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 Safety and Efficacy of BI 1744 CL in Patients With Chronic Obstructive Pulmonary Disease I (NCT00793624), a randomized phase 3 study. The primary outcome is Forced Expiratory Volume in One Second (FEV1) Area Under Curve 0-3 Hour (h) (AUC 0-3h) Response at 24 Weeks.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00793624 |
| Phase | Phase 3 |
| Condition | Pulmonary Disease, Chronic Obstructive |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 906 |
| Arms in the primary outcome | 4 |
| Lead sponsor | Boehringer Ingelheim |
| Results posted | Yes |
2. Clinical Question
Population
Adults with chronic obstructive pulmonary disease were studied. The primary endpoint analysis used the full analysis set: randomized patients who received at least one dose, had baseline data, and had at least one post-baseline measurement at or before 24 weeks for any co-primary efficacy variable. Other eligibility details are not reported in the registry record.
Intervention
The trial compared once-daily inhaled olodaterol (BI 1744 CL) at 5 mcg and 10 mcg, delivered by Respimat, with placebo and twice-daily formoterol 12 mcg, delivered by Aerolizer. Placebo inhalers were used to support the double-dummy design.
Comparator
The primary posted comparisons are each active treatment against placebo. Formoterol 12 mcg was also a randomized study arm, allowing the reported endpoint results for that arm to be considered alongside the olodaterol and placebo results.
Primary question
At 24 weeks, how did the change from baseline in FEV1 AUC 0–3h response compare among the treatment groups? FEV1 is the volume of air forcibly exhaled in the first second; the AUC measure summarizes the post-dose response over the stated observation period. The registry record reports adjusted group means and mixed-model comparisons against placebo.
The registry describes the study as a Phase 3 randomized trial and lists 906 participants as the enrollment. Its stated objective was to assess long-term efficacy and safety of once-daily olodaterol in people with COPD. The posted primary comparison is about a lung-function measure at a specified follow-up, rather than a direct measure of symptoms, daily functioning, exacerbations, or survival. Those other outcomes require their own results and interpretation. The study also lists Saint George’s Respiratory Questionnaire (SGRQ) scores among its secondary outcomes, which provide a different kind of patient-reported information.
3. Trial Design
This was a randomized, double-blind, double-dummy, placebo-controlled, parallel-group Phase 3 trial. The registry lists 906 participants as enrolled and marks the study completed. It lists a start of 2009-02 and primary completion of 2010-12. Boehringer Ingelheim is named as the sponsor. Further details on recruitment sites, eligibility criteria, allocation concealment, and the trial’s original sample-size justification are not reported in the registry record.
The four treatment groups were olodaterol 5 mcg once daily, olodaterol 10 mcg once daily, formoterol 12 mcg twice daily, and placebo. Olodaterol was delivered using the Respimat inhaler, and formoterol using the Aerolizer inhaler. The placebo arm used olodaterol placebo once daily and/or formoterol placebo twice daily, as described in the arm information. A double-dummy design uses matching placebo procedures so that the different dosing schedules and inhalers can be accommodated while maintaining masking. The registry lists masking as double, but does not report further details about who was masked or how masking was assessed.
The primary endpoint was FEV1 AUC 0–3h response at 24 weeks. It was defined as change from baseline, and the listed primary analysis used the full analysis set. The registry also identifies SGRQ total score at 12, 24, and 48 weeks among secondary outcomes, as well as FEV1 AUC 0–3h response at other listed follow-up times. The record lists 62 outcome measures and 189 analyses; the full analysis plan, endpoint hierarchy, and detailed protocol are not reported in the registry record. The original trial’s planned power and sample-size assumptions are also 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: Two subjects were randomized but not treated due to withdrawn consent and inability to perform spirometry prior to dosing.
Overall Study
| Stage | Placebo | Olodaterol (Olo) 5 mcg qd | Olodaterol (Olo) 10 mcg qd | Form 12 mcg |
|---|---|---|---|---|
| STARTED | 225 | 227 | 225 | 227 |
| COMPLETED | 168 | 191 | 186 | 184 |
| NOT COMPLETED | 57 | 36 | 39 | 43 |
Reasons for not completing this period:
| Reason | Placebo | Olodaterol (Olo) 5 mcg qd | Olodaterol (Olo) 10 mcg qd | Form 12 mcg |
|---|---|---|---|---|
| Adverse Event | 18 | 16 | 15 | 20 |
| Lost to Follow-up | 2 | 2 | 4 | 0 |
| Withdrawal by Subject | 20 | 9 | 11 | 14 |
| Lack of Efficacy | 9 | 2 | 1 | 3 |
| Non compliance with protocol | 2 | 3 | 2 | 3 |
| Other reason not described above | 6 | 4 | 6 | 3 |
Analysis population for the primary outcome, as defined in the registry: Full analysis set (FAS). FAS is defined as all randomized patients who received at least one dose of treatment and had both baseline data and at least one post-baseline measurement at or before 24 weeks for any of the co-primary efficacy variables.
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.
| Characteristic | Unit | Placebo | Olo 5 mcg qd | Olo 10 mcg qd | Form 12 mcg | Total |
|---|---|---|---|---|---|---|
| Participants analysed | 225 | 227 | 225 | 227 | 904 | |
| Age, Continuous | years | 64.0 (SD 8.4) | 63.7 (SD 9.1) | 62.6 (SD 8.8) | 64.8 (SD 8.6) | 63.8 (SD 8.7) |
| Sex: Female, Male: Female | Participants | 45 | 50 | 55 | 48 | 198 |
| Sex: Female, Male: Male | Participants | 180 | 177 | 170 | 179 | 706 |
| Tiotropium (Tio) Use Stratum: Non-tiotropium | Number of participants | 169 | 168 | 167 | 169 | 673 |
| Tiotropium (Tio) Use Stratum: Tiotropium | Number of participants | 56 | 59 | 58 | 58 | 231 |
6. Primary Endpoint
The registry lists the primary outcome as Forced Expiratory Volume in One Second (FEV1) Area Under Curve 0-3 Hour (h) (AUC 0-3h) Response at 24 Weeks, measured over 1 hour (h) and 10 minutes (min) prior to dose on the first day of randomized treatment (baseline) to -10 min, 5 min, 15 min, 30 min, 1 h, 2 h, and 3 h relative to dose on Week 24.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | Liter |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is the change from baseline in FEV1 AUC 0–3h response at 24 weeks, measured in liters. FEV1 refers to the amount of air forcibly exhaled in the first second of an effort. AUC 0–3h summarizes measurements across the three-hour post-dose observation period. The registry says the AUC was calculated using the trapezoidal rule and divided by the observation time of 3h, yielding a response expressed in liters. The response is the follow-up value minus the defined baseline value; baseline was the mean of measurements taken 1 hour and 10 minutes before the first morning dose.
General: repeated measurements can describe both the size and timing of a post-dose response. Averaging the area across the observation interval produces a measure that reflects the overall response over that interval, rather than relying on a single measurement. FEV1 is commonly used in respiratory research as an objective measure of airflow, while the change-from-baseline definition places the follow-up result in relation to each participant’s starting measurement. The endpoint is therefore a physiologic measure, not a direct report of how participants felt or functioned in daily life.
The registry reports least-squares means adjusted using a mixed-effects model. The model includes treatment, tiotropium stratum, visit, and treatment-by-visit interaction as fixed categorical effects, baseline and baseline-by-visit interaction as continuous covariates, and patient as a random effect. These adjusted means and the comparisons against placebo are the primary quantitative results described in the record. The endpoint itself does not establish how participants experienced symptoms, whether other health outcomes changed, or whether differences were clinically important; those questions require separate outcome definitions and evidence.
7. Results Posted in the Registry
- Olo 5 mcg qd: mean 0.14 versus -0.01 on control; difference 0.15 (95% CI 0.11 to 0.19), standardized effect d = 0.66; z-test p = <0.001.
- Olo 10 mcg qd: mean 0.16 versus -0.01 on control; difference 0.17 (95% CI 0.12 to 0.21), standardized effect d = 0.72; z-test p = <0.001.
- Form 12 mcg: mean 0.17 versus -0.01 on control; difference 0.18 (95% CI 0.13 to 0.22), standardized effect d = 0.77; z-test p = <0.001.
Mean difference: Olo 5 mcg qd
95% CI: 0.11 to 0.19
Recalculated from the posted summary statistics
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 outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Saint George's Respiratory Questionnaire (SGRQ) Total Score at 24 Weeks | Continuous Endpoint | Mean difference | -2.44 (-5.26 to 0.38) | 524 per arm |
| Saint George's Respiratory Questionnaire (SGRQ) Total Score at 12 Weeks | Continuous Endpoint | Mean difference | -2.78 (-5.58 to 0.01) | 395 per arm |
| Saint George's Respiratory Questionnaire (SGRQ) Total Score at 48 Weeks | Continuous Endpoint | Mean difference | -1.87 (-4.72 to 0.98) | 913 per arm |
Saint George's Respiratory Questionnaire (SGRQ) Total Score at 24 Weeks
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Olo 5 mcg qd: mean 38.63 versus 41.07 on control; difference -2.44 (95% CI -5.26 to 0.38), standardized effect d = -0.17; z-test p = 0.090.
- Olo 10 mcg qd: mean 37.67 versus 41.07 on control; difference -3.39 (95% CI -6.22 to -0.57), standardized effect d = -0.24; z-test p = 0.018.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Olo 5 mcg qd and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Olo 10 mcg qd than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Saint George's Respiratory Questionnaire (SGRQ) Total Score at 12 Weeks
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Olo 5 mcg qd: mean 39.32 versus 42.10 on control; difference -2.78 (95% CI -5.58 to 0.01), standardized effect d = -0.20; z-test p = 0.050.
- Olo 10 mcg qd: mean 36.96 versus 42.10 on control; difference -5.14 (95% CI -7.94 to -2.35), standardized effect d = -0.37; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Olo 5 mcg qd and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Olo 10 mcg qd than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Saint George's Respiratory Questionnaire (SGRQ) Total Score at 48 Weeks
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Olo 5 mcg qd: mean 38.55 versus 40.41 on control; difference -1.87 (95% CI -4.72 to 0.98), standardized effect d = -0.13; z-test p = 0.199.
- Olo 10 mcg qd: mean 36.85 versus 40.41 on control; difference -3.56 (95% CI -6.44 to -0.69), standardized effect d = -0.25; z-test p = 0.015.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Olo 5 mcg qd and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Olo 10 mcg qd than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The posted secondary findings include SGRQ total scores at 12, 24, and 48 weeks. At these follow-up times, the olodaterol 10 mcg group’s reported scores were lower than placebo’s, while the olodaterol 5 mcg comparisons were less consistent across follow-up. The sponsor’s mixed-model comparisons show intervals that include zero for olodaterol 5 mcg at the reported SGRQ follow-ups, while the intervals for olodaterol 10 mcg are below zero. The registry also lists FEV1 AUC 0–3h outcomes at other follow-up times and a combined SGRQ analysis at 24 weeks; their detailed results are not all included in the posted secondary results.
These measures complement, rather than duplicate, the primary endpoint. FEV1 AUC 0–3h is an objective lung-function response over a post-dose interval. SGRQ is a questionnaire-based measure of respiratory health status. Similar directions across distinct measures can provide context, but a result on one measure does not prove an effect on another. Nor should secondary findings be treated as confirmation of the primary result without considering the analysis plan and the number of tests.
The registry lists 62 outcome measures and 189 analyses. General: examining many outcomes and comparisons increases the opportunity for chance findings. A prespecified hierarchy or multiplicity adjustment can help control that risk, but the registry record does not report whether such a procedure was used for these secondary analyses. Their unadjusted p-values therefore carry less evidential weight than a prespecified primary analysis, particularly when interpreting isolated findings. The record does not provide enough information to determine the complete relationship between every secondary analysis and the trial’s planned testing strategy.
The SGRQ findings should also be considered with their confidence intervals and the absence of a reported clinical-importance threshold in the registry. A nominal p-value alone cannot establish how substantial a score difference is in practical terms. Overall, the secondary pattern offers additional outcome-specific information, but it does not alter the definition or interpretation of the primary FEV1 endpoint.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Saint George's Respiratory Questionnaire (SGRQ) Total Score at 24 Weeks
- Saint George's Respiratory Questionnaire (SGRQ) Total Score at 12 Weeks
- Saint George's Respiratory Questionnaire (SGRQ) Total Score at 48 Weeks
- Saint George's Respiratory Questionnaire (SGRQ) Total Score at 24 Weeks for Combined Analysis
- Forced Expiratory Volume in One Second (FEV1) Area Under Curve 0-3 Hour (h) (AUC 0-3h) Response at 2 Weeks
- Forced Expiratory Volume in One Second (FEV1) Area Under Curve 0-3 Hour (h) (AUC 0-3h) Response at 6 Weeks
- Forced Expiratory Volume in One Second (FEV1) Area Under Curve 0-3 Hour (h) (AUC 0-3h) Response at 12 Weeks
- Forced Expiratory Volume in One Second (FEV1) Area Under Curve 0-3 Hour (h) (AUC 0-3h) Response at 48 Weeks
9. Statistical Interpretation
At 24 weeks, the adjusted mean change in FEV1 AUC 0–3h was -0.009 liters for placebo, 0.142 liters for olodaterol 5 mcg once daily, 0.156 liters for olodaterol 10 mcg once daily, and 0.168 liters for formoterol 12 mcg. The posted mixed-model comparisons against placebo were 0.151 liters for olodaterol 5 mcg, 0.165 liters for olodaterol 10 mcg, and 0.177 liters for formoterol. Each sponsor-reported 95% confidence interval for these primary comparisons lies above zero, and each reported p-value is < 0.001.
The recalculated, unadjusted comparisons are close to the sponsor’s reported estimates. Their 95% confidence intervals also lie above zero, and their unadjusted p-values are <0.001. These recalculations are not substitutes for the trial’s own model-based analyses. They use posted summary statistics and a simplified comparison; the sponsor’s mixed-model analyses retain the greater relevance to the analysis performed in the trial. The record does not flag a discrepancy between the recalculations and the sponsor analyses.
Statistical evidence for a difference in this primary measure is not the same as evidence about every outcome that matters to patients. The primary endpoint is a measured lung-function response over a defined post-dose interval. SGRQ scores, reported as secondary outcomes, address a different aspect of health. The registry also lists other FEV1 and SGRQ assessments. Those results should be interpreted in light of their endpoint status and the number of analyses undertaken; unadjusted secondary comparisons are more vulnerable to chance findings when many comparisons are considered.
The results describe group averages, not the response of every participant. The confidence intervals communicate uncertainty around the estimated differences, and their widths matter alongside the point estimates. The registry record does not report a threshold for clinical importance for the primary measure, so the statistical results alone do not establish the practical importance of the observed group differences. Nor do these results establish longer-term effects beyond the reported follow-up, or effects on outcomes not represented by the posted endpoint.
These findings should be read as the trial’s reported and recalculated statistics, not as medical advice or a recommendation about treatment. Safety outcomes also require careful interpretation: the registry provides group counts for serious adverse events and other adverse events, but the event counts alone do not show whether an event was caused by treatment. The record does not report deaths in the adverse-event data shown, so no conclusion about mortality can be drawn from those fields.
10. Statistical Methods Explained
The registry’s primary analysis uses a mixed-effects model and reports least-squares means. A least-squares mean is a model-adjusted group average; it is not necessarily identical to the simple arithmetic mean of the observed values. Adjustment is useful when the analysis accounts for baseline measurements, visits, or stratification variables. The primary model description includes treatment, tiotropium stratum, visit, and treatment-by-visit interaction as fixed categorical effects. Baseline and baseline-by-visit interaction are included as continuous covariates, and patient is included as a random effect.
What does the mixed-effects model contribute?
General: a mixed-effects model can represent both systematic differences associated with trial factors and variation associated with individual participants. A random participant effect allows observations from the same participant to be treated as related rather than independent. This can be important when a study collects repeated measurements. Fixed effects describe the model’s estimated relationships for the included factors; covariates can account for observed baseline values or other specified features. The registry gives the model components, but does not report all implementation details, such as the covariance structure, estimation method, or model diagnostics.
The primary endpoint is based on measurements across the post-dose interval. The registry specifies that FEV1 AUC 0–3h was calculated with the trapezoidal rule and divided by 3h. General: the trapezoidal rule approximates the area under a curve by connecting observed measurements and summing the resulting areas. Dividing by the observation time expresses an average response across the interval. This summary uses information from multiple time points, but does not preserve every feature of the response curve; distinct time patterns can yield similar averages.
How should the comparisons be read?
The reported parameter is a mean difference in final values, and the listed treatment comparisons are against placebo. A positive difference for this endpoint means the adjusted change-from-baseline value is higher in the active-treatment group than in the placebo group. The registry reports the sponsor’s mixed-model estimates with 95% confidence intervals and p-values. The comparison calculations alongside them are unadjusted recalculations from posted group summary statistics. They are useful as a simple check on the scale and direction of the results, but do not reproduce the sponsor’s full model.
The recalculations estimate pooled variability approximately from the group standard errors. That approximation is explicitly indicated in the posted analysis information. General: standard errors describe the uncertainty of estimated means, while standard deviations describe variation among individual observations. Converting between them requires assumptions about the underlying sample information. An approximate pooled standard deviation is therefore not a substitute for participant-level data or the sponsor’s model-based standard error. The resulting recalculated confidence intervals and p-values can differ slightly from the reported mixed-model results.
What do p-values and confidence intervals convey?
General: a p-value measures how incompatible the observed data are with a specified null hypothesis under the assumptions of the statistical model. It is not the probability that the null hypothesis is true, nor does it measure the size or importance of an effect. A confidence interval gives a range of estimates reasonably compatible with the data and analysis procedure at its stated confidence level. Its endpoints convey both the estimated direction and the uncertainty around the estimate. For the primary comparisons, the sponsor-reported intervals are 95% intervals.
These inferential summaries depend on assumptions. General: model fit, measurement quality, missing-data handling, and the way repeated measures are represented can affect estimates and uncertainty. Some details of the original statistical analysis plan and the handling of missing observations are not reported in the registry record. The listed full analysis set is defined in the record, but the precise procedures used for participants with incomplete follow-up are not described there.
Why does over-dispersion matter?
General: over-dispersion occurs when observed variability is greater than a statistical model assumes. If a model understates variability, standard errors may be too small and confidence intervals too narrow, making results appear more precise than they are. The primary outcome is continuous and the registry describes a mixed-effects model; it does not report an over-dispersion assessment. This concept is therefore a general consideration, not a reported finding about this trial.
The record lists many outcomes and analyses. General: when multiple hypotheses are tested, the chance of at least one apparently unusual result can increase. Adjustment procedures or a prespecified testing hierarchy can address that issue, but the registry record does not report a multiplicity adjustment or a complete testing hierarchy. Accordingly, the primary endpoint should be distinguished from secondary findings, and unadjusted secondary p-values should not be treated as if they were the only test performed.
11. Confidence Intervals and Precision
The sponsor-reported primary comparisons have 95% confidence intervals of 0.110 to 0.193 liters for olodaterol 5 mcg versus placebo, 0.124 to 0.206 liters for olodaterol 10 mcg versus placebo, and 0.136 to 0.218 liters for formoterol 12 mcg versus placebo. The intervals are all on the positive side of zero. Their widths indicate that the estimated differences are not known exactly; each interval includes a range of values compatible with the model and observed data.
The recalculated unadjusted 95% intervals are 0.108 to 0.194 liters, 0.122 to 0.208 liters, and 0.134 to 0.22 liters for the respective comparisons. They are close to the sponsor-reported intervals, with small differences in endpoints. This is expected when simple calculations from summary statistics are compared with a mixed-model analysis that adjusts for the stated factors. The sponsor’s reported analysis is the trial analysis, while the recalculations are approximate and unadjusted.
General: a confidence interval’s precision is reflected in its width. Narrower intervals indicate less statistical uncertainty under the analysis assumptions, whereas wider intervals leave a broader range of plausible effects. An interval should be considered together with the outcome scale, the point estimate, and the clinical context. The registry does not report a threshold for a clinically important difference in this measure, so the interval cannot by itself determine whether the estimated difference is meaningful to patients.
Precision also concerns who contributed measurements. The primary analysis population is defined as the full analysis set, and the arm-specific analysis sizes are posted with the endpoint results. The registry record does not provide a full account of missing primary outcome measurements or their handling. That limits assessment of how incomplete observations might affect precision or the validity of the model-based estimates.
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 detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 37 | 49 |
| 75% of the observed effect | 65 | 87 |
| 50% of the observed effect | 146 | 195 |
The planning figures are participants per arm for these continuous-outcome comparisons; they are not total event counts. The planning illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses the observed effect as a reference and considers detecting the stated fraction of that effect. The trial’s own original design assumptions and sample-size justification are not reported in the registry record.
The 80% power column describes the number of participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting the specified effect under those assumptions, if the effect and model assumptions were correct. The 90% power column gives the corresponding illustration for a 90% chance. These are planning quantities, not descriptions of the trial’s achieved power. This is not observed power.
Each planning row uses a different fraction of the observed effect: 100%, 75%, or 50%. A smaller effect is harder to distinguish from random variation, so the planning calculation requires more participants per arm when the assumed effect is smaller. For instance, for the primary olodaterol 5 mcg comparison, the figures for detecting 100% of the observed effect are 37 participants per arm for 80% power and 49 for 90% power; for 50% of the observed effect they are 146 and 195. These are illustrations based on the observed result, not the original enrollment plan.
The curve should be interpreted as another view of how the planning estimate changes with the assumed effect. Neither the rows nor the curve incorporate unreported design choices or guarantee that a future study would achieve a particular result. The figures are sensitive to the assumptions used, including the estimated variability and the effect fraction. They should be read as planning aids rather than as evidence that the trial was adequately or inadequately designed.
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 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
- Observed difference Δ = 0.151; pooled standard deviation σ = 0.230.
- n = 2 × (1.96 + 0.842)2 × 0.2302 / 0.1512 = 36.3, rounded up to 37 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 <- 0.151 # observed difference in means
sigma <- 0.229606079939274 # 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(793624)
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 = 37 (80% power), 49 (90% power)
75% of observed effect: n per arm = 65 (80% power), 87 (90% power)
50% of observed effect: n per arm = 146 (80% power), 195 (90% power)
power.t.test: 37.3
Simulated power at n = 37 per arm: 0.798 (20000 replicates)
The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Mixed Models Analysis | Mean Difference (Final Values) 0.151 | 0.110 to 0.193 | < 0.001 |
| Mixed Models Analysis | Mean Difference (Final Values) 0.165 | 0.124 to 0.206 | < 0.001 |
| Mixed Models Analysis | Mean Difference (Final Values) 0.177 | 0.136 to 0.218 | < 0.001 |
The registry reports sponsor analyses using mixed models. For the primary comparison of olodaterol 5 mcg with placebo, the sponsor reports a mean difference of 0.151 liters, with a 95% confidence interval from 0.110 to 0.193 and p < 0.001. The corresponding recalculated unadjusted estimate is 0.151 liters, with a 95% interval from 0.108 to 0.194 and p <0.001. For olodaterol 10 mcg, the sponsor reports 0.165 liters, a 95% interval from 0.124 to 0.206, and p < 0.001; the recalculation is 0.165 liters, with an interval from 0.122 to 0.208 and p <0.001. For formoterol 12 mcg, the sponsor reports 0.177 liters, a 95% interval from 0.136 to 0.218, and p < 0.001; the recalculation is 0.177 liters, with an interval from 0.134 to 0.22 and p <0.001.
The close estimates support the same general direction in both presentations. Small differences in interval limits and p-value formatting reflect the difference between the sponsor’s adjusted mixed-model analysis and the approximate unadjusted calculation. The registry does not flag a discrepancy. The recalculation should therefore be read as a transparent check from summary statistics, not as a replacement for the sponsor’s analysis or as a new analysis of participant-level data.
The sponsor analysis is the relevant trial analysis because it uses the model described for the primary endpoint. The posted record does not include all details needed to independently reproduce that model. The reported comparisons are against placebo; they do not constitute a reported direct statistical comparison of one active treatment with another.
15. Multiplicity, Missing Data and Analysis Populations
The registry lists 62 outcome measures and 189 analyses, with the primary endpoint identified as FEV1 AUC 0–3h response at 24 weeks. It also lists multiple secondary outcomes and follow-up times. The registry record does not report a complete statistical analysis plan, a hierarchy of hypotheses, or whether p-values were adjusted for multiple comparisons. Without those details, the family of tests intended to support formal claims cannot be established from the record.
General: testing many outcomes can increase the likelihood of at least one apparently positive result arising by chance. Multiplicity procedures, such as prespecified testing sequences or adjusted significance thresholds, can address this concern. When their use is not reported, secondary results are best treated as supportive or exploratory rather than as independently definitive evidence. This does not erase the reported estimates; it affects how strongly they can be interpreted as confirmatory.
The primary endpoint population is the full analysis set. The registry defines it as randomized patients who received at least one dose, had baseline data, and had at least one post-baseline measurement at or before 24 weeks for any co-primary efficacy variable. The record does not report the missing-data method for the primary endpoint, the amount or pattern of missingness, or sensitivity analyses addressing missing observations. The procedures used to handle missing secondary measurements are also not reported in the registry record.
Other design and analysis details, including the original sample-size justification, interim analyses, and all model diagnostics, are not reported in the registry record. This does not imply that these procedures were absent; it means their use cannot be established from the registry information. The registry describes the mixed-model components, but further implementation details are not available in the record. These omissions limit independent assessment of prespecification, robustness to missing data, and the relationship between the many reported analyses.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Placebo | 31 | 225 | 13.8% |
| Olodaterol (Olo) 5 mcg qd | 33 | 227 | 14.5% |
| Olodaterol (Olo) 10 mcg qd | 26 | 225 | 11.6% |
| Form 12 mcg | 33 | 227 | 14.5% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Placebo | 83 of 225 |
| Olodaterol (Olo) 5 mcg qd | 100 of 227 |
| Olodaterol (Olo) 10 mcg qd | 96 of 225 |
| Form 12 mcg | 83 of 227 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo | Olodaterol (Olo) 5 mcg qd | Olodaterol (Olo) 10 mcg qd | Form 12 mcg |
|---|---|---|---|---|---|
| Chronic obstructive pulmonary disease | Respiratory, thoracic and mediastinal disorders | 9 of 225 | 10 of 227 | 13 of 225 | 9 of 227 |
| Pneumonia | Infections and infestations | 3 of 225 | 6 of 227 | 8 of 225 | 3 of 227 |
| Atrial fibrillation | Cardiac disorders | 0 of 225 | 1 of 227 | 3 of 225 | 1 of 227 |
| Gastroenteritis | Infections and infestations | 3 of 225 | 1 of 227 | 0 of 225 | 0 of 227 |
| Infective exacerbation of chronic obstructive airways disease | Infections and infestations | 2 of 225 | 0 of 227 | 1 of 225 | 1 of 227 |
| Acute respiratory failure | Respiratory, thoracic and mediastinal disorders | 1 of 225 | 1 of 227 | 1 of 225 | 1 of 227 |
| Anaemia | Blood and lymphatic system disorders | 1 of 225 | 1 of 227 | 0 of 225 | 0 of 227 |
| Acute myocardial infarction | Cardiac disorders | 1 of 225 | 1 of 227 | 0 of 225 | 0 of 227 |
| Cardiac failure | Cardiac disorders | 0 of 225 | 0 of 227 | 1 of 225 | 1 of 227 |
| Supraventricular tachycardia | Cardiac disorders | 1 of 225 | 0 of 227 | 0 of 225 | 1 of 227 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo | Olodaterol (Olo) 5 mcg qd | Olodaterol (Olo) 10 mcg qd | Form 12 mcg |
|---|---|---|---|---|---|
| Chronic obstructive pulmonary disease | Respiratory, thoracic and mediastinal disorders | 51 of 225 | 67 of 227 | 62 of 225 | 53 of 227 |
| Nasopharyngitis | Infections and infestations | 15 of 225 | 22 of 227 | 25 of 225 | 23 of 227 |
| Upper respiratory tract infection | Infections and infestations | 15 of 225 | 17 of 227 | 11 of 225 | 11 of 227 |
| Cough | Respiratory, thoracic and mediastinal disorders | 7 of 225 | 7 of 227 | 13 of 225 | 13 of 227 |
| Dyspnoea | Respiratory, thoracic and mediastinal disorders | 11 of 225 | 9 of 227 | 13 of 225 | 6 of 227 |
Serious events with the highest arm-level rate: chronic obstructive pulmonary disease (5.8%), pneumonia (3.6%), atrial fibrillation (1.3%), gastroenteritis (1.3%), infective exacerbation of chronic obstructive airways disease (0.9%).
The registry reports serious adverse event counts for placebo as 31 participants affected among 225 at risk; for olodaterol 5 mcg once daily, 33 among 227; for olodaterol 10 mcg once daily, 26 among 225; and for formoterol 12 mcg, 33 among 227. The counts for other adverse events are 83 among 225 for placebo, 100 among 227 for olodaterol 5 mcg, 96 among 225 for olodaterol 10 mcg, and 83 among 227 for formoterol 12 mcg.
The serious adverse event terms with the largest listed percentages include chronic obstructive pulmonary disease at 5.8%, pneumonia at 3.6%, atrial fibrillation at 1.3%, gastroenteritis at 1.3%, infective exacerbation of chronic obstructive airways disease at 0.9%, and respiratory failure at 0.9%. The registry does not report deaths in these adverse-event fields.
These are counts of participants with events and counts at risk, not estimates of causal effects. The registry information presented does not establish whether a given event was attributed to treatment, how events were defined or collected, or whether participants could have experienced more than one event. A direct comparison of these counts alone does not account for differences in exposure time or other relevant factors. The counts describe the safety information posted in the record and should not be interpreted as proof of benefit or harm.
17. What the Result Does, and Does Not, Mean
The primary result is an estimate of the difference between treatment groups in change from baseline in FEV1 AUC 0–3h response at 24 weeks. The sponsor-reported estimates for each active comparator are positive relative to placebo, and their 95% confidence intervals do not include zero. This describes statistical evidence for a difference in the specified lung-function measure under the reported analysis. It does not mean every participant had the same response, or that the group average describes any individual participant’s outcome.
The endpoint is one component of COPD assessment. It summarizes FEV1 response over a defined post-dose interval; it is not a direct measure of symptoms, everyday activity, quality of life, exacerbations, hospital use, or survival. SGRQ results provide a separate questionnaire-based perspective, but their interpretation has its own uncertainty and multiplicity considerations. The registry record does not report a clinical-importance threshold for the primary measure, so statistical evidence alone does not establish the practical importance of the estimated differences.
The posted results also do not establish how the treatments compare directly with each other. The reported primary analyses compare each active arm with placebo. Similar point estimates or confidence intervals across separate placebo comparisons do not constitute a formal active-versus-active test. Such a comparison would require a specified analysis and its own uncertainty estimate, which is not reported in the registry record.
The findings should not be generalized beyond the population, outcome, and follow-up represented by the trial without further evidence. The registry lists a full analysis set definition, but does not report detailed missing-data methods or the complete statistical analysis plan. The safety counts likewise cannot establish causation or give a complete account of treatment-related risk. The results are statistical evidence about specified group outcomes, not medical advice or a recommendation about treatment.
18. Why This Trial Matters Statistically
This trial illustrates how an endpoint definition determines what a statistical result means. The primary outcome is not a single FEV1 reading, but a change-from-baseline average response over a three-hour post-dose interval at 24 weeks. The registry also specifies the measurement timing, the baseline definition, and the trapezoidal calculation. Understanding those details helps prevent interpreting the estimate as a general measure of every aspect of respiratory health.
The analysis also demonstrates the distinction between an adjusted model-based estimate and a simple recalculation from summary statistics. The sponsor’s mixed-effects model accounts for the factors named in the registry, including visit and baseline terms. A simplified unadjusted calculation gives close estimates, but it does not recreate the trial analysis. Reporting both types of information can help readers understand the scale of the result while keeping the primary inference tied to the stated model.
Finally, this record illustrates why statistical significance, precision, clinical importance, and multiplicity are separate questions. Confidence intervals describe uncertainty, while p-values address compatibility with a null hypothesis under an analysis. Neither by itself establishes practical importance. The large number of outcomes and analyses makes it particularly important to distinguish the primary endpoint from secondary results and to know whether a testing hierarchy or adjustment was used. Those details are not reported in the registry record, which limits how strongly secondary findings can be interpreted.
19. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
The registry record does not report the original trial sample-size justification, the planned statistical analysis in full, or an explicit multiplicity strategy. Although the primary mixed-model components are described, the complete model implementation and diagnostic results are not reported. This limits independent assessment of how the analysis plan was specified and whether all model assumptions were evaluated.
The record defines the full analysis set, but does not report detailed missing-data methods, the extent or pattern of missing observations, or sensitivity analyses. Because the primary result is model-adjusted, those details matter for evaluating whether incomplete follow-up could affect the estimate. The posted summary statistics also do not permit a full participant-level reanalysis. The recalculated comparisons use approximate variability derived from standard errors and should not be mistaken for a reproduction of the sponsor’s analysis.
The trial includes multiple outcomes and analyses, but the registry information does not identify a complete hierarchy or correction for multiple testing. That is especially relevant when interpreting secondary outcomes. The record also does not report a clinical-importance threshold for the primary endpoint or SGRQ differences, making it difficult to translate statistical estimates into practical importance from these results alone.
Safety information is presented as counts at risk and counts affected. The registry does not report in these fields whether events were considered treatment-related, the timing or duration of exposure for each participant, or whether repeated events were counted separately. Death counts are not reported in the registry record. Finally, detailed eligibility criteria and information needed to assess how closely the enrolled population represents other COPD populations are not reported, limiting assessment of generalizability.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Safety and Efficacy of BI 1744 CL in Patients With Chronic Obstructive Pulmonary Disease I — NCT00793624.
- Registry record last updated 2014-06-27; status last verified 2014-06.
- Results first posted 2014-06-05.
- 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.
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23. Record Summary
The registry describes a completed randomized, double-blind, double-dummy, parallel-group Phase 3 study of inhaled olodaterol, formoterol, and placebo in patients with COPD. The listed enrollment is 906. The primary outcome was change from baseline in FEV1 AUC 0–3h response at 24 weeks, analyzed using a mixed-effects model in the defined full analysis set.
The sponsor-reported primary comparisons against placebo are positive for olodaterol 5 mcg, olodaterol 10 mcg, and formoterol 12 mcg, with 95% confidence intervals above zero. Approximate unadjusted recalculations give close estimates. Secondary SGRQ results and adverse-event counts provide additional outcome-specific information, but should be interpreted in light of the number of analyses and the limits of the registry’s reported methods.
The registry record does not report the full analysis plan, missing-data procedures, original sample-size justification, or a multiplicity strategy. The posted statistics therefore support interpretation of the specified outcomes while leaving important design and analysis details unresolved.