Carvedilol 25 mg in 36 Fasted, Healthy, Adult Subjects: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Carvedilol 25 mg in 36 Fasted, Healthy, Adult Subjects (NCT00834795), a randomized phase 1 study. The primary outcome is Cmax - Maximum Observed Concentration - Carvedilol in Plasma.

2. Clinical Question

3. Trial Design

This was a completed phase 1 study sponsored by Teva Pharmaceuticals USA. It was randomized, open label, single dose, and used a two-way crossover design. The registry lists 36 enrolled subjects and describes the population as fasted, healthy adults. The posted primary endpoint analysis includes subjects who completed the study, and each arm-level summary reports 34 subjects.

In a crossover design, participants receive both interventions over different periods. The registry describes two treatment sequences: the Carvedilol sequence received carvedilol 25 mg tablet in the first period followed by COREG® 25 mg tablet in the second; the Coreg® sequence received the reference tablet first and carvedilol second. Randomization determined the sequence. Masking was listed as none, so the study was open label.

The primary endpoint was Cmax, maximum observed concentration of carvedilol in plasma, measured in ng/mL. Blood samples were collected over a 60 hour period. The primary analysis population is described as all subjects who completed the study. The registry record does not report the number assigned to each sequence, the crossover interval, the planned statistical model, sequence or period effects, or the original sample-size justification. It also does not report an interim analysis plan. These omissions limit what can be inferred about the intended design and analysis beyond the stated crossover structure and posted results.

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.

First Intervention

Washout: 7 Days

Reasons for not completing this period:

Second Intervention

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Data from all subjects who completed the study were included in the statistical analysis.

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 Cmax - Maximum Observed Concentration - Carvedilol in Plasma, measured over Blood samples collected over 60 hour period.

The primary endpoint, Cmax, is the maximum observed concentration of carvedilol in plasma after dosing. It summarizes the highest concentration measured during the sampling period, rather than the total amount of drug exposure over time or the duration of exposure. The unit reported is ng/mL, and the registry gives a blood-sampling timeframe of 60 hours.

In a relative bioavailability comparison, Cmax can help describe whether two formulations produce similar peak concentrations under the study conditions. It is one pharmacokinetic measure, and its interpretation depends on the planned comparison and criteria. The registry labels the primary endpoint as bioequivalence based on Cmax, but does not report equivalence bounds or the full statistical specification.

The posted endpoint summaries are means with standard deviations: 105.0 ng/mL for carvedilol and 107.5 ng/mL for COREG®, with 34 subjects in each summary. These are descriptive summaries of the analyzed subjects. They do not, by themselves, provide the within-subject comparison that a crossover analysis may use, nor do they specify an acceptance range for bioequivalence. A separate registry analysis reports the test-to-reference ratio of least-squares means and its 90% confidence interval.

7. Results Posted in the Registry

• Coreg®: mean 107.47 versus 104.98 on control; difference 2.49 (95% CI -25.02 to 30.00), standardized effect d = 0.04; z-test p = 0.859.

8. Statistical Interpretation

9. Statistical Methods Explained

Several statistical quantities appear in the registry results, and they answer different questions. The arm summaries describe the observed Cmax values for each formulation. The sponsor’s reported ratio compares least-squares means. The recalculated mean difference is an unadjusted comparison based on posted summary statistics. These measures should be read separately rather than treated as interchangeable.

What does a mean and standard deviation describe?

The mean is the average value of a continuous measurement. Here, Cmax is continuous and measured in ng/mL. The posted means are 105.0 for carvedilol and 107.5 for COREG®. The standard deviation describes how spread out observations are around a mean. The reported standard deviations are 57.81 and 57.95. A standard deviation is not the uncertainty in the estimated mean; it describes variability among observations. The standard error, by contrast, concerns the sampling uncertainty of an estimate. The recalculation reports standard errors of 9.914 and 9.938 for the two arm means.

Why does the crossover design matter?

In a crossover study, each participant receives both treatments in separate periods. This can allow a comparison that accounts for the fact that measurements from the same person may be related. The order of treatments can also matter if there are period or sequence effects. The registry identifies the two treatment sequences but does not report the model, handling of period or sequence, or subject-level data. The arm-level summaries alone do not show the within-subject covariance, which is the degree to which the two measurements from a participant vary together. Without that information, an independent arm-level recalculation cannot reproduce every feature of a crossover analysis.

The recalculated mean difference and its interval are simple unadjusted calculations from posted summary statistics. They describe a difference on the original Cmax scale. The sponsor analysis instead reports a ratio of least-squares means, a relative measure. Least-squares means are model-based estimates; however, the registry does not identify the model used for this result. The two estimates thus differ in both scale and analysis basis. The recalculation is informative as a separate descriptive check, not a replacement for the sponsor’s analysis.

What does the p-value say?

The unadjusted p-value is 0.859. A p-value measures how compatible the observed data are with a specified null hypothesis under the assumptions of the test. It does not give the probability that the null hypothesis is true, and it does not establish equivalence. The registry does not post a p-value for the least-squares mean ratio analysis. The recalculated p-value should therefore be interpreted only as part of the unadjusted mean-difference calculation.

How should the confidence intervals be read?

A confidence interval conveys uncertainty around an estimate under a particular analysis. The unadjusted mean-difference interval is -25.02 to 30.0. It expresses plausible values for the difference on the concentration scale, given that calculation. The sponsor’s interval, 85.69 to 105.67, is a 90% confidence interval for the reported test-to-reference ratio of least-squares means, with the ratio estimate stated as 95.16. Its scale and confidence level differ from those of the recalculated interval. A 90% confidence interval is not a bioequivalence boundary: acceptance limits must be specified separately.

Statistical equivalence is generally assessed by comparing an interval for a treatment contrast with prespecified margins that define an acceptable range. This is a general statistical explanation, not a claim about the criteria used in this study. The registry record does not report the margins or the full analysis method, so the posted interval cannot be mapped to a stated acceptance rule.

Why can variability affect precision?

Greater variability generally makes an estimate less precise when the other design features are held constant. In a crossover study, the precision of a within-subject contrast also depends on the relationship between measurements from the same participant. The posted standard deviations describe marginal variability, but not that within-subject relationship. Consequently, they are not enough to reconstruct the precision of the sponsor’s crossover estimate. The recalculated interval reflects its own unadjusted calculation and assumptions.

General statistical methods can also be affected by over-dispersion, where observed variability exceeds what a chosen model assumes. That concern is not specifically documented for this study; the registry record does not report a model diagnostic or an over-dispersion assessment. No claim about such a problem can be drawn from the posted summaries.

10. Confidence Intervals and Precision

Precision concerns how narrowly an estimate is determined by the data and analysis. The sponsor’s ratio estimate is 95.16, with a 90% confidence interval from 85.69 to 105.67. This interval communicates uncertainty around the relative estimate under the sponsor’s analysis. Its interpretation depends on the model and assumptions used, and the registry record does not describe that method.

The recalculated unadjusted mean difference is 2.49, with a confidence interval from -25.02 to 30.0. This interval is on the Cmax concentration scale, not the ratio scale, and it is not the same estimand as the sponsor’s result. Its breadth indicates that the unadjusted comparison is compatible with a range of difference values. It should not be used to infer that the formulations meet an equivalence criterion.

Confidence intervals are not ranges containing a fixed proportion of individual observations, and they do not indicate the probability that a particular treatment effect is true. They describe uncertainty in an estimated quantity under a specified method. The 90% level applies to the sponsor’s ratio interval; the registry does not state a confidence level for the recalculated mean-difference interval in the comparison entry, so no level should be inferred for it.

The observed sample size in the endpoint summaries is 34 per formulation, and the endpoint analysis included subjects who completed the study. Precision in a crossover comparison also depends on within-subject variability and the analysis structure, neither of which can be recovered from the two arm summaries alone. Thus, the posted estimates and intervals are useful descriptions, but the record leaves important details about the precision calculation unreported.

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 illustrations based on the observed effect, rather than the trial’s original design assumptions. The planning 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 set at the stated fraction of the observed effect. The original trial’s sample-size assumptions and justification are not reported in the registry record.

The 80% power column gives the illustrative number of participants per arm for a design that would have an 80% chance of detecting the specified effect under those assumptions, if that effect and model assumptions held. The 90% power column gives the corresponding illustration for a 90% chance. These are prospective planning interpretations, not descriptions of what the completed study achieved.

For 100% of the observed effect, the figures are 8,482 participants per arm for 80% power and 11,355 for 90% power. For 75% of the observed effect, they are 15,080 and 20,187 participants per arm. For 50% of the observed effect, they are 33,928 and 45,420 participants per arm. The pattern illustrates a general property of sample-size planning: smaller effects require more participants to detect, all else being equal. These illustrations are based on the recalculated observed mean difference and assumptions stated for planning; they do not model the original crossover design. They are not observed power and do not describe the probability that the completed study detected an effect.

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 = 2.490; pooled standard deviation σ = 57.880.
2. n = 2 × (1.96 + 0.842)² × 57.880² / 2.490² = 8,482.0, rounded up to 8,482 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 <- 2.48999999999999                      # observed difference in means
sigma <- 57.880042328941                     # 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(834795)
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 = 8,482 (80% power), 11,355 (90% power)
 75% of observed effect: n per arm = 15,080 (80% power), 20,187 (90% power)
 50% of observed effect: n per arm = 33,928 (80% power), 45,420 (90% power)
power.t.test: 8482.9 
Simulated power at n = 8,482 per arm: 0.798 (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. Analyses Reported by the Sponsor

The sponsor’s posted analysis reports a test-to-reference ratio of least-squares means of 95.16, with a 90% confidence interval from 85.69 to 105.67. The registry record labels the analysis as a legacy non-inferiority or equivalence analysis. It does not report the statistical method or the acceptance bounds. The ratio should therefore be read as the posted relative estimate and interval, without asserting that a formal bioequivalence threshold was met.

The recalculated result is a mean difference of 2.49, with a confidence interval from -25.02 to 30.0 and an unadjusted p-value of 0.859. It is derived from posted summary statistics and uses a different scale and comparison from the sponsor’s ratio. A simple arm-level calculation cannot reproduce an analysis based on an unspecified least-squares model, particularly when the study is a crossover and the record does not include subject-level data or the within-subject relationship.

The two results are not reported as discrepant. The sponsor’s analysis is the registry’s own analysis; the recalculation is supplementary and should not be treated as a correction or replacement. Since the equivalence margins and model details are not reported in the registry record, the sponsor’s numerical interval cannot be compared with a stated decision rule based on the available record.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists 3 outcome measures and 3 analyses, while no secondary results are posted in the available record. The detailed results described for interpretation concern the primary Cmax endpoint. The registry record does not report a multiplicity adjustment, a hierarchy among endpoints, or a prespecified strategy for controlling the chance of false-positive findings across multiple analyses. It is therefore not possible to determine from the record whether or how multiplicity was addressed.

The primary endpoint population is described as data from all subjects who completed the study. The registry reports 36 enrolled subjects and arm summaries with 34 subjects each. It does not explain the difference between enrollment and the analyzed summaries, give reasons for non-completion or exclusion, or describe how missing endpoint measurements were handled. The missing-data approach is not reported in the registry record.

The registry identifies two treatment sequences and gives the intended order of formulations for each. It does not report whether the analysis accounted for period, sequence, or subject effects, or whether any sensitivity analyses were conducted. The statistical model and the method used to calculate the least-squares means are not reported. Nor is there a posted interim-analysis plan or information about stopping rules.

These omissions matter because analysis choices can affect estimates and uncertainty, particularly in a crossover study. The available endpoint summaries and sponsor result can be described as posted, but the record does not allow a full assessment of missing-data handling, multiplicity control, or the details of the analysis population beyond the statement that completers were included.

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

The results describe Cmax after a single dose of test carvedilol 25 mg tablet and COREG® 25 mg tablet in fasted, healthy adults. The posted arm means are 105.0 ng/mL and 107.5 ng/mL, respectively, with 34 subjects in each summary. The sponsor reports a test-to-reference ratio of least-squares means of 95.16 and a 90% confidence interval from 85.69 to 105.67. The unadjusted recalculation gives a mean difference of 2.49, with an interval from -25.02 to 30.0 and p = 0.859.

These figures describe the observed data and their statistical uncertainty under the relevant analyses. They do not establish that the formulations are equivalent or not equivalent. A formal equivalence conclusion requires prespecified acceptance margins and an analysis that can be judged against those margins. The registry record does not report the margins or full analysis method. In addition, a non-significant difference test is not itself evidence of equivalence: it may be compatible with a range of effects, as reflected in the confidence interval.

The endpoint is a pharmacokinetic measure of peak concentration, not a clinical outcome. The registry record does not report clinical outcomes or results for secondary endpoints. The study’s setting was a single-dose assessment in fasted, healthy adults, so the findings should not be extended beyond that studied context without additional evidence. The record also does not provide enough detail to assess the effect of crossover-specific factors or missing data on the estimates.

The appropriate reading is limited: the registry posts similar-looking arm mean summaries, a relative estimate with a 90% confidence interval, and an unadjusted recalculation with its own uncertainty. The formal interpretation of the relative interval depends on information not reported in the registry record.

16. Why This Trial Matters Statistically

This study illustrates the distinction between describing two observed means and answering an equivalence question. A conventional difference estimate is expressed on the measurement scale, while a relative bioavailability comparison is naturally expressed as a ratio. The posted mean difference and the sponsor’s ratio are therefore not competing versions of the same number; they address the comparison using different scales and analysis approaches.

The crossover design is also statistically important. Since participants received both formulations, the comparison may use within-person information. That can affect precision, but the arm summaries do not reveal the relationship between each participant’s two measurements. This makes the distinction between a simple summary-statistic recalculation and the sponsor’s model-based result especially relevant.

The record also demonstrates why an estimate should be interpreted alongside its interval and the decision criterion. The sponsor reports a 90% confidence interval for the ratio, but the acceptance bounds are not reported in the registry record. Without those bounds, the interval cannot establish whether the study met its stated bioequivalence objective. A p-value from an unadjusted difference calculation cannot fill that gap.

Finally, planning numbers based on an observed effect are not a retrospective measure of whether a study was adequately powered. The large illustrative requirements reflect the specified planning approach and effect fractions, not the original sample-size rationale. The registry record does not report that rationale. Together, these features make the study a useful example of how design, estimand, model, interval, and decision rule must be considered together when interpreting bioavailability results.

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 record provides limited detail for assessing the study’s statistical implementation. It identifies a randomized, open-label, two-way crossover design and gives both treatment sequences, but does not report the crossover interval, the statistical model, or how period and sequence were handled. The least-squares mean method is not specified. These details are important to understanding the sponsor’s ratio estimate and its interval.

The record does not report the equivalence margins needed to interpret the primary result against a formal bioequivalence criterion. It also does not provide a sample-size justification or original design assumptions. The planning illustrations based on the observed effect are not substitutes for those missing design details.

The posted arm summaries do not include participant-level paired measurements or the within-subject covariance. As a result, the unadjusted recalculation cannot reproduce a crossover analysis from the aggregate values alone. The registry’s primary endpoint analysis includes completers, but the reasons for the difference between enrollment and the arm-summary counts, and the handling of missing data, are not reported in the registry record.

The registry lists three outcome measures and three analyses, but no secondary results are posted. Multiplicity procedures and any sensitivity analyses are not reported. The study population was fasted, healthy adults receiving a single dose; the record does not establish whether the findings generalize to other settings or populations. These limitations concern what can be determined from the registry record and do not imply that a particular unreported procedure was or was not used.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Carvedilol 25 mg in 36 Fasted, Healthy, Adult Subjects — NCT00834795.
• Registry record last updated 2024-08-19; status last verified 2024-08.
• Results first posted 2009-08-18.
• 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

NCT00834795 is a completed phase 1, randomized, open-label, two-way crossover study sponsored by Teva Pharmaceuticals USA. It enrolled 36 fasted, healthy adults and compared single doses of test carvedilol 25 mg tablets and COREG® 25 mg tablets. Each treatment sequence received both formulations in a different order.

The primary endpoint was maximum observed plasma concentration of carvedilol, measured in ng/mL over a 60 hour blood-sampling period. The posted arm means were 105.0 for carvedilol and 107.5 for COREG®, with 34 subjects in each summary. The sponsor reported a test-to-reference ratio of least-squares means of 95.16 and a 90% confidence interval from 85.69 to 105.67. Equivalence bounds and detailed model specifications are not reported in the registry record, limiting formal interpretation of that interval.