A Double-blind, Placebo-controlled, Crossover Study to Assess the Effect of Aclidinium Bromide 400 μg Bid on COPD Symptoms and Sleep Quality After 3 Weeks of Treatment in Patients With Stable Moderate-to-severe Chronic Obstructive Pulmonary Disease (COPD): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Double-blind, Placebo-controlled, Crossover Study to Assess the Effect of Aclidinium Bromide 400 μg Bid on COPD Symptoms and Sleep Quality After 3 Weeks of Treatment in Patients With Stable Moderate-to-severe Chronic Obstructive Pulmonary Disease (COPD) (NCT02153489), a randomized phase 4 study. The primary outcome is Change From Baseline in Normalized Forced Expiratory Volume in One Second (FEV1) AUC0-24hr.

2. Clinical Question

3. Trial Design

This was a randomized, phase 4, pilot study with a placebo-controlled, two-period crossover model. Its official title identifies it as a 2-period crossover study, while the registry describes masking as quadruple. The longer study title calls the trial double-blind. The record does not explain which roles were masked or how masking was maintained.

The registry lists 30 participants as enrolled. The planned treatment comparison was aclidinium bromide against placebo, with each intervention given by oral inhalation twice daily, 12 hours apart. The intended treatment period relevant to the primary question was 3 weeks. The crossover structure means that treatment comparisons are made across treatment periods, rather than solely between two separate groups that each receive one treatment. The sequence allocation, washout details, and timing between periods are not reported in the registry record.

The study focused on patients with stable moderate-to-severe COPD. Its stated aims included airway dilation, COPD symptoms, sleep quality, and physical activity after treatment. The primary outcome posted in the results is narrower: change from baseline in normalized FEV1 AUC0-24hr at Week 3. Although the registry counts 17 outcome measures, it reports no secondary results in the information summarized for this analysis.

The record identifies AstraZeneca as sponsor and reports the study as completed. It lists the start as 2014-04 and primary completion as 2015-06. The original protocol's statistical analysis plan, the rationale for the planned enrollment, and any changes to the analysis are not reported in the registry record.

4. Participant Flow and Accounting

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

Before assignment: All patients who met the study entry criteria and completed the screening assessments and the 7-day run-in period were randomized. Nine (9/39) subjects were not randomized due to screening failure (primarily for non-fulfillment of inclusion/exclusion criteria)

Period 1

Period 2

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 Change From Baseline in Normalized Forced Expiratory Volume in One Second (FEV1) AUC0-24hr, measured over 0, 0.5, 1, 2, 3, 4, 6, 8, 10, 11, 12, 12.5, 13, 14, 15, 16, 19, 22, 23, and 24 hours at Week 3 of treatment.

The primary endpoint is change from baseline in normalized forced expiratory volume in one second (FEV1) AUC0-24hr, reported in L/sec*hr. FEV1 is a lung-function measure: it records the volume of air exhaled during the first second of a forced expiration. An area-under-the-curve summary combines measurements across the stated post-treatment time points to describe the pattern over the assessment period, rather than relying on a single reading.

The registry lists measurements at 0, 0.5, 1, 2, 3, 4, 6, 8, 10, 11, 12, 12.5, 13, 14, 15, 16, 19, 22, 23, and 24 hours at Week 3 of treatment. The endpoint is described as normalized, but the registry record does not explain the normalization procedure. It also does not state the precise baseline definition or the detailed construction of the area summary.

As a general statistical rationale, repeated lung-function measurements can capture how an intervention's measured effect varies over a dosing interval. AUC condenses that trajectory into a single continuous outcome, which can be compared across treatments. The endpoint therefore addresses a physiological aspect of the study's stated bronchodilation question. It is not itself a direct measure of symptoms, sleep quality, or physical activity, and the registry does not post primary results for those outcomes in this record.

7. Results Posted in the Registry

• Aclidinium: mean 0.10 versus -0.04 on control; difference 0.14 (95% CI 0.03 to 0.24), standardized effect d = 0.66; z-test p = 0.010.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: it is a measured quantity expressed in L/sec*hr. The registry labels the arm results as least-squares means and the accompanying dispersion as standard errors. The comparison is a mean difference between the aclidinium and placebo estimates. The posted contrast is 0.138, with an interval from 0.033 to 0.244 and an unadjusted p-value of 0.01. These are the reported statistics; the record does not provide a full analysis specification.

What does a least-squares mean represent?

As a general statistical concept, a least-squares mean is a model-based estimate of an average outcome. It can differ from a simple arithmetic average when a model includes adjustments or accounts for the structure of the data. The registry does not name the model, identify its covariates, or describe how it incorporated the crossover design. It is therefore not possible to determine from this record which adjustments produced the reported estimates.

The posted arm estimates are 0.095 for aclidinium and -0.043 for placebo. Both are changes from baseline, and each has a standard error of 0.038. The contrast is stated as aclidinium relative to placebo. Because the values are model-based and the analysis details are absent, they should be reported as the registry's least-squares mean results rather than relabeled as unadjusted sample averages.

What does the standard error describe?

As a general explanation, a standard error describes the statistical uncertainty in an estimate arising from sampling variability under the assumed analysis. It is not the spread of individual participant measurements. A standard error can help characterize how precisely a mean has been estimated, but its interpretation depends on the model and design. The registry gives standard errors for the two arm estimates, but does not describe the method used to calculate them.

The record also includes an approximate pooled standard deviation of 0.209 and a standardized effect estimate of 0.662. These are summary statistics accompanying the comparison. The pooled standard deviation is marked approximate; the registry does not explain the approximation procedure. A standardized effect expresses a contrast relative to a measure of variability, but its practical meaning depends on the outcome and context. It is not a separate clinical endpoint.

How should the p-value be read?

As a general concept, a p-value evaluates how unusual data at least as discrepant as those observed would be if a specified null hypothesis and the analysis assumptions were true. The reported value is 0.01 and is explicitly unadjusted. It is not the probability that the null hypothesis is true, nor does it measure the size or importance of the estimated contrast. Because the registry does not state the testing procedure or its assumptions, the value can be reported but not independently reproduced from the posted summaries.

The interval from 0.033 to 0.244 gives a range of estimates compatible with the data under the interval method. As a general principle, an interval communicates uncertainty about the contrast and is more informative about its scale than a p-value alone. The confidence level and interval construction are not reported in the registry record. No additional claim about the interval's coverage can be made from the registry entry alone.

Why does the crossover model matter?

In a crossover design, participants receive more than one treatment over separate periods. General statistical analysis may account for the fact that observations from the same participant are related, and may include treatment, period, or sequence terms. Carryover can also matter if an earlier period's treatment influences measurements in a later period. The registry identifies the study as crossover but does not report the analysis model, the within-participant covariance structure, period or sequence handling, washout details, or a carryover assessment. These are important unknowns when interpreting model-based estimates from this design.

The number of participants listed for each arm is 30. The record does not clarify how that arm-level count maps to the crossover analysis population, whether all participants completed both periods, or whether any observations were excluded. Details about missing outcomes and analysis populations are not reported in the registry record. The reported summary should not be treated as evidence that every enrolled participant contributed complete data to every treatment-period estimate.

The registry reports 17 outcome measures and zero posted secondary results in this record. The primary comparison's p-value is unadjusted. No multiplicity strategy is reported, so the record does not show whether the primary result was interpreted in a broader family of tests or whether testing adjustments were prespecified. This limits assessment of the full statistical plan but does not change the fact that the registry labels this outcome primary.

10. Confidence Intervals and Precision

The estimated aclidinium-minus-placebo contrast is 0.138 L/sec*hr, with a reported interval from 0.033 to 0.244. The interval communicates uncertainty about the estimated difference: values across that range are compatible with the data under the method used to construct it. The full width of the interval is not recalculated. The confidence level and construction method are not reported in the registry record.

The interval lies above zero, while the point estimate is positive. That indicates the posted estimates are consistent with a positive difference in change for aclidinium relative to placebo under the reported analysis. The interval still spans a range of possible contrast sizes, so the point estimate should not be treated as exact. The reported p-value is 0.01 and is unadjusted; it complements the interval but does not replace its information about magnitude and uncertainty.

Each arm-level least-squares mean has a standard error of 0.038. A standard error describes uncertainty in an estimated mean, not the range of outcomes among participants. It does not provide a complete picture of precision without the model and covariance details, particularly for a crossover study where measurements within a participant can be related.

The registry posts no confidence level, model specification, or detailed analysis population for this contrast. Those omissions prevent a full appraisal of how the interval reflects the design and data. Precision should therefore be described using the posted interval and standard errors, while recognizing that their analytical construction is not documented in the registry record.

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, not the original trial's enrollment justification. The registry record does not report the trial's own sample-size assumptions or calculation.

The stated 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 as a stated fraction of the observed effect. For 100% of the observed effect, the illustration gives 36 participants per arm for 80% power and 48 participants per arm for 90% power. For 75% of the observed effect, it gives 64 participants per arm for 80% power and 86 participants per arm for 90% power. For 50% of the observed effect, it gives 144 participants per arm for 80% power and 192 participants per arm for 90% power.

In plain language, the 80% power column is the estimated number of participants per arm for a design with an 80% chance of detecting the specified effect under the listed assumptions. The 90% power column describes the corresponding number per arm for a design with a 90% chance. Smaller effects need more participants to detect under otherwise unchanged assumptions, as reflected by the increasing planning figures for smaller fractions of the observed effect.

These values are planning illustrations, not observed power and not evidence about the trial's original design. They use a simplified two-arm calculation, whereas the study itself is described as a crossover trial. The illustration should not be read as a reconstruction of the protocol's design choices.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 0.138; pooled standard deviation σ = 0.209.
2. n = 2 × (1.96 + 0.842)² × 0.209² / 0.138² = 35.8, rounded up to 36 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 <- 0.1382                      # observed difference in means
sigma <- 0.208682294409468                     # 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(2153489)
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 = 36 (80% power), 48 (90% power)
 75% of observed effect: n per arm = 64 (80% power), 86 (90% power)
 50% of observed effect: n per arm = 144 (80% power), 192 (90% power)
power.t.test: 36.8 
Simulated power at n = 36 per arm: 0.789 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Multiplicity, Missing Data and Analysis Populations

The registry identifies one primary outcome: change from baseline in normalized FEV1 AUC0-24hr at Week 3. It counts 17 outcome measures overall, but the record reports zero secondary results for this analysis. The registry does not provide a full list of the secondary outcome findings in the posted results, so their estimates and uncertainty cannot be evaluated.

The primary p-value is explicitly unadjusted. As a general statistical issue, testing multiple outcomes or multiple hypotheses can increase the chance of at least one small p-value when all null hypotheses are true. Methods such as prespecifying a hierarchy or adjusting significance levels can address some multiplicity concerns. The registry record does not report whether any such strategy was planned, whether the primary endpoint was tested within a defined family, or whether other analyses were conducted.

Missing-data methods are not reported. The registry does not say how incomplete outcome measurements, missed visits, or participants who did not complete both treatment periods were handled. It also does not identify the analysis population, such as whether the reported estimates were based on all randomized participants or a subset with usable data. Although 30 participants are listed for each arm, that information alone does not establish how many contributed to each component of the crossover comparison.

The statistical analysis plan, model specification, handling of period and sequence, and rules for excluding observations are not reported in the registry record. These gaps do not negate the posted estimate, but they restrict assessment of the assumptions underlying its p-value and interval. The registry results therefore support a description of the primary comparison as posted, not a complete reconstruction of the protocol's inferential framework.

14. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

Most frequent non-serious adverse event terms

The registry reports serious adverse events for 0 of 30 participants in the aclidinium group and 0 of 30 participants in the placebo group. No serious adverse-event terms are listed. The number of deaths is not reported in the registry record.

These figures describe the reported event counts during the registry's stated safety collection; the detailed collection period and definitions are not provided in the record. Zero reported serious events in these groups means none were listed for the participants at risk in the posted results. It does not establish that an event is impossible, nor does it characterize risk beyond this study's participants and observation period.

The registry separately lists other, non-serious adverse events affecting 3 of 30 participants with aclidinium and 0 of 30 with placebo. The record does not provide event terms in the information summarized for this analysis, so the nature and clinical context of those events cannot be assessed. Serious and non-serious adverse-event counts are distinct summaries and should not be combined.

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

The posted result estimates a positive difference in change from baseline in normalized FEV1 AUC0-24hr for aclidinium relative to placebo at Week 3. The least-squares mean contrast is 0.138 L/sec*hr, with an interval from 0.033 to 0.244 and an unadjusted p-value of 0.01. The arm estimates are 0.095 L/sec*hr for aclidinium and -0.043 L/sec*hr for placebo. These figures describe the registry's primary continuous outcome.

The result does not provide a direct estimate of improvement in COPD symptoms, sleep quality, or physical activity. Those outcomes appear among the study's stated aims, but secondary results are not posted in the registry record. Nor does the primary endpoint establish how individual participants responded; group-level means do not show the distribution of participant-level outcomes.

The comparison does not establish how the effect would vary beyond the enrolled population of patients with stable moderate-to-severe COPD, or whether it would persist beyond the 3-week treatment period used for this endpoint. The registry does not report longer-term outcomes. It also does not provide the model details needed to assess how period, treatment sequence, missing measurements, or possible carryover were addressed in the crossover analysis.

As a general interpretive principle, statistical evidence about an estimated contrast is not the same as a judgment about clinical importance. The registry does not provide a threshold for a clinically meaningful difference on this endpoint. The estimate and its interval can be described statistically, but the record alone does not establish the importance of the measured difference for patients or broader care decisions.

16. Why This Trial Matters Statistically

This study illustrates how an endpoint can focus a clinical question on a defined physiological measurement. FEV1 AUC0-24hr summarizes repeated lung-function readings across the stated assessment interval, while change from baseline frames the comparison as change during treatment. The resulting contrast is interpretable in the endpoint's units, L/sec*hr, and is accompanied by an interval and standard errors.

The crossover design also highlights the importance of matching statistical interpretation to study structure. Repeated treatment periods can create within-participant dependence and raise questions about period, sequence, and carryover. The registry identifies the design but does not report how the analysis addressed these considerations. That distinction matters: knowing the design is not the same as knowing the model used to estimate the treatment contrast.

The record further shows why a p-value alone is incomplete. The unadjusted p-value of 0.01 accompanies a mean-difference estimate and an interval from 0.033 to 0.244. The estimate describes scale, and the interval conveys uncertainty under an unspecified method. Since the confidence level, analysis model, and multiplicity strategy are not reported, precise interpretation depends on recognizing both the posted statistics and their documentation limits.

Finally, a small pilot study can produce useful estimates for understanding an endpoint and planning future research, but planning illustrations based on its observed effect remain assumption-dependent. The posted calculations list explicit simplified assumptions, while the original trial's design justification is not reported. Separating those two kinds of information prevents a planning scenario from being mistaken for the trial's own sample-size rationale.

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 describes a pilot study with 30 participants enrolled. A study of this size may yield imprecise estimates, and the interval for the primary contrast spans 0.033 to 0.244 L/sec*hr. The confidence level and interval method are not reported, so precision cannot be fully assessed from the entry alone.

The study used a crossover design, but the registry does not describe the treatment sequence, washout interval, period effects, carryover assessment, or the model's treatment of repeated observations within participants. These details are especially relevant to interpreting a crossover contrast. The record also does not state whether all enrolled participants completed both periods or how incomplete data were handled.

The primary endpoint is described as normalized, but the normalization method is not reported. The record lists the measurement time points but does not specify the baseline definition or detailed AUC construction. The statistical analysis plan, covariate adjustments, and analysis population are likewise not reported. These omissions limit reproducibility of the posted least-squares mean estimates and their uncertainty.

Secondary results are not posted, despite the registry counting 17 outcome measures. The primary p-value is unadjusted, and no multiplicity plan is reported. The record also does not report the original enrollment justification or clinical threshold for a meaningful difference. Finally, the posted endpoint is assessed after 3 weeks, so the registry result does not characterize longer-term outcomes.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: A Double-blind, Placebo-controlled, Crossover Study to Assess the Effect of Aclidinium Bromide 400 μg Bid on COPD Symptoms and Sleep Quality After 3 Weeks of Treatment in Patients With Stable Moderate-to-severe Chronic Obstructive Pulmonary Disease (COPD) — NCT02153489.
• Registry record last updated 2016-11-09; status last verified 2016-09.
• Results first posted 2016-11-09.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

The registry record describes a completed phase 4, randomized, quadruple-masked, two-period crossover pilot study of aclidinium bromide versus placebo in patients with stable moderate-to-severe COPD. Enrollment was 30. The study start is listed as 2014-04 and primary completion as 2015-06; AstraZeneca is identified as sponsor.

The primary outcome was change from baseline in normalized FEV1 AUC0-24hr at Week 3. The reported least-squares mean difference for aclidinium relative to placebo was 0.138 L/sec*hr, with an interval from 0.033 to 0.244 and an unadjusted p-value of 0.01. Secondary results, full analysis methods, and the original sample-size rationale are not reported in the registry record.