Vascular Effects of Carvedilol Versus Metoprolol in Hypertensive Patients With Type 2 Diabetes: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Vascular Effects of Carvedilol Versus Metoprolol in Hypertensive Patients With Type 2 Diabetes (NCT00123604), a randomized phase 4 study. The primary outcome is Flow Mediated Dilation.

2. Clinical Question

3. Trial Design

The registry describes a completed, randomized, quadruple-masked, parallel-group phase 4 trial sponsored by St. Paul Heart Clinic. Its title concerns vascular effects of carvedilol versus metoprolol in hypertensive patients with type 2 diabetes. The listed enrollment is 36. The study began in 2004-06, and primary completion is recorded as 2006-06. These dates and design labels describe the registry entry; they do not establish further details about how the trial was conducted.

The two listed interventions were carvedilol and metoprolol. Carvedilol was given orally at 25 mg twice daily for five months; metoprolol was given orally at 200 mg twice daily for five months. The parallel model means the recorded design assigns participants to one of the treatment groups rather than describing a crossover. Randomized allocation and quadruple masking are registry design labels, but the record does not explain the randomization procedure, who was masked, or how masking was maintained. Those details are not reported in the registry record.

The primary outcome was flow-mediated dilation, with a timeframe of change from baseline to 5 months. It is a continuous measure, summarized by means and standard deviations. The posted outcome data list 16 participants for carvedilol and 18 for metoprolol. The registry does not explain the relationship between these outcome counts and the enrollment figure, nor does it report a detailed analysis population. No secondary outcomes are posted. Further information about sites, recruitment, eligibility, adherence, protocol deviations, and follow-up completion is 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.

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 Flow Mediated Dilation, measured over change from baseline to 5 months.

Flow-mediated dilation is described in the registry as a measure of endothelial function. It is assessed through the percent change in artery diameter before and after manual artery occlusion. The primary endpoint is the change from baseline to 5 months, expressed as percentage of change in dilation. The registry summarizes this continuous outcome with a mean and standard deviation for each group.

General statistical context: a continuous endpoint preserves information about the magnitude of each recorded measurement, rather than reducing the result to a count of participants above or below a threshold. Comparing group means can therefore describe the average difference in the measured vascular response. The standard deviation describes how much individual measurements vary around a group mean; it is not the uncertainty in the estimated mean difference.

Flow-mediated dilation is being used as a physiological or surrogate measure. Its role in the trial is to assess a vascular response, not to count clinical events or directly report how participants felt or functioned. The registry does not report a threshold for a clinically important change, nor does it state how changes in this measurement relate to outcomes beyond the endpoint itself. The result should therefore be interpreted as a comparison of the recorded dilation measure, with the precision and analysis limitations described in the registry record.

7. Results Posted in the Registry

• Metoprolol: mean 4.10 versus 6.20 on control; difference -2.10 (95% CI -4.57 to 0.37), standardized effect d = -0.58; z-test p = 0.096.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous, and the posted summaries are group means with standard deviations. The registry comparison reports a mean difference for metoprolol relative to carvedilol. This gives the direction and scale of the contrast in the original outcome units: negative values correspond to a lower mean in the metoprolol group under this comparison convention. The reported estimate is -2.1. The comparison is unadjusted and recalculated from the posted summary statistics; the registry does not list a sponsor analysis.

What does a group mean describe?

A mean is the arithmetic average of the observed measurements in a group. It offers a compact description of the group’s central value, but it does not show the full distribution of individual measurements. Two groups can have different means while their individual observations overlap substantially. The outcome standard deviations help describe within-group spread: 3.9 for carvedilol and 3.4 for metoprolol. A standard deviation is not a confidence interval and should not be read as a range containing every participant’s outcome.

What does the mean difference express?

The mean difference compares the two group averages on the endpoint’s original scale. Here, the comparison is metoprolol relative to carvedilol, and the reported difference is -2.1. This is not a percentage reduction or a ratio. It is a difference in the recorded outcome measure. General statistical context: an unadjusted comparison uses the group summaries without accounting for additional covariates. Whether adjustment was part of an original analysis is not reported in the registry record.

What is a p-value?

The unadjusted p-value is 0.096. In general, a p-value measures how unusual data at least as extreme as those observed would be under a specified null hypothesis and statistical model. Its interpretation depends on the analysis assumptions, including how the outcome is distributed and how observations are related. It is not a measure of the probability that the observed difference occurred by chance, nor does it tell readers whether a difference matters clinically. The registry does not report a sponsor analysis plan or further details of the test underlying the posted recalculation.

What does the confidence interval add?

A confidence interval expresses uncertainty around an estimated quantity. In general, a confidence interval produced by a statistical procedure gives a range of estimates that would have the stated coverage over repeated applications of that procedure, under its assumptions. It is not a guarantee that the true value lies within a particular interval, and it does not include uncertainty about unreported design or analysis decisions. The interval reported for this comparison spans zero, indicating that both negative and positive differences are consistent with the range of estimates in the interval.

Why does variability matter?

General statistical context: greater variation among individual measurements makes a group mean less precise unless offset by more observations. Precision also depends on the number of observations contributing to each mean. The posted outcome groups list 16 for carvedilol and 18 for metoprolol. With these summaries, the comparison has appreciable uncertainty, reflected in the confidence interval. The standard deviations describe the observed spread; they do not by themselves establish whether the groups are comparable in baseline characteristics.

What is over-dispersion, and is it relevant?

Over-dispersion arises when count data vary more than a model assumes, which can make standard errors too small if that extra variability is ignored. General statistical context: methods designed for counts or event rates may need to account for over-dispersion. This primary endpoint is continuous and is reported as a mean with standard deviation, not as a count outcome. The registry does not report a distributional assessment or model details, so no specific distributional assumption can be verified from the record.

What information is absent about the analysis?

The registry lists zero posted analysis records and no posted secondary outcomes. It does not report the statistical analysis plan, the test used for the comparison, any covariate adjustment, handling of missing endpoint measurements, or an intention-to-treat or per-protocol population. The outcome population field is blank. These omissions matter because analysis choices can affect which participants contribute data and how uncertainty is estimated. The unadjusted recalculation is useful for describing the posted summaries, but it cannot fill in unreported protocol decisions or establish what analysis was prespecified.

10. Confidence Intervals and Precision

The mean difference is reported as -2.1, with a confidence interval whose lower bound is -4.574 and whose upper bound is above zero. The interval therefore crosses zero. This means the posted data do not narrowly determine whether the average difference is negative or positive under the comparison convention. The interval also allows differences that are not close to the point estimate, so the estimate is not highly precise.

In general, a confidence interval conveys the range of estimates reasonably compatible with the data and the method’s assumptions. It is not a range of individual participant outcomes, and it does not show that all values inside the interval are equally likely. The registry does not report the confidence level used for this comparison, so that detail is not reported in the registry record. The interval can still be read as evidence that uncertainty around the mean difference is substantial relative to the point estimate.

The posted outcome groups are small, and the observed standard deviations are 3.9 and 3.4. General statistical context: estimates of a mean difference become less precise when the data are variable or the number of observations is limited. These features help explain why a point estimate alone is insufficient. The interval should be considered together with the unadjusted p-value of 0.096 and the absence of a reported analysis population or missing-data method.

Precision is distinct from clinical importance. A narrow interval could still center on an unimportant difference, while a broad interval can include differences that would matter in either direction. The registry does not state a clinically meaningful threshold for flow-mediated dilation. The interval therefore describes statistical uncertainty, but the record does not provide a basis for deciding which values would be clinically important.

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 events. They are planning illustrations based on the observed effect, not the original trial’s design assumptions. The stated assumptions 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 original trial’s sample-size assumptions are not reported in the registry record.

For the planning scenario using 100% of the observed effect, the estimates are 48 participants per arm for 80% power and 64 participants per arm for 90% power. For 75% of the observed effect, the estimates are 84 participants per arm for 80% power and 113 participants per arm for 90% power. For 50% of the observed effect, the estimates are 189 participants per arm for 80% power and 253 participants per arm for 90% power.

In general, power is the probability that a study will detect an effect of a specified size under the planning assumptions if that effect is present. The 80% column describes a design targeting an 80% chance of detecting the chosen effect; the 90% column targets a higher chance under the same stated framework. Smaller effects require more participants to distinguish them from random variation, which is why the planning estimates increase as the assumed fraction of the observed effect decreases.

These figures are illustrations, not observed power. They use the observed effect as their starting point and do not establish what the completed trial was designed to detect. The sample-size curve should be read as a planning relationship between the assumed effect and the number of participants required under the stated assumptions, not as a description of the trial’s actual enrollment or its chance of obtaining a statistically significant result.

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 = -2.100; pooled standard deviation σ = 3.643.
2. n = 2 × (1.96 + 0.842)² × 3.643² / -2.100² = 47.2, rounded up to 48 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 <- -2.1                      # observed difference in means
sigma <- 3.64292979619427                     # 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(123604)
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 = 48 (80% power), 64 (90% power)
 75% of observed effect: n per arm = 84 (80% power), 113 (90% power)
 50% of observed effect: n per arm = 189 (80% power), 253 (90% power)
power.t.test: 48.2 
Simulated power at n = 48 per arm: 0.795 (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 posts one primary outcome measure and no secondary outcome measures. It lists zero analysis records. This limits what can be assessed about multiplicity, meaning the statistical consequences of making several comparisons or testing several outcomes. The registry does not report whether the protocol included additional outcomes or analyses that were not posted, or whether any multiplicity adjustment was planned or used. Those details are not reported in the registry record.

The empty population field does not identify which participants contributed to the primary outcome summaries. The registry lists outcome data for 16 participants in the carvedilol group and 18 in the metoprolol group, but does not explain why those counts differ from the enrollment figure or whether the outcome counts represent every randomized participant with available data. It also does not report withdrawals, missing measurements, reasons for missingness, or a missing-data method.

The analysis population is not described. It is therefore not possible to determine from the registry record whether the summaries follow an intention-to-treat approach, a per-protocol approach, or another definition. The statistical analysis plan, covariate-adjustment strategy, and handling of protocol deviations are also not reported in the registry record. These omissions do not invalidate the posted descriptive summaries, but they prevent a full appraisal of whether the comparison follows prespecified methods or how sensitive it may be to missing observations and analysis choices.

General statistical context: multiple testing can increase the chance of finding at least one apparently unusual result when many hypotheses are examined. The number of posted outcomes is limited, but that alone does not establish how many analyses were planned or conducted. Without the analysis plan and details about unposted analyses, the scope of multiplicity control cannot be determined.

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.

The registry lists zero serious adverse events affecting 0 of 19 participants at risk in the metoprolol group and 0 of 17 participants at risk in the carvedilol group. It also lists zero other adverse events affecting 0 of 19 at risk with metoprolol and 0 of 17 at risk with carvedilol. No serious adverse event terms are listed. Death counts are not reported in the registry record.

These entries describe the safety data posted in the registry; they should not be interpreted as proof that no adverse events occurred beyond those recorded or as a comparison establishing safety. The record does not provide definitions, event-collection procedures, severity criteria, exposure-adjusted rates, or details about follow-up for adverse events. The adverse-event risk-group counts differ from the posted primary outcome group counts, and the record does not explain that difference. The figures are therefore best read as registry-reported counts with limited contextual detail.

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

The posted result describes the average change in flow-mediated dilation over the interval from baseline to 5 months in the two treatment groups. The carvedilol mean was 6.2, the metoprolol mean was 4.1, and the reported unadjusted mean difference for metoprolol relative to carvedilol was -2.1. The estimate is accompanied by a confidence interval that crosses zero and an unadjusted p-value of 0.096. Together, these statistics indicate uncertainty about the magnitude and direction of the average difference.

The result does not establish that the treatments are equivalent. Failure to demonstrate a clear difference is not the same as showing that any difference is small enough to be unimportant; that would require an appropriate equivalence or non-inferiority framework and a prespecified margin, neither of which is reported in the registry record. Nor does the point estimate alone establish that one treatment has a clinically meaningful advantage on this endpoint.

The endpoint is a measure of endothelial function, not a direct measure of symptoms, cardiovascular events, blood-pressure control, or diabetes outcomes. No secondary outcomes are posted. The registry record also lacks details about the analysis population, missing data, and the original statistical plan. These limits restrict conclusions to the posted summaries and do not support broader claims about clinical benefit, harm, or comparative effectiveness.

The serious adverse event entries report no affected participants in either group, but the registry record offers limited information about event ascertainment and follow-up. These counts cannot be used to conclude that either treatment is free of risk. The appropriate interpretation is narrow: the record presents a randomized comparison of a vascular surrogate outcome, with an unadjusted estimate and uncertainty that should remain central to reading the result.

16. Why This Trial Matters Statistically

This trial illustrates why the endpoint and estimand matter when interpreting clinical research. Flow-mediated dilation is a continuous physiological measure. The reported mean difference is expressed on that measure’s scale and should not be treated as a difference in clinical events or as a percentage effect on health outcomes. Recognizing the endpoint’s role prevents a surrogate measurement from being mistaken for a direct patient-centered outcome.

It also demonstrates the importance of reading an estimate together with its uncertainty. The mean difference is -2.1, but the confidence interval crosses zero. The point estimate gives a concise direction and magnitude; the interval shows that the data are compatible with a broader range of differences. The p-value of 0.096 does not replace that assessment and does not determine clinical importance.

The registry’s omissions are statistically consequential. Without a stated analysis population, missing-data method, or analysis plan, readers cannot fully assess which observations informed the comparison or whether the calculation reflects prespecified decisions. The absence of posted secondary outcomes and analysis records also limits evaluation of the full testing context. These are not merely reporting details: they shape how confidently the posted comparison can be interpreted.

Finally, the planning illustrations show how sample-size needs depend on the effect targeted. Smaller assumed effects require larger per-arm samples under the stated assumptions. Because these illustrations are based on the observed effect rather than the original design, they must not be mistaken for the trial’s actual planning rationale or for observed power. Together, the result and its reporting gaps offer a useful example of separating descriptive findings, inferential uncertainty, and design information.

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 registry entry provides limited clinical and methodological detail beyond the design labels, intervention descriptions, and posted outcome summaries. Eligibility criteria, participant characteristics, study sites, recruitment procedures, and treatment adherence are not reported in the registry record. The registry also does not identify who was masked despite recording quadruple masking, or explain the randomization procedure.

The primary outcome population field is empty, and the outcome counts are not reconciled with the enrollment figure. Reasons for missing outcome data, participant withdrawals, protocol deviations, and the analysis population are not reported in the registry record. There is no posted statistical analysis plan, no explanation of the comparison procedure, and no reported adjustment strategy. The displayed comparison is an unadjusted recalculation from the posted summary statistics.

Only one primary outcome is posted, with no secondary outcomes or analysis records. It is not possible to determine from the registry record whether other outcomes or analyses were planned or completed but not posted. The record does not state a clinically meaningful threshold for flow-mediated dilation, limiting interpretation of the practical importance of the estimated difference. Follow-up and adverse-event collection details are also absent, and deaths are not reported in the registry record.

These limitations affect interpretation of precision, completeness, and generalizability. They do not change the values that the registry reports, but they leave important context unavailable. The result should consequently be treated as a comparison of the posted endpoint summaries rather than a comprehensive account of the trial’s conduct or all of its findings.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Vascular Effects of Carvedilol Versus Metoprolol in Hypertensive Patients With Type 2 Diabetes — NCT00123604.
• Registry record last updated 2014-11-18; status last verified 2014-11.
• Results first posted 2014-11-18.
• 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

The registry identifies NCT00123604 as a completed phase 4 randomized, quadruple-masked, parallel-group trial sponsored by St. Paul Heart Clinic. It lists hypertension and type 2 diabetes mellitus as conditions and an enrollment of 36. The study began in 2004-06, with primary completion in 2006-06.

The trial compared oral carvedilol, 25 mg twice daily for five months, with oral metoprolol, 200 mg twice daily for five months. Its sole posted primary outcome is change in flow-mediated dilation from baseline to 5 months. The group means were 6.2 and 4.1, respectively; the unadjusted mean difference for metoprolol relative to carvedilol was -2.1. The confidence interval crosses zero, and the unadjusted p-value is 0.096.

No secondary outcomes or registry-posted analysis records are listed. Important details about the analysis population, missing data, and statistical plan are not reported in the registry record.