and its confidence interval communicate direction and uncertainty, while the p-value alone cannot show clinical importance or establish that the analysis respects the design. The absence of a reported threshold for meaningful change further limits interpretation of the endpoint's practical importance.

The secondary outcomes illustrate another common issue: unadjusted comparisons across multiple outcomes can be difficult to interpret without a prespecified hierarchy or multiplicity approach. The results may be useful descriptively, but their evidential weight depends on decisions that are not reported in the registry record. The planning illustrations likewise show how assumed effect size affects required sample size, but they are not evidence about the trial's actual design adequacy or observed power.

More broadly, the record demonstrates the value of complete reporting of analysis populations, missing-data procedures, period and sequence handling, and statistical plans. Without those details, even clearly stated summary values cannot answer every design-based question. The trial's statistical contribution in the posted record is therefore best understood as a set of physiological outcome summaries whose interpretation depends on important methodological details that are not reported.

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 are specific to interpreting this trial's posted results. The registry identifies a crossover design, but the primary comparison is not accompanied by a description of whether the estimate was obtained from paired participant measurements. The record does not report treatment sequence, washout details, period effects, or how incomplete crossover participation was handled. These omissions prevent evaluation of whether the reported uncertainty reflects the design.

The primary result labels identify a first metoprolol intervention at 12 weeks and a second nebivolol intervention at 24 weeks, while the endpoint timeframe is described as 12 weeks after each specified medication. The record does not explain all timing details or how the treatment periods map to the reported values. The arm descriptions include medication durations, but do not provide the full sequence and analysis information needed to resolve these questions.

The posted record also lacks a reported analysis population, missing-data method, statistical analysis plan, and original sample-size justification. The p-values are unadjusted, and no multiplicity approach is reported. Secondary analyses are not listed as reported analyses. The counts do not show whether all randomized participants contributed complete outcome data.

Finally, the primary outcome is a physiological measure, and the record does not report a threshold for clinically meaningful change or a direct clinical outcome. Safety reporting gives zero recorded events in the listed categories but does not provide detail on ascertainment or observation. These limitations do not show that the study was conducted improperly; they define what can and cannot be evaluated from the registry record.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Comparison of Nebivolol and Metoprolol With Exercise and Angiotensin II in Hypertensive Patients — NCT01502787.
• Registry record last updated 2020-07-07; status last verified 2020-07.
• Results first posted 2014-12-31.
• 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

The registry record describes a completed randomized, unmasked, phase 4 crossover study of nebivolol and metoprolol in hypertensive patients, with enrollment of 46. The primary endpoint is mean forearm blood flow in ml/min at 12 weeks after each specified medication. The posted primary comparison reports a mean difference of 9.0 ml/min, with a 95% confidence interval from 3.423 to 14.58 and an unadjusted p-value of 0.002.

Secondary outcomes cover blood pressure during exercise and during angiotensin II infusion. Their posted comparisons are unadjusted, and no reported secondary analyses are listed. The record does not report the crossover analysis method, analysis population, missing-data handling, multiplicity plan, or original sample-size assumptions. Posted adverse-event counts list zero serious and other adverse events in each group; death counts are not reported. These results are descriptive of the registry entries and should be interpreted in light of the missing methodological detail.