Effect of Nebivolol on Oxidative Stress and Endothelial Progenitor Cells: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effect of Nebivolol on Oxidative Stress and Endothelial Progenitor Cells (NCT01041287), a randomized phase 4 study. The primary outcome is Pulse Wave Velocity (Measure of Arterial Stiffness).

2. Clinical Question

3. Trial Design

This was a completed Phase 4, randomized, triple-masked crossover trial sponsored by Emory University. The registry records the study start as 2009-12 and primary completion as 2013-12. Its stated condition was hypertension, and its enrollment was 96.

Participants were assigned to a treatment sequence: nebivolol followed by metoprolol succinate, or metoprolol succinate followed by nebivolol. Each treatment period is described as lasting 3 months. In the nebivolol sequence descriptions, the starting dose was 5 mg daily, with titration to 10 mg daily after 2 weeks if blood pressure remained >125/80, and a further titration to 20 mg daily after another 2 weeks if the blood pressure condition was met. The metoprolol dosing details are not fully reported in the registry record.

A crossover design lets participants receive each study treatment in sequence, potentially allowing comparisons within the same participant. Such comparisons need to account for treatment period and sequence, and may also need to address carryover from an earlier period. Whether there was a washout period, how treatment order was handled in the analysis, and what model was used are not reported in the registry record. The posted primary outcome is explicitly marked as baseline, and the posted comparison is between the two sequence groups. It should therefore not be read as a reported within-person comparison of outcomes during nebivolol and metoprolol treatment.

The registry lists 3 outcome measures but posts no secondary results. It records no analyses in its analysis listing. Statistical methods used by the trial team, details of masking implementation, and the original design assumptions are not reported in the registry 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.

Before assignment: There were 96 subjects enrolled. 58 of the subjects were withdrawn prior to group assignment. 39 subjects did not meet eligibility criteria and 19 subjects withdrew.

Treatment Period 1 (3 Months)

Treatment Period 2 (3 Months)

Reasons for not completing this period:

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.

Population: The population analysis for baseline characteristics are from subjects that completed both treatment periods.

6. Primary Endpoint

The registry lists the primary outcome as Pulse Wave Velocity (Measure of Arterial Stiffness), measured over Baseline.

Pulse wave velocity (PWV) is the speed at which a pressure wave travels between the carotid and femoral arteries. The registry describes measurement using a single-lead electrocardiogram and a tonometer to record pressure waveforms at the two sites in sequence. PWV is calculated from the distance between the sites divided by the time taken for the waveform to travel between them, and is expressed in meters per second (m/s).

PWV is used as a measure of arterial stiffness. In general, the speed of a pressure wave through an artery reflects properties of the artery wall, making PWV a physiological measure relevant to vascular function. This is a measurement of a vascular characteristic, not a direct measure of a clinical event such as stroke or heart attack.

The registry gives the primary outcome timeframe as baseline and summarizes it as a mean with standard deviation. The nebivolol/metoprolol sequence group had a mean of 9.4 m/s with a standard deviation of 2.6, based on 16 participants. The metoprolol/nebivolol sequence group had a mean of 8.9 m/s with a standard deviation of 1.5, based on 14 participants. Because these are baseline values grouped by randomized sequence, they do not by themselves describe a change during treatment or an effect of one drug compared with the other.

7. Results Posted in the Registry

• Metoprolol/Nebivolol: mean 8.90 versus 9.40 on control; difference -0.50 (95% CI -2.00 to 1.00), standardized effect d = -0.23; z-test p = 0.513.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is a continuous measurement, and the registry summarizes it with a mean and standard deviation. A mean describes the central value of a group, while a standard deviation describes how dispersed the individual measurements are around that mean. The standard deviation is not the uncertainty interval for the mean or for a between-group difference; those quantities depend on the sample sizes and the statistical method used.

What does the mean difference represent?

The posted comparison reports a mean difference of -0.5 m/s, using the nebivolol/metoprolol sequence group as the reference and the metoprolol/nebivolol sequence group as the other group. In plain terms, the observed baseline mean was lower in the latter sequence group. The sign depends on the order in which groups are subtracted, so it should always be read alongside the group labels. This contrast is between sequence groups at baseline, not a comparison of measurements during the two treatments.

The registry also lists a pooled standard deviation of 2.16 and a standardized difference of -0.232. A standardized difference expresses the contrast in units of pooled variability rather than in m/s, which can help describe the size of a difference on a common scale. It does not turn a baseline comparison into a treatment effect, and it does not establish clinical importance.

How should the confidence interval and p-value be read?

A confidence interval describes a range of estimates compatible with the observed data under the method used. A wider interval indicates less precision. For this comparison, the posted interval spans zero, meaning that the data are compatible with no difference as well as differences in either direction. The posted unadjusted p-value is 0.513. A p-value measures how surprising data at least this incompatible with a null hypothesis would be under the assumptions of a particular test; it is not the probability that the null hypothesis is true.

The registry gives an unadjusted p-value but does not report the analysis model or any adjusted analysis. The displayed difference and its uncertainty should therefore be understood as the posted summary comparison, not as evidence that a particular crossover model was fitted. The registry record lists no analyses in its analysis listing.

Why does crossover structure matter?

In general, a crossover trial can compare outcomes from the same participants under different treatments. This can account for stable differences between individuals, but valid analysis also needs to address treatment sequence and period. Carryover is a concern when the effects of an earlier treatment could persist into a later period. The analysis may also need to account for repeated measurements within participants. These are general statistical considerations, not descriptions of analyses confirmed for this trial.

The posted primary outcome is at baseline, and the comparison is organized by randomized sequence. It is not described as a participant-level contrast between periods. Whether the investigators analyzed repeated measures, modeled period or sequence, or assessed carryover is not reported in the registry record. A reader should not infer that these features were handled merely because the overall trial used a crossover design.

What can the posted statistics support?

The group means, standard deviations, mean difference, confidence interval, and unadjusted p-value support a description of the baseline PWV values by sequence group. They do not show treatment-associated change or establish a causal treatment contrast. That distinction is important because randomization assigns sequence, while the question of interest concerns outcomes under each treatment period.

General statistical interpretation also depends on the quality and completeness of outcome data and on the population included in an analysis. The registry gives the outcome-group counts, but missing-data methods, analysis populations, and details of exclusions are not reported in the registry record. Consequently, the posted summaries cannot establish how missing observations or deviations from the assigned sequence were handled.

For continuous outcomes, uncertainty often decreases when measurements are less variable or when more informative observations are available. In crossover studies, within-participant correlation can affect the precision of a treatment contrast. No within-participant correlation or treatment-period estimate is posted for this outcome, so the precision of an intended paired contrast cannot be assessed from the registry summaries alone.

10. Confidence Intervals and Precision

The posted confidence interval for the baseline mean difference extends below and above zero. Its lower bound is -1.997 m/s; the upper bound is positive. Since zero lies within the interval, the posted data do not pin down the direction of the baseline difference with precision. The estimate of -0.5 m/s is only one value among the range of values compatible with the data under the interval's assumptions.

Confidence intervals are useful because they show both the estimated contrast and its uncertainty. A narrow interval would indicate greater precision, while a wide interval would leave more plausible values unresolved. Here, the interval allows a difference in either direction, so the baseline comparison does not precisely distinguish the sequence groups. This uncertainty is consistent with the unadjusted p-value of 0.513.

The interval applies to the posted sequence-group contrast at baseline. It does not quantify uncertainty in a within-person treatment effect, because such an estimate is not reported. In a crossover trial, the precision of a treatment comparison can depend on the variability of changes within participants and the association between repeated measurements. Those details are not reported in the registry record.

Precision is distinct from clinical importance. The registry record does not state a threshold for a meaningful PWV difference, and the baseline results alone do not establish whether any possible contrast matters clinically. The findings should be read as an imprecise baseline comparison, rather than as a precise estimate of the relative effects of nebivolol and metoprolol.

11. 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 event counts. They illustrate sample sizes for a future comparison using fractions of the observed effect: 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. At 100% of the observed effect, the planning figures are 293 participants per arm for 80% power and 393 participants per arm for 90% power. At 75% of the observed effect, they are 521 participants per arm for 80% power and 698 participants per arm for 90% power. At 50% of the observed effect, they are 1,172 participants per arm for 80% power and 1,569 participants per arm for 90% power.

In plain language, 80% power describes a planning target intended to give the specified chance of detecting an effect of the stated size under the assumptions used. The 90% power column uses a higher chance of detecting that effect and therefore requires more participants in these illustrations. Smaller effects are harder to distinguish from random variation, so the planning figures increase as the assumed effect becomes smaller.

The calculation assumes 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. These are planning illustrations based on the observed effect, not the trial's original design assumptions. They are not observed power and do not describe the probability that the completed trial detected its treatment effect. The registry record does not report the trial's original sample-size justification or design assumptions.

12. 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 = -0.500; pooled standard deviation σ = 2.160.
2. n = 2 × (1.96 + 0.842)² × 2.160² / -0.500² = 293.0, rounded up to 293 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 <- -0.5                      # observed difference in means
sigma <- 2.16010912422762                     # 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(1041287)
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 = 293 (80% power), 393 (90% power)
 75% of observed effect: n per arm = 521 (80% power), 698 (90% power)
 50% of observed effect: n per arm = 1,172 (80% power), 1,569 (90% power)
power.t.test: 294 
Simulated power at n = 293 per arm: 0.794 (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.

13. Multiplicity, Missing Data and Analysis Populations

The registry lists 3 outcome measures, while the primary posted result concerns baseline PWV. It records no posted secondary results. The record therefore does not allow a reader to assess results across the full set of outcomes or determine how multiple outcomes may have influenced interpretation.

Multiplicity arises when several outcomes, comparisons, time points, or analyses are examined. In general, conducting many statistical tests can increase the chance of finding an apparently notable result by chance. Statistical approaches can address that issue, but the registry record does not report a multiplicity plan or adjustments. The posted p-value is identified as unadjusted; no adjusted result is listed.

Missing-data handling is also not reported in the registry record. The endpoint summaries include 16 participants in the nebivolol/metoprolol sequence group and 14 in the metoprolol/nebivolol sequence group, but the registry does not explain why these outcome counts differ from the enrollment figure or from the adverse-event risk counts. The reason for any unavailable measurements, the amount of missing outcome data, and any imputation or sensitivity analyses are not reported.

The analysis population is not described. The record does not state whether results were based on all randomized participants, participants who completed both treatment periods, or another defined group. It also does not provide details on treatment adherence, withdrawal, protocol deviations, or how these were handled in the analysis.

These gaps matter particularly for a crossover trial, where completing both periods and accounting for period-specific measurements can affect the analysis. Whether the trial used paired data, how sequence and period were modeled, and whether carryover was evaluated are not reported in the registry record. The posted baseline comparison can be described, but it does not resolve these analysis questions.

14. 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.

Most frequent serious adverse event terms

Serious events with the highest arm-level rate: stroke (10.5%).

The registry reports serious adverse events by randomized sequence group, with 19 participants at risk in each group. It records 0 serious adverse events in the nebivolol/metoprolol group and 2 in the metoprolol/nebivolol group. The listed top serious-event term is stroke, at 10.5%. The registry also records 0 other adverse events in each group.

These are descriptive counts from the registry record. They do not by themselves establish that the treatments differ in safety: the record does not provide a statistical comparison, event timing, or a complete account of exposure during each treatment period. The adverse-event risk groups also have different counts from the primary outcome groups; the reason is not reported in the registry record. Death counts are not reported in the registry record.

In a crossover study, adverse events may occur during a particular treatment period, so sequence-level totals alone do not show which treatment was being taken when an event occurred. The record does not provide that treatment-period detail. The listed serious-event term and counts should therefore be interpreted as registry-reported safety information, not as a comparative risk estimate.

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

The posted primary result describes baseline pulse wave velocity in the two randomized sequence groups. Their means were 9.4 m/s and 8.9 m/s, with a posted mean difference of -0.5 m/s. The unadjusted p-value is 0.513, and the confidence interval includes zero. Taken together, these statistics show an uncertain baseline contrast rather than a clear distinction between sequence groups.

They do not answer whether nebivolol and metoprolol differed in their effects on PWV during treatment. The endpoint timeframe is baseline, and the registry record does not post a within-person comparison across the crossover periods. Nor do these statistics establish that either treatment changed arterial stiffness, or that a change in PWV would alter the risk of clinical events.

The result also should not be interpreted as proof of equivalence. The confidence interval permits differences in both directions, and the registry does not report an equivalence margin or a treatment-period analysis designed to assess equivalence. An unadjusted p-value that does not indicate a clear difference cannot establish that effects are the same.

The safety counts offer a separate descriptive record. They do not provide a treatment-specific risk comparison because event timing and treatment-period attribution are not reported. The registry's top serious-event term is stroke at 10.5%, but this information should not be read as a complete account of comparative safety.

In general, this record is most informative about the design and the baseline endpoint summaries. It is limited as evidence about the trial's intended drug comparison because treatment-period outcome results and analysis methods are not posted. The available statistics should be interpreted within that boundary, without extending them to conclusions about clinical benefit or harm.

16. Why This Trial Matters Statistically

This trial raises statistical issues common to randomized crossover studies. Randomization assigned treatment sequence, and participants were intended to receive both nebivolol and metoprolol succinate in different periods. That structure can support within-participant comparisons, but it also means the analysis must distinguish treatment effects from period and sequence effects and consider whether effects could carry over between periods. The registry record does not report how those issues were handled.

The primary posted outcome is baseline PWV rather than a treatment-period contrast. This makes the distinction between a randomized baseline comparison and the intended treatment comparison especially important. The reported means and unadjusted comparison describe the sequence groups at baseline; they do not constitute evidence about differences during treatment. Identifying the estimand—the exact contrast a statistical analysis aims to estimate—is essential to interpreting any trial result.

The uncertainty around the baseline mean difference also illustrates why a point estimate and a p-value are not enough on their own. The interval spans both sides of zero, leaving the direction uncertain. Reporting the estimate with its uncertainty is more informative than treating a p-value as a verdict, while still recognizing that these statistics do not answer the treatment question when the outcome is baseline.

Finally, the registry record lists no analyses and posts no secondary results. Missing analysis details limit reproducibility and prevent assessment of choices about repeated measures, missing data, multiplicity, or the analysis population. These are not merely reporting technicalities: they determine what comparison is being made and how much confidence readers can place in its interpretation.

17. 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 main limitation of the posted result is that the primary outcome timeframe is baseline. The group means and comparison are organized by randomized treatment sequence, not by outcomes during nebivolol and metoprolol treatment. No within-person treatment-period contrast is reported, so the intended crossover comparison cannot be evaluated from the posted primary result.

The registry record does not report the crossover analysis method, period effects, sequence effects, or assessment of carryover. A washout period is not reported in the registry record. The record also does not give a complete description of metoprolol dosing. These omissions make it difficult to evaluate how the intended treatment periods were implemented and analyzed.

Outcome counts are smaller than the overall enrollment figure, and the primary outcome counts differ by sequence group. The record does not explain these counts or report missing-data methods, reasons for missing measurements, or analysis-population definitions. It is therefore not possible to determine from the registry record whether the outcome summaries represent all randomized participants or a selected subset.

The posted comparison has an unadjusted p-value and an interval that includes zero, but no analysis model or adjusted results are listed. The record also posts no secondary outcome results despite listing 3 outcome measures. Safety counts are reported separately, but treatment-period attribution and death counts are not reported in the registry record.

These limitations do not negate the descriptive baseline statistics. They do restrict the conclusions that can be drawn about the randomized treatment comparison, the handling of the crossover structure, and the completeness of outcome and safety reporting.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Effect of Nebivolol on Oxidative Stress and Endothelial Progenitor Cells — NCT01041287.
• Registry record last updated 2014-12-19; status last verified 2014-12.
• Results first posted 2014-12-19.
• 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.

21. Record Summary

NCT01041287 is a completed Phase 4 randomized, triple-masked crossover trial sponsored by Emory University. It enrolled people with hypertension and compared sequences of nebivolol and metoprolol succinate, with each treatment period described as lasting 3 months.

The primary posted outcome is baseline pulse wave velocity, a continuous measure of arterial stiffness. The sequence-group means were 9.4 m/s and 8.9 m/s; the posted mean difference was -0.5 m/s, with an unadjusted p-value of 0.513 and a confidence interval spanning zero. These are baseline sequence-group statistics, not a reported treatment-period contrast.

The registry lists 3 outcome measures but posts no secondary results and records no analyses in its analysis listing. Treatment-period outcome analyses, missing-data methods, and the original sample-size justification are not reported in the registry record.