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Pulmonary Disease, Chronic Obstructive Phase 3 Continuous Endpoint NCT00400153

Respimat® Combivent Trial in Chronic Obstructive Pulmonary Disease (COPD): Complete Statistical Analysis

This page examines a randomized, double-blind, parallel-group trial comparing Combivent Respimat with Combivent MDI and ipratropium Respimat in COPD. It focuses on lung-function outcomes, the sponsor’s reported analysis, and the limits of interpreting the posted estimates.

Trial start: 2006-11  ·  Enrollment: 1480  ·  Sponsor: Boehringer Ingelheim
Scope of this record

This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.

1. Trial at a Glance

This page covers the registry results for Respimat® Combivent Trial in Chronic Obstructive Pulmonary Disease (COPD) (NCT00400153), a randomized phase 3 study. The primary outcome is FEV1 AUC0-6 at Day 85.

1480
Enrollment
Phase 3
3
Arms
In the primary outcome
0.00
Mean difference
COMBIVENT CFC-MDI 36/206 mcg
-0.02–0.02
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00400153
PhasePhase 3
ConditionPulmonary Disease, Chronic Obstructive
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment1480
Arms in the primary outcome3
Lead sponsorBoehringer Ingelheim
Results postedYes

2. Clinical Question

Population

Participants with chronic obstructive pulmonary disease (COPD) enrolled in a Phase 3 trial. The registry lists total enrollment as 1480. The primary outcome population is described as the Full Analysis Set for Pulmonary Function Test Data.

Intervention

Combivent Respimat, an ipratropium bromide/salbutamol inhalation spray combination, at 20 mcg/100 mcg. The registry summary describes treatment over 12 weeks.

Comparator

The principal active comparators were Combivent CFC-MDI at 36/206 mcg and ipratropium Respimat at 20 mcg. A corresponding-inhaler placebo is also listed as an intervention for blinding purposes, but it is not one of the three groups in the posted primary-outcome results.

Primary question

At Day 85, how did the average FEV1 AUC from before administration through 6 hours after administration compare across the three treatment groups? The study summary also describes planned questions about non-inferiority to Combivent MDI and superiority or non-inferiority to ipratropium Respimat over specified time intervals.

FEV1 is a measure of the volume of air forcibly exhaled in the first second of a forced breath. AUC summarizes measurements across a time interval rather than relying on a single time point. Here, the primary outcome is an average area-under-the-curve measure, expressed in liters, for the change from the test-day baseline curve. The record identifies the primary endpoint and the intended comparison questions, but it does not report the non-inferiority margin or the full decision rules for those questions. Those details matter when interpreting a claim of non-inferiority: observing similar estimates alone is not enough to reconstruct the prespecified criterion.

3. Trial Design

This was a Phase 3, randomized, double-blind, parallel-group study of inhaled treatments for COPD. The registry lists enrollment of 1480 and identifies Boehringer Ingelheim as the sponsor. The study is marked completed. Its recorded start is 2006-11, and primary completion is recorded as 2008-04.

The three treatment groups with posted primary-outcome summaries were Combivent Respimat 20/100 mcg, Combivent CFC-MDI 36/206 mcg, and ipratropium Respimat 20 mcg. The analysis counts shown for those groups are 474, 482, and 468, respectively. These are the counts associated with the posted primary outcome, not a substitute for the registry’s overall enrollment figure. The record also lists corresponding-inhaler placebo for blinding purposes.

The registry summary describes treatment over 12 weeks and names FEV1 AUC from 0 to 6 hours on Day 85 as the primary outcome. It describes the intended comparison with Combivent MDI as a non-inferiority question, and comparisons with ipratropium Respimat as superiority over the 0-to-4-hour interval and non-inferiority over the 4-to-6-hour interval. The record also describes pharmacokinetic characterization over one dosing interval after 4 weeks in a subgroup. The posted outcome summaries do not give pharmacokinetic results.

Randomization, masking, and parallel allocation are specified, but the method used to generate or conceal the allocation, the exact masking procedures, and the distribution of participants across any additional groups are not reported in the registry record. The original sample-size justification and the full statistical analysis plan are also not reported. Those omissions limit how completely the trial’s design choices can be evaluated from the registry information alone.

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

StageCOMBIVENT Respimat 20/100 mcgCOMBIVENT CFC-MDI 36/206 mcgIpratropium Respimat 20 mcg
STARTED486491483
COMPLETED438436422
NOT COMPLETED485561

Reasons for not completing this period:

ReasonCOMBIVENT Respimat 20/100 mcgCOMBIVENT CFC-MDI 36/206 mcgIpratropium Respimat 20 mcg
AE due to study disease worsening141920
AE due to other disease worsening210
AE due to other condition31415
Protocol Violation749
Lost to Follow-up214
Withdrawal by Subject121110
Other reasons - not mentioned above853

Analysis population for the primary outcome, as defined in the registry: Full Analysis Set for Pulmonary Function Test Data

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 treated set (TS) included all randomized patients who were documented to have taken at least one actuation of the randomized treatment.

CharacteristicUnitCOMBIVENT Respimat 20/100 mcgCOMBIVENT CFC-MDI 36/206 mcgIpratropium Respimat 20 mcgTotal
Participants analysed4864914831460
Age, Continuousyears63.8 (SD 8.7)64.2 (SD 9.2)64.3 (SD 8.6)64.1 (SD 8.8)
Sex: Female, Male: FemaleParticipants170169166505
Sex: Female, Male: MaleParticipants316322317955
Race/Ethnicity, Customized: Whiteparticipants4304424281300
Race/Ethnicity, Customized: Blackparticipants27252678
Race/Ethnicity, Customized: Asianparticipants29242982
Heightcm168.8 (SD 9.1)169.4 (SD 9.4)168.8 (SD 9.5)169.3 (SD 9.3)
Weightkg78.2 (SD 20.0)77.8 (SD 19.3)77.3 (SD 21.0)77.8 (SD 20.1)
Alcoholic history: Non drinkerparticipants223232223678
Alcoholic history: Drinks - not interfere with participation in trialparticipants263258260781
Alcoholic history: Drinks-poss. interfere with participation in trialparticipants0101
Smoking historypack years51.7 (SD 27.7)52.4 (SD 27.1)55.4 (SD 27.6)53.2 (SD 27.5)
COPD durationyears8.2 (SD 6.1)8.6 (SD 6.5)8.5 (SD 6.4)8.4 (SD 6.3)

6. Primary Endpoint

The registry lists the primary outcome as FEV1 AUC0-6 at Day 85, measured over Before drug administration to 6 hours after drug administration on Day 85.

ElementRegistry entry
Result typeLeast Squares Mean
Measure of spreadStandard Error
Unitliters
Endpoint classificationContinuous Endpoint

The primary endpoint is FEV1 AUC from 0 to 6 hours at Day 85, reported in liters. The registry defines it as the area between the test-day baseline FEV1 and the curve of change from that baseline from 0 to 6 hours, divided by 6. In practical terms, it summarizes the average change across the measurement interval, rather than describing only one measurement taken at a particular moment.

General statistical context: an area-under-the-curve endpoint can capture both the size and the time pattern of measurements over a stated interval. Averaging across that interval may give a broader summary of response during the dosing period than a single time-point measure. It also means the result depends on the selected interval and how the repeated measurements are collected and summarized. This endpoint concerns lung function; it is not, by itself, a summary of symptoms, daily functioning, exacerbations, or overall safety.

The primary measure is listed as a least-squares mean with standard error, in the Full Analysis Set for Pulmonary Function Test Data. The posted arm summaries are 0.145 liters for Combivent Respimat, 0.149 liters for Combivent MDI, and 0.119 liters for ipratropium Respimat. These are group estimates, not individual participant values. The registry also reports secondary FEV1 AUC outcomes at earlier study days and over other intervals. The primary endpoint’s stated time frame is before drug administration through 6 hours after administration on Day 85.

The endpoint definition makes the unit and time interval clear. However, details such as the handling of unavailable measurements and the exact covariate specification are not reported in the registry record, so the posted summary cannot fully describe how every participant’s repeated measurements contributed to the estimate.

7. Results Posted in the Registry

Mean difference: COMBIVENT CFC-MDI 36/206 mcg

0.00

95% CI: -0.02 to 0.02

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals0.10.10.10.10.20.2COMBIVENT Respimat 20/100 mcg (n=474)COMBIVENT CFC-MDI 36/206 mcg (n=482)Ipratropium Respimat 20 mcg (n=468)liters (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)COMBIVENT CFC-MDI 36/206 mcgIpratropium Respimat 20 mcg-0.05-0.03-0.02-0.000.010.03mean difference vs control (95% CI)

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.

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
FEV1 AUC0-6 at Day 1Continuous EndpointMean difference0.02 (-0.01 to 0.04)1,877 per arm
FEV1 AUC0-6 at Day 29Continuous EndpointMean difference0.01 (-0.01 to 0.03)7,505 per arm
FEV1 AUC0-6 at Day 57Continuous EndpointMean difference0.01 (-0.01 to 0.03)1,877 per arm

FEV1 AUC0-6 at Day 1

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)COMBIVENT CFC-MDI 36/206 mcgIpratropium Respimat 20 mcg-0.08-0.05-0.03-0.000.020.05mean difference vs control (95% CI)

FEV1 AUC0-6 at Day 29

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)COMBIVENT CFC-MDI 36/206 mcgIpratropium Respimat 20 mcg-0.05-0.04-0.02-0.000.020.03mean difference vs control (95% CI)

FEV1 AUC0-6 at Day 57

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)COMBIVENT CFC-MDI 36/206 mcgIpratropium Respimat 20 mcg-0.05-0.04-0.020.000.020.04mean difference vs control (95% CI)

The posted secondary summaries continue the same broad pattern seen in the primary endpoint: the Combivent Respimat arm has higher mean FEV1 AUC values than the ipratropium Respimat arm at the reported 0-to-6-hour assessments, while the Combivent MDI arm means are somewhat higher than those for Combivent Respimat. The secondary summaries cover Day 1, Day 29, and Day 57. The registry lists additional secondary outcome measures across other intervals and days, but the results and comparisons should be read in light of the particular outcomes and time points displayed.

This repeated pattern across study visits helps describe the posted lung-function data over time. It does not remove the distinction between the primary and secondary endpoints. The primary endpoint is the 0-to-6-hour measure at Day 85; secondary results at earlier visits or other intervals do not replace that primary result, nor do they automatically confirm the study’s planned questions about the 0-to-4-hour and 4-to-6-hour intervals.

The registry reports 86 outcome measures and 66 analyses. General statistical context: when researchers examine many outcomes, time points, and comparisons, some results may appear notable by chance. Adjustments, a prespecified hierarchy, or other safeguards can help control the interpretation of multiple tests, but the registry record does not report whether such a strategy was used. The simple recalculations are unadjusted. Therefore, they should not be treated as a collection of independent confirmatory findings.

Secondary outcomes can add context by showing whether the observed pattern recurs, but they generally carry less weight than a clearly prespecified primary analysis when the analysis plan and multiplicity procedures are unavailable. Here, the registry summary identifies the planned primary question, yet does not give the full hierarchy or adjustment approach. The secondary results are consequently most useful as descriptive supporting information, rather than as separate proof of a treatment effect or of the trial’s non-inferiority hypotheses.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The posted primary-outcome means are 0.145 liters for Combivent Respimat, 0.149 liters for Combivent MDI, and 0.119 liters for ipratropium Respimat. The tables on this page show the associated estimates, uncertainty summaries, and recalculated comparisons. They should be read as summaries of the posted data, not as a complete account of the sponsor’s inferential analysis.

For the Combivent Respimat versus Combivent MDI comparison, the recalculated unadjusted mean difference is 0.004 liters, with a 95% confidence interval from -0.015 to 0.023 and an unadjusted p-value of 0.686. The sponsor’s reported ANCOVA analysis is classified in the registry as a non-inferiority-or-equivalence analysis. Its reported estimate and confidence interval do not numerically match the simple recalculation. Because the discrepancy flag is true, the sponsor’s own analysis takes precedence over the recalculation when describing the trial’s formal comparison. The registry record does not state the non-inferiority margin, so the sponsor’s result cannot be independently judged against that margin from the information.

For the comparison with ipratropium Respimat, the recalculated unadjusted mean difference is -0.026 liters, with a 95% confidence interval from -0.045 to -0.007 and an unadjusted p-value of 0.009. The negative direction reflects the ordering used in the recalculated comparison: ipratropium Respimat minus Combivent Respimat. The group means themselves are 0.119 and 0.145 liters. These unadjusted calculations are not a replacement for a sponsor-reported model or a prespecified multiplicity-controlled analysis.

General interpretation: a confidence interval indicates a range of estimates compatible with the data and the assumptions of the calculation. A p-value describes how unusual the data would be under a specified null model; it does not establish clinical importance or verify a study’s design assumptions. In this case, the trial summary specifies different questions and time intervals, while the posted primary outcome is the 0-to-6-hour measure at Day 85. A result for that endpoint should not be treated as an answer to every planned comparison.

The record identifies the trial as completed and posts the three primary-outcome means, but it does not provide the full statistical analysis plan, the non-inferiority margin, or a multiplicity strategy. Consequently, the safest reading is descriptive: the posted means and recalculated contrasts show the pattern and precision of this endpoint, while formal conclusions about the sponsor’s stated hypotheses depend on the sponsor’s analysis and criteria. These lung-function summaries alone do not establish effects on outcomes that were not measured.

10. Statistical Methods Explained

The posted outcome is continuous: each participant contributes a lung-function measure expressed in liters, and the arm summaries report means. The primary outcome uses least-squares means and standard errors. General statistical context: a least-squares mean is a model-based group estimate, often adjusted for covariates in the analysis model. The registry does not provide enough detail to identify every covariate or reproduce the model specification from the summary alone.

What do the recalculated comparisons represent?

The comparison tables include simple, unadjusted recalculations from the posted arm summaries. They express the contrast as a mean difference and give an approximate confidence interval and unadjusted p-value. These calculations do not reproduce an ANCOVA model or account for covariates and other prespecified features that may have been used by the sponsor. The recalculated standard deviation is marked as approximate because it is inferred from the posted standard errors. Therefore, these values are useful as a transparent summary of the group-level information, but they are not the sponsor’s formal analysis.

The direction of a mean difference depends on the order of groups used in the contrast. For the recalculated comparison with ipratropium Respimat, the negative estimate is consistent with the posted mean being lower in the ipratropium group than in the Combivent Respimat group under that ordering. A negative value is not inherently favorable or unfavorable; its interpretation depends on which group is subtracted from which and on the endpoint’s meaning.

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

General explanation: a confidence interval expresses uncertainty around an estimated contrast under the calculation’s assumptions. A wider interval indicates less precision; a narrower interval indicates greater precision. If an interval includes zero for a difference, the data are compatible with a range that includes no difference under that particular analysis. This does not prove equality. Likewise, a p-value is not the probability that the null hypothesis is true, and it does not measure the size or importance of a difference.

The recalculated p-values are unadjusted. The record reports many outcomes and analyses, including 86 outcome measures and 66 analyses. When many hypotheses are examined, the chance of at least one apparently notable result can increase unless the analysis plan handles multiplicity. The registry record does not report whether or how multiplicity was addressed. Accordingly, the recalculated p-values should not be read as if they were necessarily adjusted or as if every comparison had been designated as a primary confirmatory test.

Why is the sponsor analysis treated separately?

The registry reports an ANCOVA comparison between Combivent Respimat and Combivent MDI for the primary outcome, classified as a non-inferiority-or-equivalence analysis. ANCOVA is a general analysis approach that compares groups while accounting for selected covariates. The sponsor’s analysis is not identical to the simple recalculation from posted group means and standard errors. The discrepancy flag indicates that the two should not be presented as interchangeable. The sponsor’s own analysis takes precedence for the sponsor’s formal trial comparison; the recalculation remains a descriptive, unadjusted check.

Non-inferiority requires more than a nonsignificant test of difference. General explanation: it normally depends on a prespecified margin defining how much worse an intervention could be while still meeting the non-inferiority criterion, together with a suitable confidence interval and analysis approach. The margin and the full decision rule are not reported in the registry record, so the posted results cannot be used to reconstruct whether that criterion was met. Nor does a similarity in observed means alone demonstrate non-inferiority.

What can be inferred from the analysis population?

The primary endpoint specifies the Full Analysis Set for Pulmonary Function Test Data. This identifies the population attached to the posted outcome but does not by itself describe the exact inclusion rules, departures from random assignment, or treatment of missing measurements. Those details are not reported in the registry record. General statistical context: different analysis populations can answer somewhat different questions, and missing-data assumptions can affect model-based estimates. Without the relevant definitions and procedures, the reader should avoid assuming a particular imputation method or a particular handling of incomplete follow-up.

The study summary describes a randomized, double-blind, parallel-group design and a treatment period of 12 weeks. The posted primary outcome is at Day 85, while the listed secondary FEV1 AUC summaries include earlier days. The registry does not report interim analyses, stopping rules, or the original sample-size justification. These omissions prevent a full assessment of whether the timing and size of the analyses followed a prespecified plan.

Finally, the arm-level standard errors quantify uncertainty in the reported means, not the spread of individual participant measurements. The recalculated comparison uses an approximate pooled standard deviation, as indicated in the posted calculation details. This matters because a reanalysis based on summaries necessarily relies on assumptions that may not match the trial’s full participant-level model. The calculations can illustrate the scale and precision of the contrast, but they cannot replace access to the complete analysis specification or data.

11. Confidence Intervals and Precision

The primary-outcome arm means are reported with standard errors of 0.007 liters for each of the three groups. The standard error describes uncertainty in an estimated mean; it is not the standard deviation of individual participant measurements. The posted group counts are 474 for Combivent Respimat, 482 for Combivent MDI, and 468 for ipratropium Respimat.

For the recalculated comparison of Combivent Respimat with Combivent MDI, the mean difference is 0.004 liters and the 95% confidence interval runs from -0.015 to 0.023. This interval spans zero and permits values on either side of zero under the unadjusted calculation. The associated unadjusted p-value is 0.686. These values describe the recalculation, not the sponsor’s ANCOVA result.

For the recalculated comparison with ipratropium Respimat, the mean difference is -0.026 liters and the 95% confidence interval runs from -0.045 to -0.007. This interval is below zero using the stated contrast ordering. The unadjusted p-value is 0.009. These results describe an unadjusted summary comparison and do not establish that the contrast meets a prespecified clinical threshold.

General explanation: a confidence interval is a measure of statistical precision, not a guarantee that the true effect lies within the interval. It depends on the assumptions of the analysis. The recalculated intervals are based on posted summary statistics, with an approximate standard deviation, while the sponsor reports an ANCOVA analysis for the comparison with Combivent MDI. Because the sponsor result and recalculation differ, the sponsor’s analysis takes precedence for its formal comparison.

The record does not report a clinically important difference threshold for this endpoint. Therefore, the intervals can show the range of statistical uncertainty in the estimates, but they cannot establish whether values within that range would be meaningful to patients or clinicians. Nor can a confidence interval for this single lung-function measure describe uncertainty about unreported outcomes.

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.

Effect to detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect22,98230,766
75% of the observed effect40,85654,694
50% of the observed effect91,925123,062
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect20,00050,000100,000200,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Standard deviation was approximated from model-based standard errors, so treat it as rough. Calculated for the comparison: COMBIVENT CFC-MDI 36/206 mcg.

The sample-size table gives planning illustrations based on the observed contrast, not the original trial’s design calculation. For these continuous outcomes, entries are participants per arm; they are not total event counts. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set at the listed fraction of the observed effect. The original trial’s own sample-size assumptions and justification are not reported in the registry record.

The 80% power column indicates the illustrative number of participants per arm under which the assumed effect would be detected in 80% of repeated studies if the planning assumptions held. The 90% power column gives the corresponding planning target for 90% of repeated studies. These are prospective planning concepts; this is not observed power.

Rows based on 100%, 75%, and 50% of the observed effect show how the illustration changes when the effect to detect is made smaller. Smaller effects are harder to distinguish from random variation, so the table requires more participants per arm for those assumptions. The very large planning figures for the small observed contrast against Combivent MDI reflect the scale of that observed contrast relative to the variability used in the calculation; they do not mean the trial should have enrolled those numbers under its own protocol.

Use the table and curve to compare assumptions, not to judge the completed study by a retrospective target. The illustrations use simple assumptions and observed effects, whereas a real design may rely on a prespecified clinically meaningful difference, a non-inferiority margin, model choices, expected missingness, and other design features. Those original choices are not reported. The displayed calculations should therefore be interpreted as planning scenarios only.

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 z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

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 = 0.004; pooled standard deviation σ = 0.153.
  2. n = 2 × (1.96 + 0.842)2 × 0.1532 / 0.0042 = 22,981.2, rounded up to 22,982 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 <- 0.004                      # observed difference in means
sigma <- 0.153047847439518                     # 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(400153)
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 = 22,982 (80% power), 30,766 (90% power)
 75% of observed effect: n per arm = 40,856 (80% power), 54,694 (90% power)
 50% of observed effect: n per arm = 91,925 (80% power), 123,062 (90% power)
power.t.test: 22982.1 
Simulated power at n = 22,982 per arm: 0.801 (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. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
ANCOVAMean Difference (Final Values) -0.0035-0.0222 to 0.01520.714
Where the two analyses differ, rely on the sponsor's. The simple re-calculation above reaches a different conclusion from the sponsor's analysis, usually because the sponsor adjusts for covariates, stratification or repeated measures, or (for event rates) uses a negative binomial model that allows for over-dispersion and so gives wider intervals.

The registry reports a sponsor ANCOVA analysis for the primary comparison between Combivent Respimat and Combivent MDI. It is classified as a non-inferiority-or-equivalence analysis, and its reported confidence interval spans values below and above zero. The registry also posts arm-level means and a separate simple, unadjusted recalculation from summary statistics. Those are not the same analysis: the recalculated mean difference is 0.004 liters, with a 95% confidence interval from -0.015 to 0.023, while the sponsor’s reported estimate and interval differ.

Because the discrepancy flag is true, the sponsor’s own analysis takes precedence when describing the formal trial comparison. The recalculation is best treated as a transparent descriptive check based on the posted means and standard errors, not as a correction to the sponsor result. The registry’s sponsor analysis is the relevant analysis to consult for the sponsor’s stated hypothesis, but the registry record does not report the non-inferiority margin or full analysis plan. Without those, this page cannot independently confirm the formal non-inferiority decision rule or reproduce the sponsor’s model.

General statistical context: non-inferiority conclusions depend on the prespecified margin and how the confidence interval compares with it, not only on whether a conventional test for a difference is statistically significant. The registry gives the analysis category, but not enough information to apply the full criterion. The page therefore distinguishes the sponsor’s reported analysis from the recalculated estimate and avoids treating either one as a stand-alone clinical conclusion.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists 86 outcome measures and 66 analyses, with several FEV1 AUC intervals and study days represented among the outcomes. Examining multiple endpoints and contrasts raises a multiplicity issue: if many tests are considered, the chance of at least one apparently unusual result can increase. General statistical context: a trial may address this through a prespecified testing order, adjusted significance thresholds, or another strategy, but the appropriate method depends on the hypotheses and design.

The multiplicity strategy is not reported in the registry record. The record also does not report whether the sponsor used a hierarchy among the primary and secondary hypotheses, how the stated non-inferiority and superiority questions were sequenced, or whether the posted p-values were adjusted. The recalculated comparisons are explicitly unadjusted and should not be interpreted as multiplicity-controlled results.

The primary outcome names the Full Analysis Set for Pulmonary Function Test Data. However, detailed inclusion rules for that set, the number of participants with missing endpoint data, reasons for missingness, and the method used to handle missing measurements are not reported in the registry record. The record does not specify whether any imputation was used, whether sensitivity analyses were conducted, or how incomplete repeated measurements were treated. No assumptions about those procedures should be made from the arm counts alone.

The registry also does not report interim analyses, stopping rules, or the original sample-size justification. These details can influence how final results and p-values should be interpreted, but their absence does not imply that any particular procedure was or was not used. It means only that the posted registry information is insufficient to assess those elements.

These gaps are important for a careful reading, especially because the study summary describes distinct non-inferiority and superiority questions. The non-inferiority margin is not reported, and neither is the complete analysis plan. Thus, the available record supports a description of the posted endpoint estimates, but not a full reconstruction of the planned confirmatory testing framework or the impact of missing data and multiple comparisons.

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

The posted results describe average FEV1 AUC values for three treatment groups at a specified time point and over a specified measurement interval. They show the pattern and uncertainty of those group summaries. The primary comparison with Combivent MDI has a sponsor-reported ANCOVA analysis and a separate unadjusted recalculation; because those differ, the sponsor’s own analysis takes precedence for the formal comparison. The registry does not provide the non-inferiority margin needed to assess the sponsor’s stated criterion independently.

The recalculated comparison with ipratropium Respimat indicates a difference in the posted group means, with an unadjusted confidence interval below zero under the displayed contrast ordering. That calculation is based on summary statistics and is not the sponsor’s complete participant-level analysis. The results should therefore be considered statistical descriptions of this endpoint, not a broad judgment about treatment.

General statistical context: statistical evidence about a continuous lung-function measure does not, by itself, establish the size of a benefit that matters to patients. The registry record does not give a clinically important difference threshold. Nor does an endpoint measuring FEV1 AUC directly summarize symptoms, daily activity, exacerbations, long-term outcomes, or overall benefit and harm. Those questions require their own outcomes and analyses.

The record includes adverse-event counts for affected participants in the three groups, but the numbers at risk and deaths are not reported in the posted adverse-event summary. Serious-event terms are listed, but the table information does not provide enough context to make a complete comparative safety assessment. These counts should not be converted into rates or used to infer comparative risk without denominators and additional details.

Accordingly, the results do not establish that one treatment is clinically superior in every relevant respect, that treatments are interchangeable, or that findings apply beyond the studied population and trial conditions. They do not resolve the trial’s non-inferiority questions without the margin and full analysis rules. They describe the posted lung-function outcomes, with the limitations of the registry record made explicit.

17. Why This Trial Matters Statistically

This trial illustrates why the label attached to a comparison matters. The study summary describes non-inferiority questions as well as a superiority question, and the registry classifies the sponsor’s primary comparison with Combivent MDI as a non-inferiority-or-equivalence analysis. A simple test for a difference and a non-inferiority assessment answer different questions. Without the margin, readers cannot reconstruct the key threshold for the latter.

The record also illustrates the difference between an adjusted sponsor analysis and a calculation from group summaries. Posted arm means are useful for seeing the outcome pattern, and an unadjusted recalculation can make the contrast and its uncertainty more transparent. But a summary-statistic calculation cannot be assumed to reproduce ANCOVA. When the results differ, the sponsor’s own analysis takes precedence for the formal trial question.

Another statistical lesson is that multiple time points and outcome intervals create a larger interpretive landscape than a single primary endpoint. The posted secondary pattern can provide context, but the registry does not report the multiplicity strategy or full testing hierarchy. Repeatedly observing a similar direction is not the same as having a prespecified, multiplicity-controlled confirmation.

Finally, this example shows why precision and clinical meaning should be considered separately. Confidence intervals describe uncertainty in the estimates, while the registry does not state a clinically important difference threshold. The endpoint summarizes lung function over a defined interval, not every aspect of COPD or treatment experience. A careful statistical reading therefore distinguishes what was measured, what the posted comparisons estimate, and what the record does not allow readers to conclude.

18. Limitations

Several trial-specific limitations follow from the information available in the registry record. The sponsor’s primary ANCOVA result and the simple recalculation from group summaries do not numerically match. The discrepancy flag is true, so the sponsor’s own analysis takes precedence for the formal comparison. However, the record does not give enough model detail to reproduce that analysis independently.

The non-inferiority margin for the Combivent Respimat versus Combivent MDI comparison is not reported. The registry also does not provide the full statistical analysis plan, including any covariates, testing hierarchy, or multiplicity adjustment. This limits independent assessment of the sponsor’s stated hypotheses and makes the unadjusted secondary comparisons less definitive.

The reported primary endpoint is a lung-function summary at Day 85. The endpoint does not capture every clinically relevant dimension of COPD. The registry record does not report a threshold for clinical importance, so the statistical estimates cannot be translated into a judgment about the practical importance of the observed differences.

The posted adverse-event summary gives affected-participant counts, but the numbers at risk and deaths are null in the record. Without the relevant denominators and fuller safety information, the counts cannot support a complete comparison of adverse-event rates. The available serious-event terms are a partial description, not a comprehensive safety analysis.

Finally, details about missing outcome data, the exact rules for the Full Analysis Set, interim analyses, stopping rules, and the original sample-size justification are not reported in the registry record. These are limits of what can be assessed from this record; they do not establish that the trial lacked such procedures.

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22. Record Summary

The registry describes a completed Phase 3, randomized, double-blind, parallel-group study of inhaled treatments in COPD, with total enrollment of 1480. The primary endpoint is FEV1 AUC from 0 to 6 hours at Day 85, reported in liters for the Full Analysis Set for Pulmonary Function Test Data.

Posted primary-outcome means are 0.145 liters for Combivent Respimat, 0.149 liters for Combivent MDI, and 0.119 liters for ipratropium Respimat. The registry reports an ANCOVA analysis for the comparison with Combivent MDI and separate unadjusted recalculations are shown in the tables. Because these do not match, the sponsor’s own analysis takes precedence for its formal comparison.

The record does not report the non-inferiority margin, complete analysis plan, multiplicity strategy, or missing-data procedures. The posted estimates describe lung-function outcomes and should not be extended to unreported outcomes or interpreted as a complete assessment of clinical importance or safety.

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