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Asthma Phase 3 Continuous Endpoint NCT01181895

Study B2C112060: A Study of the Efficacy and Safety of Vilanterol Inhalation Powder in Adults and Adolescents With Persistent Asthma: Complete Statistical Analysis

This analysis examines a randomized, placebo-controlled asthma trial of vilanterol and salmeterol, focusing on the change in weighted-mean 24-hour FEV1 at Week 12. It also considers posted secondary outcomes, adverse-event counts, confidence intervals, and illustrative sample-size planning.

Trial start: 2010-09-01  ·  Enrollment: 348  ·  Sponsor: GlaxoSmithKline
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 Study B2C112060: A Study of the Efficacy and Safety of Vilanterol Inhalation Powder in Adults and Adolescents With Persistent Asthma (NCT01181895), a randomized phase 3 study. The primary outcome is Change From Baseline in Weighted-mean 24-hour Serial Forced Expiratory Volume in One Second (FEV1) at Week 12.

348
Enrollment
Phase 3
3
Arms
In the primary outcome
0.07
Mean difference
Vilanteral 25 µg OD
-0.05–0.19
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01181895
PhasePhase 3
ConditionAsthma
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment348
Arms in the primary outcome3
Lead sponsorGlaxoSmithKline
Results postedYes

2. Clinical Question

Population

Adults and adolescents 12 years of age and older with persistent asthma uncontrolled on inhaled corticosteroids. The primary outcome population was the Intent-to-Treat population: randomized participants who received at least one dose of study medication, with assessment limited to those available at the indicated time point.

Intervention

Vilanterol inhalation powder, listed as 25 µg once daily, with placebo inhalation powder via Diskus twice daily for 12 weeks.

Comparator

Placebo inhalation powder via NDPI once daily and placebo inhalation powder via Diskus twice daily for 12 weeks. A salmeterol inhalation powder group, listed as 50 µg twice daily, was also included.

Primary question

What was the change from baseline to Week 12 in weighted-mean 24-hour FEV1 in the vilanterol and salmeterol groups compared with placebo? FEV1 is the volume of air forcefully exhaled in one second.

The trial record describes persistent asthma in participants whose asthma was uncontrolled on inhaled corticosteroids. The central comparison concerns lung function at Week 12, measured as change from the Day 1 pre-dose baseline. The analysis includes three parallel groups: placebo, vilanterol, and salmeterol. The placebo regimen used matching inhaled powders on the same once-daily and twice-daily schedules described for the active regimens.

The clinical question is not limited to the primary lung-function measure. Registered secondary outcomes include rescue-free and symptom-free periods, serial FEV1 measurements, peak expiratory flow, early changes in FEV1, and global assessments of change. These outcomes broaden the questions about symptoms, rescue medication, and lung function over the treatment period. However, the primary comparison remains the Week 12 weighted-mean 24-hour FEV1 endpoint. The registry record does not report a specific threshold for a clinically important difference.

3. Trial Design

This was a completed Phase 3, randomized, double-blind, double-dummy, parallel-group, placebo-controlled, multicenter study. It evaluated vilanterol and salmeterol against placebo in adults and adolescents with persistent asthma uncontrolled on inhaled corticosteroids. Enrollment was 348. The study began on 2010-09-01, and primary completion was 2011-08-01.

Randomization assigns participants to treatment groups by chance, while double masking is intended to reduce the influence of treatment knowledge on participant experience and outcome assessment. The double-dummy design used placebo inhalation powders to accompany the different active dosing schedules. Participants assigned to vilanterol received vilanterol once daily plus placebo via Diskus twice daily. Those assigned to salmeterol received placebo via NDPI once daily plus salmeterol twice daily. The placebo group received placebo by both routes and schedules. The registry record does not report further details about how randomization was generated, how allocation was concealed, or who was masked.

The reported primary outcome analysis used available participants at the indicated time point within the stated Intent-to-Treat population. The number assessed for the primary endpoint differed among groups: 95 for placebo, 101 for vilanterol, and 100 for salmeterol. These outcome counts are not the same as the adverse-event risk counts, which are reported separately. The registry record does not explain the relationship between those counts or give a detailed participant flow.

The study objective was to evaluate efficacy and safety over a 12-week treatment period. The record lists eight outcome measures, with seven secondary outcomes posted. It does not report the original sample-size justification, the trial's planned power, or its complete statistical analysis plan. The record also does not describe interim analyses or stopping rules.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Before assignment: Participants (par.) meeting eligibility criteria at the Screening visit completed a 28-day Run-in Period for Baseline, safety evaluations, and measures of asthma status. Par. were then randomized to an 8-week Treatment Period. A total of 583 par. were screened, and 347 were randomized, of which 298 received at least one dose of study treatment.

Overall Study

StagePlaceboVilanteral 25 µg ODSalmeterol 50 µg BID
STARTED116115116
COMPLETED9910198
NOT COMPLETED171418

Reasons for not completing this period:

ReasonPlaceboVilanteral 25 µg ODSalmeterol 50 µg BID
Adverse Event311
Lack of Efficacy899
Protocol Violation210
Lost to Follow-up012
Investigator Discretion121
Withdrawal by Subject305

Analysis population for the primary outcome, as defined in the registry: Intent-to-Treat (ITT) Population: all participants randomized to treatment who received at least one dose of study medication. Only those participants available at the indicated time point were assessed.

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.

CharacteristicUnitPlaceboVilanteral 25 µg ODSalmeterol 50 µg BIDTotal
Participants analysed116115116347
Age, ContinuousYears41.7 (SD 16.64)41.0 (SD 17.81)41.1 (SD 16.84)41.3 (SD 17.06)
Sex: Female, Male: FemaleParticipants596877204
Sex: Female, Male: MaleParticipants574739143
Race/Ethnicity, Customized: African American/African HeritageParticipants115622
Race/Ethnicity, Customized: American Indian or Alaska NativeParticipants374441122
Race/Ethnicity, Customized: Japanese/East Asian HeritageParticipants0011
Race/Ethnicity, Customized: WhiteParticipants686668202

6. Primary Endpoint

The registry lists the primary outcome as Change From Baseline in Weighted-mean 24-hour Serial Forced Expiratory Volume in One Second (FEV1) at Week 12, measured over Baseline and Week 12.

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

The primary endpoint is change from baseline in weighted-mean 24-hour serial FEV1 at Week 12, measured in liters. FEV1 is the volume of air that can be forcefully exhaled in one second and is used as a measure of lung function. The baseline measurement was the Day 1 pre-dose FEV1. Change was defined as the Week 12 weighted-mean 0-24 hour FEV1 minus that baseline value.

The weighted mean combines pre-dose and post-dose measurements. The listed post-dose times were 5, 15, and 30 minutes and 1, 2, 3, 4, 11, 12, 12.5, 13, 14, 16, 20, 23, and 24 hours. Taking measurements across the day gives an endpoint intended to represent lung function over the full 24-hour interval, rather than relying on a single measurement. This is a general explanation of why repeated measurements can be combined into a time-weighted summary; the registry record defines the specific measurements used in this trial.

The posted group estimates are least-squares means with standard errors. The primary analysis was an analysis of covariance, or ANCOVA, with baseline FEV1, region, sex, age, and treatment as covariates. In general, ANCOVA compares outcome means while adjusting for specified characteristics, including the baseline value. The endpoint is therefore an adjusted comparison of mean change, not simply a comparison of unadjusted individual observations. The registry record does not report the clinical threshold that would distinguish a small from a meaningful change for participants.

7. Results Posted in the Registry

Mean difference: Vilanteral 25 µg OD

0.07

95% CI: -0.05 to 0.19

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals0.20.20.30.30.40.5Placebo (n=95)Vilanteral 25 µg OD (n=101)Salmeterol 50 µg BID (n=100)Liters (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Vilanteral 25 µg ODSalmeterol 50 µg BID-0.15-0.08-0.000.070.140.21mean 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
Change From Baseline in the Percentage of Rescue-free 24-hour (hr) Periods During the 12-week Treatment PeriodContinuous EndpointMean difference7.10 (-0.37 to 14.57)261 per arm
Change From Baseline in the Percentage of Symptom-free 24-hour (hr) Periods During the 12-week Treatment PeriodContinuous EndpointMean difference6.70 (-0.41 to 13.81)265 per arm
Change From Baseline in Daily Trough (Pre-dose and Pre-rescue Bronchodilator) PM (Evening) Peak Expiratory Flow (PEF) Averaged Over the 12-week Treatment PeriodContinuous EndpointMean difference13.90 (5.18 to 22.62)93 per arm

Change From Baseline in the Percentage of Rescue-free 24-hour (hr) Periods During the 12-week Treatment Period

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Vilanteral 25 µg ODSalmeterol 50 µg BID-1.672.095.859.611317mean difference vs control (95% CI)

Change From Baseline in the Percentage of Symptom-free 24-hour (hr) Periods During the 12-week Treatment Period

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Vilanteral 25 µg ODSalmeterol 50 µg BID-1.561.785.118.451215mean difference vs control (95% CI)

Change From Baseline in Daily Trough (Pre-dose and Pre-rescue Bronchodilator) PM (Evening) Peak Expiratory Flow (PEF) Averaged Over the 12-week Treatment Period

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Vilanteral 25 µg ODSalmeterol 50 µg BID-2.852.628.09141925mean difference vs control (95% CI)

The posted secondary outcomes cover several aspects of asthma symptoms and lung function, including rescue-free and symptom-free periods, peak expiratory flow, and serial FEV1 assessments. The registry lists eight outcome measures overall and posts results for seven secondary outcomes. The secondary results broaden the outcome picture beyond the primary Week 12 weighted-mean FEV1 comparison, but they do not replace it.

Across the posted continuous secondary outcomes, the group estimates and recalculated contrasts do not all point in the same direction or have the same degree of separation. Some comparisons have intervals that include zero, while other posted recalculations have intervals that do not. This variation means the secondary outcomes should be interpreted as a collection of related findings rather than as a single uniform pattern. The registry does not post sponsor analyses for the secondary outcomes in the record covered by these results.

Secondary outcomes can help describe whether the primary result is accompanied by patterns in symptoms, rescue medication use, or other lung-function measures. However, a secondary measure answers a different question and may have a different measurement scale, timeframe, and precision. A finding on a secondary outcome does not by itself establish a corresponding effect on the primary endpoint.

Unadjusted secondary results carry less weight when many outcomes or comparisons are examined because the chance of at least one apparently notable result can increase across a set of tests. This is a general statistical concern. The registry record does not report whether a multiplicity procedure was planned or applied, so the secondary p-values should not be treated as if they were confirmed under an adjustment that is not documented. The posted endpoint estimates remain descriptive evidence, with their uncertainty and analysis status considered individually.

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

9. Statistical Interpretation

Clinical Biostats interpretation

At Week 12, the posted least-squares mean change in weighted-mean 24-hour FEV1 was 0.289 liters for placebo, 0.359 liters for vilanterol, and 0.283 liters for salmeterol. The sponsor-reported ANCOVA comparison of vilanterol with placebo was a mean difference of 0.070 liters, with a 95% confidence interval from -0.048 to 0.188 and p = 0.244. The sponsor-reported comparison of salmeterol with placebo was -0.006 liters, with a 95% confidence interval from -0.124 to 0.113 and p = 0.926.

Both sponsor-reported confidence intervals include zero, so the posted estimates are compatible with no mean difference as well as with differences in either direction. For vilanterol, the interval also includes positive values, while for salmeterol it includes both negative and positive values. The estimates therefore do not specify a precise treatment contrast. The p-values describe how compatible the data are with the null comparison under the analysis model; they do not measure the probability that a treatment is effective or ineffective.

The unadjusted recalculations based on posted summary statistics are similar to the sponsor's reported estimates. For vilanterol, the recalculated difference is 0.07 liters, with a confidence interval from -0.047 to 0.187 and an unadjusted p-value of 0.241. For salmeterol, the recalculated difference is -0.006 liters, with a confidence interval from -0.123 to 0.112 and an unadjusted p-value of 0.92. These recalculations are not replacements for the registry's ANCOVA results: they use summary statistics and do not reproduce the adjustment for the listed covariates. The registry record does not identify a discrepancy that would require the recalculated values to take precedence.

The comparison should be read alongside the group means and the uncertainty intervals. The vilanterol estimate is positive relative to placebo, but its confidence interval spans zero and a range of possible differences. The salmeterol estimate is close to zero, with an interval that also spans zero and permits differences in either direction. Neither estimate alone establishes whether a difference matters clinically; the registry record does not state a clinical-importance threshold.

The trial was randomized and double-blind, features that support a structured comparison, but these design features do not remove uncertainty in the estimates. The primary result describes the posted Week 12 outcome among the assessed participants in the stated analysis population. It should not be read as a conclusion about outcomes that were not measured, effects beyond the treatment period, or effects in people outside the trial population.

10. Statistical Methods Explained

The primary analysis used ANCOVA. This method models an outcome while adjusting for selected covariates. In this trial, the listed covariates were baseline FEV1, region, sex, age, and treatment. Adjusting for baseline FEV1 can account for differences in starting lung function when estimating the treatment-group contrast. The registry record reports the covariates, but does not provide the full model specification, diagnostics, or details about how model assumptions were assessed.

What does a least-squares mean represent?

A least-squares mean is an adjusted mean from a statistical model. Unlike a simple arithmetic mean, it reflects the model's adjustment for included covariates. The posted group values are least-squares mean changes, and the reported comparisons are ANCOVA mean differences. In general, adjusted estimates can differ from unadjusted differences because the model accounts for covariate information. The record does not provide individual participant data, so the posted adjusted estimates cannot be reconstructed from the group summaries alone.

The primary endpoint is continuous: change in FEV1 measured in liters. For a continuous outcome, a mean difference expresses the average contrast between two groups in the endpoint's measurement units. A positive difference in the vilanterol comparison means the estimated change was greater in that group than in placebo; a negative difference in the salmeterol comparison means the estimated change was lower than in placebo. Those directions describe the estimates, not whether a difference is important to patients.

Why are confidence intervals used?

A confidence interval conveys uncertainty around an estimated contrast. In general, it gives a range of values that are reasonably compatible with the data under the analysis method and its assumptions. Wider intervals indicate less precision than narrower intervals. The primary confidence intervals include zero, the value corresponding to no mean difference. Their breadth also indicates that estimates on either side of zero remain compatible with the posted results. The interval does not give the probability that the true effect lies within its endpoints.

The registry reports 95% confidence intervals for its ANCOVA comparisons. The recalculated intervals are unadjusted and are based on posted summary statistics. For those recalculations, the pooled standard deviations are approximate because the group-level dispersion values are standard errors. These summary-statistic calculations do not reproduce the sponsor's covariate adjustment. In general, standard errors quantify uncertainty in an estimate, while standard deviations describe variability among observations; they are related but are not interchangeable without information about sample size and the calculation used.

What do the p-values convey?

A p-value describes how unusual the observed data, or more extreme data, would be under a specified null model. It is not a measure of effect size, clinical relevance, or the chance that the null hypothesis is true. The registry reports p = 0.244 for vilanterol versus placebo and p = 0.926 for salmeterol versus placebo in the ANCOVA analyses. The unadjusted recalculations report p-values of 0.241 and 0.92, respectively. Those recalculated p-values belong to a different, unadjusted analysis and should not be presented as the trial's reported ANCOVA results.

General statistical practice often considers estimates, intervals, and p-values together rather than treating one statistic as a complete answer. Here, the estimates describe the observed direction and size of the mean contrasts; the intervals convey uncertainty; and the p-values summarize compatibility with a null comparison under the analysis. The registry record does not report whether any multiplicity adjustment was used for the primary or secondary outcomes.

Why does the analysis population matter?

The stated population includes randomized participants who received at least one dose, with only participants available at the indicated time point assessed. This definition matters because the endpoint estimates are based on the participants contributing data at that time. The record does not report how missing Week 12 measurements were handled, whether any imputation was used, or the reasons participants were unavailable. It also does not give enough information to assess the consequences of missing observations.

General statistical reasoning distinguishes the randomized population from the set with an observed outcome. Excluding unavailable outcomes can affect interpretation if the reasons for missingness are related to treatment or outcome. That possibility cannot be evaluated from the registry record alone. The posted analysis population definition should therefore be kept in view when interpreting the estimates, without assuming an unreported missing-data method.

What is meant by over-dispersion?

Over-dispersion is a general concern for certain count-data models when observed variability exceeds what a model assumes. The primary endpoint in this trial is a continuous FEV1 change, not a count outcome, so over-dispersion is not the central issue for the primary analysis. The registry does not report a count-model analysis for the primary endpoint. For continuous outcomes, the relevant modeling considerations include the assumptions behind the mean model and the uncertainty estimates; the record does not report diagnostic results for those assumptions.

11. Confidence Intervals and Precision

The registry's 95% confidence interval for vilanterol versus placebo is -0.048 to 0.188 liters around a reported mean difference of 0.070 liters. The interval crosses zero, so it includes both a negative contrast and a positive contrast. Its endpoints also indicate that the data do not pin the mean difference to a narrow range. The confidence interval is a measure of statistical precision, not a range of individual participant responses.

For salmeterol versus placebo, the reported mean difference is -0.006 liters, and the 95% confidence interval is -0.124 to 0.113 liters. This interval also crosses zero and extends in both directions. The estimate is close to zero, but the interval is the better guide to how much uncertainty remains around it. The posted result is not precise enough to rule out differences in either direction within the interval.

The intervals are based on the trial's reported ANCOVA analyses. Recalculated intervals from the summary statistics are close but not identical: -0.047 to 0.187 for vilanterol and -0.123 to 0.112 for salmeterol. Those are unadjusted recalculations and should not be confused with the sponsor-reported ANCOVA intervals. The registry record does not report a discrepancy requiring the recalculations to take precedence.

In general, precision depends on the amount of information contributing to an estimate, including the number of participants assessed and the variability of the outcome. The primary outcome counts were 95 for placebo, 101 for vilanterol, and 100 for salmeterol. The reported standard errors were 0.043, 0.042, and 0.042, respectively. These standard errors help characterize uncertainty in the group means, but they do not substitute for the adjusted confidence intervals for the treatment contrasts.

Neither confidence interval answers whether a possible difference is clinically meaningful. The registry record does not report a threshold for clinical importance. Statistical precision and clinical importance are distinct: a precise estimate may still be of limited clinical relevance, while an imprecise estimate may leave meaningful possibilities unresolved.

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 effect561750
75% of the observed effect9961,333
50% of the observed effect2,2412,999
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect5001,0002,0005,00040%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: Vilanteral 25 µg OD.

The sample-size figures are planning illustrations based on the observed effect, not the trial's original design assumptions. For continuous outcomes such as the primary FEV1 endpoint, the figures are participants per arm. The event-total convention applies to time-to-event planning displays; it does not apply to this continuous endpoint.

The listed 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 to the stated fraction of the observed effect. The 80% power column indicates the approximate number of participants per arm needed, under those assumptions, for an 80% chance of detecting the chosen effect if it is present. The 90% column gives the corresponding planning number for a 90% chance. These percentages describe the operating characteristics of a hypothetical design under its assumptions; they do not describe the probability that the observed result is correct.

Planning for a smaller effect requires more participants because a smaller difference is harder to distinguish from random variation. The figures therefore increase when the target is a smaller fraction of the observed effect. The effect used for planning is based on the observed estimate in this trial, which may not be the effect a future study should expect or target. The registry record does not report the trial's original sample-size justification or its own design assumptions. These figures are not observed power.

For interpretation, a planning number is conditional on the assumptions used to produce it. It is not a recommendation about the appropriate size of a future study and does not establish that a study with that number would answer every clinical question. The planning display concerns a two-group comparison with equal allocation, whereas the trial itself included placebo and two active-treatment groups. It should be read as an illustration of how the stated effect size and power target relate to sample size, rather than as a reconstruction of the trial design.

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 = 0.070; pooled standard deviation σ = 0.418.
  2. n = 2 × (1.96 + 0.842)2 × 0.4182 / 0.0702 = 560.0, rounded up to 561 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 <- 0.07                      # observed difference in means
sigma <- 0.418105183949399                     # 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(1181895)
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 = 561 (80% power), 750 (90% power)
 75% of observed effect: n per arm = 996 (80% power), 1,333 (90% power)
 50% of observed effect: n per arm = 2,241 (80% power), 2,999 (90% power)
power.t.test: 561 
Simulated power at n = 561 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) 0.070-0.048 to 0.1880.244
ANCOVAMean Difference (Final Values) -0.006-0.124 to 0.1130.926

The registry reports the sponsor's primary comparisons as ANCOVA results. For vilanterol versus placebo, the reported mean difference is 0.070 liters, with a 95% confidence interval from -0.048 to 0.188 and p = 0.244. For salmeterol versus placebo, the reported difference is -0.006 liters, with a 95% confidence interval from -0.124 to 0.113 and p = 0.926. These are the trial's posted adjusted analyses and should be the main reference for the primary result.

The unadjusted recalculations from the posted summary statistics are close to those estimates, but their intervals and p-values differ slightly. They do not use the listed ANCOVA adjustment for baseline FEV1, region, sex, age, and treatment. They are useful as a check on the direction and approximate scale of the posted contrasts, not as a substitute for the registry-reported analysis.

The registry record does not report a discrepancy between the sponsor's analysis and the recalculation. If a discrepancy were present, the sponsor's own analysis would take precedence. In general, this preference reflects the difference between a trial's reported model-based analysis and a simple reanalysis of summary data, which cannot reproduce all features of the original analysis.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary endpoint and multiple secondary outcomes, but a multiplicity strategy is not reported in the registry record. Multiplicity refers, in general, to the increased risk of false-positive findings when several hypotheses are tested. Statistical plans may address this by defining a hierarchy, adjusting significance thresholds, or using another procedure. None of those approaches can be assumed for this study from the record.

The primary outcome is the central confirmatory measure described in the trial objective. The additional outcomes can add context, but unadjusted secondary comparisons need cautious interpretation when the record does not say how multiple testing was handled. A nominal p-value from one secondary contrast does not automatically retain the same interpretation it would have had as a single prespecified test. The registry does not report whether the primary analysis was part of a prespecified testing sequence.

The endpoint population is described as randomized participants who received at least one dose, with only participants available at the indicated time point assessed. The registry record does not report the number missing for the primary outcome, the reasons for missingness, or the method used to handle missing outcome data. It also does not report whether sensitivity analyses were conducted. Without those details, it is not possible to assess how missing observations may have affected the estimates.

The record identifies the primary analysis as ANCOVA with baseline FEV1, region, sex, age, and treatment as covariates. It does not provide the complete statistical plan, model diagnostics, or details about handling deviations from model assumptions. Nor does it report interim analyses or any procedures related to early stopping. These absences limit what can be concluded about the full analysis process; they do not demonstrate that a particular procedure was or was not used outside what the registry reports.

16. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Placebo11160.9%
Vilanteral 25 µg OD11150.9%
Salmeterol 50 µg BID01160.0%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo0.9%Vilanteral 25 µg OD0.9%Salmeterol 50 µg BID0.0%% of participants with at least one serious adverse event

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 3% reporting threshold.

ArmParticipants affected of at risk
Placebo26 of 116
Vilanteral 25 µg OD26 of 115
Salmeterol 50 µg BID21 of 116

Most frequent serious adverse event terms

Event termOrgan systemPlaceboVilanteral 25 µg ODSalmeterol 50 µg BID
Sudden deathGeneral disorders1 of 1160 of 1150 of 116
AsthmaRespiratory, thoracic and mediastinal disorders0 of 1161 of 1150 of 116

Most frequent non-serious adverse event terms

Event termOrgan systemPlaceboVilanteral 25 µg ODSalmeterol 50 µg BID
NasopharyngitisInfections and infestations12 of 1169 of 1157 of 116
HeadacheNervous system disorders5 of 11610 of 1159 of 116
Oropharyngeal painRespiratory, thoracic and mediastinal disorders7 of 1166 of 1152 of 116
Upper respiratory tract infectionInfections and infestations8 of 1162 of 1152 of 116
PyrexiaGeneral disorders0 of 1164 of 1151 of 116
Musculoskeletal painMusculoskeletal and connective tissue disorders0 of 1160 of 1155 of 116

Serious events with the highest arm-level rate: asthma (0.9%), sudden death (0.9%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The registry reports serious adverse events among 116 participants at risk in the placebo group, 115 in the vilanterol group, and 116 in the salmeterol group. The serious adverse event counts were 1, 1, and 0, respectively. Asthma and sudden death are listed among the serious adverse event terms, each at 0.9%. The record does not assign those terms to a particular treatment group in the term listing, so they should not be attributed to a group on that basis alone.

Other adverse-event counts were 26 among 116 at risk in the placebo group, 26 among 115 in the vilanterol group, and 21 among 116 in the salmeterol group. These counts are separate from the serious-event counts as presented in the registry. The record does not report deaths in the group-level deaths field.

These figures describe the posted event counts and risk-group sizes. They do not establish whether events were caused by treatment, and the registry record does not provide event narratives or a detailed assessment of relatedness. Event counts should be read as safety information from this study, not as a complete account of risks in other populations or over other durations.

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

The primary result describes average change in weighted-mean 24-hour FEV1 from baseline to Week 12 among participants included in the stated analysis. The posted ANCOVA estimate for vilanterol versus placebo is positive, while the estimate for salmeterol versus placebo is close to zero and slightly negative. Both confidence intervals include zero. The data therefore do not identify a precise difference between either active group and placebo in this endpoint.

This does not mean that the groups had identical outcomes. The estimated contrasts are not exactly zero, and the intervals leave room for differences in either direction. It also does not establish that a difference is clinically important or unimportant: the registry does not report a clinical-importance threshold. Statistical uncertainty and clinical meaning are separate questions.

The trial addresses a specific population, treatment schedule, comparator, endpoint, and 12-week period. Its results do not directly answer questions about people outside the described population, other treatment schedules, outcomes not reported, or effects beyond the treatment period. The record also does not provide enough information to evaluate all aspects of missing-data handling or the multiplicity plan.

The secondary outcomes offer additional descriptions of lung function and symptom-related measures, but their results should be interpreted in light of the number of outcomes and the absence of a reported multiplicity approach. Safety counts are also descriptive and do not by themselves establish causation. Overall, the registry results provide estimates with meaningful uncertainty rather than a definitive statement about the presence, absence, or clinical importance of treatment effects.

18. Why This Trial Matters Statistically

This trial illustrates why a treatment-group estimate should be read together with its confidence interval. A point estimate gives the observed direction and scale of a contrast, but uncertainty around it determines how narrowly the data constrain plausible values. Here, both primary ANCOVA intervals extend across zero, so the posted estimates do not resolve the direction of the underlying mean difference.

The example also shows the distinction between adjusted trial analyses and simple recalculations. ANCOVA uses baseline FEV1 and other listed covariates, while recalculations from group summaries are unadjusted. The recalculated numbers are close to the sponsor's reported estimates, but they are not identical and are not the same analysis. This matters when readers compare results from registry records with calculations based only on summary statistics.

Finally, the record demonstrates why analysis populations, outcome availability, and multiplicity are important parts of interpretation. The primary population includes participants with an available measurement at the indicated time point, while details about missing data and multiplicity are not reported. Secondary outcomes can broaden understanding, but their inferential weight depends partly on how multiple comparisons were planned and analyzed. Clear reporting of these choices helps readers distinguish an estimate from the assumptions and analysis decisions that support it.

19. Limitations

The registry record does not report the original sample-size justification, so it is not possible to determine from this record what effect the trial was designed to detect or what power was planned. The sample-size illustrations based on observed effects are not a substitute for that design information. The record also does not give the complete statistical analysis plan, including any multiplicity procedure or detailed missing-data strategy.

The primary outcome population is defined as randomized participants who received at least one dose and were available at the indicated time point. The primary analysis counts were 95, 101, and 100 across placebo, vilanterol, and salmeterol. The record does not explain why these counts differ from the adverse-event risk counts, nor does it provide a detailed flow of participants through the study. It does not report the number with missing primary measurements or the reasons for unavailability.

The recalculated comparisons are based on posted summary statistics and use approximate pooled variability. They are unadjusted and cannot reproduce the sponsor's ANCOVA model. The registry's reported intervals and p-values should therefore be distinguished from those recalculations. In addition, the posted secondary outcomes include multiple comparisons, and the registry does not report a multiplicity adjustment.

The primary endpoint is measured at Week 12, and the treatment period lasted 12 weeks. The record does not establish how results may persist beyond that period. It also does not report a clinical-importance threshold for FEV1 change. Safety results are counts rather than a complete causal assessment, and deaths are not reported in the registry record. These limitations narrow what can be inferred from the posted information without invalidating the reported estimates.

20. Related Tutorials

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23. Record Summary

NCT01181895 is a completed Phase 3 randomized, double-blind, double-dummy, parallel-group, placebo-controlled multicenter study in persistent asthma. It enrolled 348 adults and adolescents 12 years of age and older whose asthma was uncontrolled on inhaled corticosteroids. The study evaluated vilanterol and salmeterol against placebo over a 12-week treatment period.

The primary endpoint was change from baseline in weighted-mean 24-hour FEV1 at Week 12, analyzed by ANCOVA with baseline FEV1, region, sex, age, and treatment as covariates. The sponsor-reported confidence intervals for both active-treatment comparisons with placebo include zero. The registry also posts secondary outcomes and adverse-event counts, while the original sample-size justification, multiplicity strategy, and detailed missing-data methods are not reported in the registry record.

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