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 Combination of Orally Inhaled BI1744CL/Tiotropium Bromide in Patients With Chronic Obstructive Pulmonary Disease ( COPD) (NCT00696020), a randomized phase 2 study. The primary outcome is Trough FEV1 Response [L] After 4 Weeks of Treatment.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00696020 |
| Phase | Phase 2 |
| Condition | Pulmonary Disease, Chronic Obstructive |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 360 |
| Arms in the primary outcome | 4 |
| Lead sponsor | Boehringer Ingelheim |
| Results posted | Yes |
2. Clinical Question
Population
Patients with chronic obstructive pulmonary disease (COPD) who were randomized and treated. The registry describes the Full Analysis Set as patients who received at least 1 dose of study medication and had baseline data for at least 1 efficacy endpoint.
Intervention
Once-daily inhaled fixed-dose combinations of BI 1744 CL and 5 microgram tiotropium bromide, in low, medium, or high doses of BI 1744 CL. Treatment was delivered by the Respimat inhaler.
Comparator
5 microgram tiotropium bromide alone, delivered by the Respimat inhaler.
Primary question
How did change from baseline in trough FEV1 after 4 weeks compare between each combination dose and tiotropium alone? The stated primary objective was to determine the optimum dose or doses of BI 1744 CL given with tiotropium.
The primary outcome was a lung-function measure: trough FEV1 response, in liters. The registry defines trough as the mean of two FEV1 measurements taken at the end of the dosing interval, 24 hours after study medication administration. The response is the change from baseline in that measure.
This is a comparison of adjusted group means, rather than a comparison of individual patients’ outcomes. The posted results give a mean response for tiotropium alone and each combination group, along with comparisons against the control group. The trial lasted 4 weeks, so the primary question concerns the measured response over that treatment period. It does not establish what would happen over longer treatment or answer questions that were not measured in the registry record.
3. Trial Design
This was a randomized, double-blind, parallel-group phase 2 study. The registry lists an enrollment of 360 and reports the study as completed. It began in 2008-06, with primary completion in 2009-02. Participants were assigned to one of three fixed-dose combination groups or to tiotropium bromide alone. The combination groups are labeled low dose, medium dose, and high dose in the arm descriptions; the posted outcome results identify them as Tiotropium+Olodaterol 5/2 μg, 5/5 μg, and 5/10 μg.
Study medication was administered once daily for 4 weeks by oral inhalation using the Respimat inhaler. The comparator was 5 µg Tiotropium. The primary outcome population was the Full Analysis Set. The registry describes this set as including patients who received at least 1 dose and had baseline data for at least 1 efficacy endpoint, and states that all randomized and treated patients were included in the FAS for this trial.
The primary endpoint was assessed at baseline and after 4 weeks. Secondary outcomes covered additional lung-function measures and assessment times, including trough FEV1 and FVC responses, FEV1 and FVC area-under-the-curve responses, and PEF area-under-the-curve responses. The registry lists 27 outcome measures and 42 analyses; 26 secondary outcomes have posted results.
The registry record does not report the original sample-size justification, planned interim analyses, or the full statistical analysis plan. Details such as any planned hierarchy among doses or formal multiplicity adjustment are not reported in the registry record. Those omissions limit how much can be inferred about the intended confirmatory role of each comparison.
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: A randomised, double-blind, parallel group study. Each patient received their randomised treatment for 28 days.
Overall Study
| Stage | 5 µg Tiotropium | Tiotropium+Olodaterol 5/2 μg | Tiotropium+Olodaterol 5/5 μg | Tiotropium+Olodaterol 5/10 μg |
|---|---|---|---|---|
| STARTED | 90 | 89 | 93 | 88 |
| COMPLETED | 86 | 87 | 90 | 84 |
| NOT COMPLETED | 4 | 2 | 3 | 4 |
Reasons for not completing this period:
| Reason | 5 µg Tiotropium | Tiotropium+Olodaterol 5/2 μg | Tiotropium+Olodaterol 5/5 μg | Tiotropium+Olodaterol 5/10 μg |
|---|---|---|---|---|
| Adverse Event | 3 | 1 | 2 | 1 |
| Lack of Efficacy | 1 | 0 | 0 | 0 |
| Protocol Violation | 0 | 0 | 0 | 1 |
| Withdrawal by Subject | 0 | 1 | 0 | 1 |
| Other not stated above | 0 | 0 | 1 | 1 |
Analysis population for the primary outcome, as defined in the registry: Full Analysis Set (FAS). The FAS consisted of all patients who received at least 1 dose of study medication and had baseline data (pre-treatment at the end of the 2-week baseline) for at least 1 efficacy endpoint. For this trial all randomized and treated patients were included in the FAS.
5. Baseline Characteristics
The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.
Population: Treated Set (TS). The TS included all randomized patients who received at least 1 dose of study medication.
| Characteristic | Unit | 5 µg Tiotropium | Tiotropium+Olodaterol 5/2 μg | Tiotropium+Olodaterol 5/5 μg | Tiotropium+Olodaterol 5/10 μg | Total |
|---|---|---|---|---|---|---|
| Participants analysed | 90 | 89 | 93 | 88 | 360 | |
| Age, Continuous | years | 61.87 (SD 8.50) | 64.44 (SD 9.18) | 64.19 (SD 9.59) | 62.66 (SD 8.86) | 63.30 (SD 9.07) |
| Sex: Female, Male: Female | Participants | 47 | 33 | 45 | 39 | 164 |
| Sex: Female, Male: Male | Participants | 43 | 56 | 48 | 49 | 196 |
6. Primary Endpoint
The registry lists the primary outcome as Trough FEV1 Response [L] After 4 Weeks of Treatment, measured over Baseline and 4 weeks.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | L |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is the change from baseline in trough FEV1 after 4 weeks, measured in liters. FEV1 means forced expiratory volume in 1 second. In this trial, trough FEV1 was defined as the average of two measurements taken at the end of the dosing interval, 24 hours after medication administration. Baseline was defined using the mean of two pre-treatment measurements. The response is the difference between the post-treatment trough measure and baseline.
A trough measurement captures lung function near the end of the interval before the next scheduled dose, rather than shortly after inhalation. That makes it useful for examining the measured response at the dosing interval’s end. In general, using a baseline-adjusted change can account for differences in starting measurements and focus the comparison on change during treatment.
The registry reports adjusted means based on an ANCOVA model with terms for baseline, treatment, and centre; centre was treated as random, and the other effects as fixed. These are least-squares means, which are model-adjusted group estimates. The registry reports their standard errors as the measure of dispersion. The endpoint therefore summarizes an adjusted average response in the Full Analysis Set, not the range of individual responses or the proportion of participants who experienced a particular change.
The endpoint is specific to the trial’s measurement schedule and treatment period. It does not by itself describe other lung-function measures, symptoms, quality of life, long-term outcomes, or safety.
7. Results Posted in the Registry
- Tiotropium+Olodaterol 5/2 μg: mean 0.13 versus 0.11 on control; difference 0.02 (95% CI -0.03 to 0.08), standardized effect d = 0.12; z-test p = 0.419.
- Tiotropium+Olodaterol 5/5 μg: mean 0.14 versus 0.11 on control; difference 0.03 (95% CI -0.02 to 0.09), standardized effect d = 0.17; z-test p = 0.255.
- Tiotropium+Olodaterol 5/10 μg: mean 0.17 versus 0.11 on control; difference 0.06 (95% CI -0.00 to 0.12), standardized effect d = 0.29; z-test p = 0.051.
Mean difference: Tiotropium+Olodaterol 5/2 μg
95% CI: -0.03 to 0.08
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 |
|---|---|---|---|---|
| FEV1 AUC(0-6h) Response [L] After 4 Weeks of Treatment | Continuous Endpoint | Mean difference | 0.09 (0.02 to 0.15) | 96 per arm |
| FVC AUC(0-6h) Response [L] After 4 Weeks of Treatment | Continuous Endpoint | Mean difference | 0.12 (-0.00 to 0.24) | 189 per arm |
| PEF AUC(0-6h) Response [L] After 4 Weeks of Treatment | Continuous Endpoint | Mean difference | 22.87 (9.16 to 36.57) | 66 per arm |
FEV1 AUC(0-6h) Response [L] After 4 Weeks of Treatment
- 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:
- Tiotropium+Olodaterol 5/2 μg: mean 0.28 versus 0.19 on control; difference 0.09 (95% CI 0.02 to 0.15), standardized effect d = 0.40; z-test p = 0.007.
- Tiotropium+Olodaterol 5/5 μg: mean 0.28 versus 0.19 on control; difference 0.09 (95% CI 0.02 to 0.15), standardized effect d = 0.39; z-test p = 0.008.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Tiotropium+Olodaterol 5/2 μg than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Tiotropium+Olodaterol 5/5 μg than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
FVC AUC(0-6h) Response [L] After 4 Weeks of Treatment
- 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:
- Tiotropium+Olodaterol 5/2 μg: mean 0.43 versus 0.31 on control; difference 0.12 (95% CI -0.00 to 0.24), standardized effect d = 0.29; z-test p = 0.054.
- Tiotropium+Olodaterol 5/5 μg: mean 0.49 versus 0.31 on control; difference 0.18 (95% CI 0.06 to 0.30), standardized effect d = 0.44; z-test p = 0.003.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Tiotropium+Olodaterol 5/2 μg 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 higher for Tiotropium+Olodaterol 5/5 μg than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
PEF AUC(0-6h) Response [L] After 4 Weeks of Treatment
- 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:
- Tiotropium+Olodaterol 5/2 μg: mean 53.44 versus 30.58 on control; difference 22.87 (95% CI 9.16 to 36.57), standardized effect d = 0.49; z-test p = 0.001.
- Tiotropium+Olodaterol 5/5 μg: mean 50.32 versus 30.58 on control; difference 19.74 (95% CI 6.19 to 33.29), standardized effect d = 0.42; z-test p = 0.004.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Tiotropium+Olodaterol 5/2 μg than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Tiotropium+Olodaterol 5/5 μg than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The registry lists secondary measures covering lung-function response across different measurement types and time points, including FEV1, FVC, and PEF. The posted secondary results include 26 outcome measures. Across the reported summaries, combination-arm mean responses are generally numerically higher than the tiotropium-alone mean for the presented lung-function measures. The reported comparisons also show that patterns vary by outcome and dose; they should not be condensed into a single claim about all secondary endpoints.
These outcomes provide context for the primary trough FEV1 result because they examine related lung-function measures, including responses over a period after inhalation and measurements at other treatment times. They are related measurements, not interchangeable versions of the primary endpoint. Different measures and time points can give different estimates and levels of precision.
Secondary findings carry less weight when the registry record does not report whether the analyses were prespecified in a hierarchy or adjusted for multiple comparisons. In general, examining many endpoints and comparisons increases the chance that some results may appear notable by chance. The record lists numerous outcome measures and analyses, but does not report a multiplicity strategy. Accordingly, secondary p-values should be treated as exploratory evidence rather than as a set of independent confirmatory findings.
The secondary results do not replace the primary analysis, and they do not resolve the difference between the sponsor’s ANCOVA and the unadjusted recalculations. They add descriptive information about other measured lung-function outcomes during the same short treatment period. The registry record does not report enough detail to establish how these results were prioritized relative to the primary objective.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Trough FEV1 Response [L] After 1 and 2 Weeks of Treatment.
- Trough FVC Response [L] After 1, 2 and 4 Weeks of Treatment
- FEV1 AUC(0-3h) Response [L] After First Administration and After 1, 2 and 4 Weeks of Treatment
- FVC AUC(0-3h) Response [L] After First Administration and After 1, 2 and 4 Weeks of Treatment.
- PEF AUC(0-3h) Response [L/Min] After First Administration and After 1, 2 and 4 Weeks of Treatment.
- FEV1 AUC(0-6h) Response [L] After 4 Weeks of Treatment
- FVC AUC(0-6h) Response [L] After 4 Weeks of Treatment
- PEF AUC(0-6h) Response [L] After 4 Weeks of Treatment
9. Statistical Interpretation
For the primary endpoint, the registry reports adjusted mean trough FEV1 responses of 0.11 L with 5 µg Tiotropium, 0.134 L with Tiotropium+Olodaterol 5/2 μg, 0.143 L with 5/5 μg, and 0.168 L with 5/10 μg. The reported group means are numerically higher in each combination arm than in the tiotropium-alone arm. The groups included 90, 89, 93, and 88 participants, respectively.
The sponsor’s reported ANCOVA comparisons estimate mean differences of 0.024 L for 5/2 μg, 0.033 L for 5/5 μg, and 0.057 L for 5/10 μg, each compared with tiotropium alone. Their reported 95% confidence intervals are -0.029 to 0.076, -0.019 to 0.085, and 0.004 to 0.110, respectively. The associated p-values are 0.379, 0.213, and 0.034. These are the sponsor’s analyses and take precedence over the simple unadjusted recalculations from posted summary statistics.
The recalculations produce slightly different estimates and intervals. For example, the recalculated interval for the 5/10 μg comparison runs from -< 0.001 to 0.116, while the sponsor’s interval is 0.004 to 0.110. This difference matters for interpretation: the recalculation is not a replacement for the registry’s own ANCOVA result. The registry’s analysis is adjusted for baseline and centre, while the recalculation is an approximate unadjusted comparison based on posted group summaries.
In general, a confidence interval expresses the uncertainty around an estimated difference under the analysis assumptions. The sponsor’s reported intervals for the lower-dose comparisons include zero; the interval for the 5/10 μg comparison does not. That describes the posted statistical results, but it does not establish clinical importance. No threshold for a clinically important change is reported in the registry record.
The primary outcome is one part of a short phase 2 study whose stated objective was dose selection. The results describe adjusted average changes over 4 weeks in the trial population. They do not establish a longer-term effect, and the registry record does not provide enough detail to determine how the comparisons were prioritized or whether statistical multiplicity was controlled.
10. Statistical Methods Explained
The primary outcome is continuous: it is a measurement in liters, and the registry reports group means. The analysis described in the registry is ANCOVA, or analysis of covariance. In general, ANCOVA compares groups while adjusting for one or more covariates. Here, the listed terms were baseline, treatment, and centre, with centre treated as random and the other effects as fixed. The resulting least-squares means are adjusted estimates rather than simple raw averages.
What does baseline adjustment do?
In general, baseline adjustment accounts for the starting value of the outcome when estimating treatment-group differences. If participants begin with different measured values, adjustment can make the comparison more focused on the post-baseline response, conditional on the model. The registry states that baseline was included in the ANCOVA, but does not report further model diagnostics or the detailed specification of the model.
What is a standard error?
The registry reports standard errors alongside the adjusted means. In general, a standard error describes the estimated sampling variability of an estimate: smaller standard errors indicate greater precision under the model and its assumptions. A standard error is not the same as the spread of individual participant measurements. The posted group means and standard errors should therefore be read as summaries of estimated group averages, not as a description of every participant’s response.
How should the recalculated comparisons be read?
The recalculated comparisons are simple, unadjusted estimates based on the posted group summaries. They do not reproduce the sponsor’s ANCOVA, which adjusts for baseline and centre. The recalculated pooled standard deviations are approximate because they are derived from the posted standard errors. In general, an unadjusted summary-statistic comparison cannot incorporate the same covariate structure as a fitted ANCOVA model. When the recalculation and the sponsor’s own analysis differ, the sponsor’s analysis takes precedence.
For the primary outcome, the recalculated mean differences are paired with approximate confidence intervals and unadjusted p-values. Those calculations are useful as an independent descriptive check on the reported summaries, but they are not the trial’s adjusted analysis. The estimates should not be interpreted as if they came from the same model or used the same information as the registry’s ANCOVA.
What does a confidence interval convey?
In general, a confidence interval gives a range of values compatible with the estimate under the statistical procedure and its assumptions. A wider interval indicates less precision than a narrower interval. Whether an interval includes zero is relevant to the direction and statistical compatibility of a difference, but it does not establish whether the difference is important to patients or clinically meaningful. That requires an appropriate clinical context, which is not reported in the registry record.
Multiplicity is another general statistical concern when several doses, endpoints, or time points are tested. Each additional comparison creates another opportunity for a result to appear notable by chance if the analyses are treated independently. A prespecified multiplicity strategy can address this concern, for example through adjustment or a testing hierarchy. The registry record does not report such a strategy, so the displayed p-values should be interpreted with caution, especially for secondary outcomes.
The analysis population also matters. The registry defines the FAS by treatment exposure and availability of baseline data for at least one efficacy endpoint, and says all randomized and treated patients were included in this trial’s FAS. This definition does not, by itself, explain how missing follow-up measurements were handled. The approach to missing outcome data is not reported in the registry record.
Finally, p-values and estimates answer different questions. An estimate describes the size and direction of the group contrast; its interval describes precision; a p-value describes compatibility with a specified null model under the analysis assumptions. None of these alone establishes clinical importance or settles questions about outcomes not assessed in this trial.
11. Confidence Intervals and Precision
The sponsor’s 95% confidence intervals for the primary comparisons are -0.029 to 0.076 L for Tiotropium+Olodaterol 5/2 μg versus 5 µg Tiotropium, -0.019 to 0.085 L for 5/5 μg, and 0.004 to 0.110 L for 5/10 μg. These intervals describe the precision of the sponsor’s ANCOVA estimates under that analysis. The registry reports corresponding mean differences of 0.024 L, 0.033 L, and 0.057 L.
The first two sponsor intervals include zero, while the interval for the 5/10 μg comparison is above zero. This is a statistical description of the reported estimates and intervals, not a judgment about clinical importance. The registry record does not report a threshold for a clinically meaningful difference.
The recalculated intervals differ from the sponsor’s intervals because the recalculations use unadjusted posted summaries rather than the ANCOVA model. For the 5/10 μg comparison, the recalculated interval is -< 0.001 to 0.116, with an unadjusted p-value of 0.051; the sponsor reports an interval of 0.004 to 0.110 and p = 0.034. The sponsor’s own analysis takes precedence. The mismatch illustrates why approximate calculations should not be treated as a substitute for the trial’s analysis.
In general, intervals communicate uncertainty more fully than a single estimate or p-value. Their width reflects precision, while their location indicates the range of differences compatible with the analysis. Precision is limited to the estimates and model reported for this outcome and treatment period. It does not capture uncertainty about unreported analysis choices, missing-data handling, or the generalizability of the findings beyond the enrolled study population.
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 | 1,076 | 1,441 |
| 75% of the observed effect | 1,913 | 2,561 |
| 50% of the observed effect | 4,303 | 5,761 |
The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design assumptions. For continuous outcomes such as these, the displayed figures are participants per arm, not total events. 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 the stated fraction of the observed effect. Original design assumptions are not reported in the registry record.
The 80% power column gives the estimated participants per arm for a future study to have an 80% chance of detecting the stated effect under those planning assumptions, if that effect and the other assumptions hold. The 90% power column uses a higher target chance of detecting the same effect, and therefore generally requires more participants per arm. These are planning quantities, not observed power.
Rows that plan for 100%, 75%, or 50% of the observed effect ask how large a future study might need to be if the effect of interest were the observed estimate or a smaller fraction of it. Smaller effects are harder to distinguish from random variation and require more participants per arm to meet the same target power. Because the observed effect is uncertain, these calculations are illustrations rather than guarantees of a future study’s performance.
The displayed planning calculations use the observed summary effect and the listed assumptions; they do not show what sample size the sponsor originally chose or why. They also do not account for design features that are not included in the stated assumptions. Their purpose is to show how sample-size requirements change as the target effect and desired power change.
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 = 0.024; pooled standard deviation σ = 0.199.
- n = 2 × (1.96 + 0.842)2 × 0.1992 / 0.0242 = 1,075.7, rounded up to 1,076 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 <- 0.024 # observed difference in means
sigma <- 0.198672458490632 # 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(696020)
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 = 1,076 (80% power), 1,441 (90% power)
75% of observed effect: n per arm = 1,913 (80% power), 2,561 (90% power)
50% of observed effect: n per arm = 4,303 (80% power), 5,761 (90% power)
power.t.test: 1076.7
Simulated power at n = 1,076 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 |
|---|---|---|---|
| ANCOVA | Mean Difference (Final Values) 0.024 | -0.029 to 0.076 | 0.379 |
| ANCOVA | Mean Difference (Final Values) 0.033 | -0.019 to 0.085 | 0.213 |
| ANCOVA | Mean Difference (Final Values) 0.057 | 0.004 to 0.110 | 0.034 |
The registry reports sponsor ANCOVA comparisons for the primary outcome, including adjusted mean differences, 95% confidence intervals, and p-values. Those analyses adjust for baseline and centre, according to the endpoint description. The recalculated comparisons instead use simple unadjusted calculations from posted group summaries and approximate standard deviations. They are not intended to reproduce the sponsor’s model.
The two approaches yield different estimates, intervals, and p-values. For example, for Tiotropium+Olodaterol 5/10 μg versus 5 µg Tiotropium, the recalculation gives a mean difference of 0.058 L and an interval of -< 0.001 to 0.116, while the sponsor reports a mean difference of 0.057 L and an interval of 0.004 to 0.110. The sponsor reports p = 0.034; the recalculated unadjusted p-value is 0.051. Differences are also present for the other primary comparisons.
The sponsor’s own analysis takes precedence because it is the trial’s reported adjusted analysis. The recalculation is best viewed as a transparent, approximate check using the posted summaries, not a competing reconstruction of the ANCOVA. Differences between the results should not be resolved by selecting whichever estimate or p-value appears more favorable.
15. Multiplicity, Missing Data and Analysis Populations
The registry reports several treatment groups, a primary endpoint, and a broad set of secondary outcome measures and analyses. In general, when many comparisons are made, the chance of at least one seemingly notable result arising by chance can increase. Statistical plans may address this through a prespecified testing hierarchy, adjustment of significance levels, or other methods. The registry record does not report whether any such multiplicity procedure was planned or used.
That absence does not establish that no adjustment occurred; it means the approach is not reported in the registry record. Without that information, the posted p-values should be interpreted as reported results, without assuming that they control the overall error rate across doses, outcomes, and time points. The same caution applies to secondary analyses, which are less persuasive as confirmatory evidence when their role and multiplicity handling are unclear.
The registry identifies the Full Analysis Set as patients who received at least 1 dose and had baseline data for at least 1 efficacy endpoint, and states that all randomized and treated patients were included in the FAS for this trial. It does not report the handling of missing follow-up measurements, the amount of missing outcome data, or whether any sensitivity analyses were performed. The approach to missing data is therefore not reported in the registry record.
The record also does not report the original sample-size justification, interim analyses, or the complete statistical analysis plan. These details would help clarify which comparisons were intended to be primary for inference, how repeated testing was handled, and how analysis choices were made. Their absence limits the interpretation of the full analysis strategy; it does not invalidate the posted estimates, but it calls for restraint when drawing broader conclusions from multiple results.
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 |
|---|---|---|---|
| 5 µg Tiotropium | 2 | 90 | 2.2% |
| Tiotropium+Olodaterol 5/2 μg | 3 | 89 | 3.4% |
| Tiotropium+Olodaterol 5/5 μg | 1 | 93 | 1.1% |
| Tiotropium+Olodaterol 5/10 μg | 0 | 88 | 0.0% |
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 |
|---|---|
| 5 µg Tiotropium | 0 of 90 |
| Tiotropium+Olodaterol 5/2 μg | 0 of 89 |
| Tiotropium+Olodaterol 5/5 μg | 0 of 93 |
| Tiotropium+Olodaterol 5/10 μg | 0 of 88 |
Most frequent serious adverse event terms
| Event term | Organ system | 5 µg Tiotropium | Tiotropium+Olodaterol 5/2 μg | Tiotropium+Olodaterol 5/5 μg | Tiotropium+Olodaterol 5/10 μg |
|---|---|---|---|---|---|
| Chronic obstructive pulmonary disease | Respiratory, thoracic and mediastinal disorders | 1 of 90 | 3 of 89 | 0 of 93 | 0 of 88 |
| Pneumonia | Infections and infestations | 0 of 90 | 0 of 89 | 1 of 93 | 0 of 88 |
| Drug Hypersensitivity | Immune system disorders | 1 of 90 | 0 of 89 | 0 of 93 | 0 of 88 |
| Femur fracture | Injury, poisoning and procedural complications | 1 of 90 | 0 of 89 | 0 of 93 | 0 of 88 |
| Fibula fracture | Injury, poisoning and procedural complications | 1 of 90 | 0 of 89 | 0 of 93 | 0 of 88 |
Serious events with the highest arm-level rate: chronic obstructive pulmonary disease (3.4%), drug hypersensitivity (1.1%), femur fracture (1.1%), fibula fracture (1.1%), pneumonia (1.1%).
The serious adverse event figures are counts of affected participants within each group, with the number at risk also reported. The registry lists 2 participants affected among 90 at risk in the 5 µg Tiotropium group, 3 among 89 in the Tiotropium+Olodaterol 5/2 μg group, 1 among 93 in the 5/5 μg group, and 0 among 88 in the 5/10 μg group.
For the other adverse events category, the registry reports 0 affected participants in each group. These figures describe the posted counts during the study; they do not show the full clinical detail, timing, duration, or relationship to treatment for individual events. Death counts are not reported in the registry record.
The listed serious-event terms include chronic obstructive pulmonary disease, drug hypersensitivity, femur fracture, fibula fracture, and pneumonia. These terms should be read as event listings, not as proof that an event was caused by a study treatment. The brief study duration and group counts also mean that the figures should not be used alone to make broad comparisons of safety between treatments.
17. What the Result Does, and Does Not, Mean
The posted results describe adjusted average changes in trough FEV1 over 4 weeks among participants in the trial’s Full Analysis Set. The group means are numerically higher in the combination arms than in the tiotropium-alone arm. The sponsor’s ANCOVA reports a 95% confidence interval that excludes zero for the 5/10 μg comparison, while the reported intervals for the lower-dose comparisons include zero.
These findings do not, by themselves, establish that a measured difference is clinically important. The registry record does not report a threshold for clinical importance or connect the primary measurement to an individual patient’s experience. A mean difference also does not show how outcomes varied among participants.
The results do not establish what would happen beyond the 4-week treatment period, or answer questions about outcomes that were not measured. They should not be read as a general conclusion about all patients with COPD or all use of the study treatments. The trial was phase 2, and its stated primary objective was to determine the optimum dose or doses of BI 1744 CL given with tiotropium.
There is also a distinction between the sponsor’s adjusted analysis and the approximate unadjusted recalculations. The sponsor’s ANCOVA is the trial’s reported analysis and takes precedence. The recalculations provide a separate descriptive check and yield different uncertainty estimates. Secondary endpoints add context, but their interpretation is limited by the unreported multiplicity strategy and other missing analysis details.
In short, the registry presents evidence about short-term, adjusted average lung-function responses and a small set of serious adverse event counts. It does not provide a complete basis for judgments about clinical importance, long-term outcomes, or the full statistical plan.
18. Why This Trial Matters Statistically
This trial illustrates why statistical interpretation depends on more than comparing group means. The primary estimates are adjusted using ANCOVA, whereas the recalculations use unadjusted posted summaries. Those approaches do not answer precisely the same statistical question and can produce different intervals and p-values. The sponsor’s analysis therefore takes precedence over the approximate recalculation.
It also illustrates the value of examining confidence intervals alongside point estimates. A mean difference alone gives no indication of its precision. The sponsor’s intervals show that the uncertainty differs across dose comparisons, and the reported interval for the highest combination dose does not match the recalculated interval’s relation to zero. Understanding which analysis produced each interval is essential to avoid mixing results from different methods.
The trial also raises general issues in dose-ranging studies. Several dose groups and many secondary outcomes create multiple opportunities for comparisons. Because the registry record does not report a multiplicity plan or testing hierarchy, interpretation should remain focused on the stated primary objective and be cautious about isolated secondary results.
Finally, sample-size planning illustrations help show how the number of participants needed depends on the effect a future study aims to detect. They are not observed power and do not reveal the original design rationale. Keeping that distinction clear prevents planning calculations from being mistaken for evidence about the trial’s ability to detect its observed findings.
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.
This was a 4-week study, so the posted efficacy results concern a short treatment period. The registry record does not report longer-term outcomes. The primary endpoint is an adjusted average change in trough FEV1; it does not describe the distribution of individual responses or establish a clinical-importance threshold.
The registry’s sponsor-reported ANCOVA and the simple recalculations differ. The latter use approximate standard deviations and unadjusted comparisons, so they cannot reproduce the baseline- and centre-adjusted analysis. The discrepancy makes it especially important to rely on the sponsor’s reported analysis for the primary comparison rather than treating the recalculation as an equivalent result.
The registry does not report the original sample-size justification, interim analyses, full statistical analysis plan, missing-data handling, or multiplicity procedure. Those omissions prevent a detailed assessment of the planned analysis strategy and the treatment of multiple endpoints, comparisons, and incomplete measurements. Although the FAS definition is reported, it does not explain whether or how missing follow-up measurements affected the estimates.
The serious adverse event counts are modest and are reported without death counts or fuller event-level context. The record also does not establish whether listed events were attributed to treatment. These limitations constrain interpretation of safety comparisons. Finally, the phase 2 dose-ranging purpose and the trial population limit how broadly the results can be generalized from the registry record alone.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Combination of Orally Inhaled BI1744CL/Tiotropium Bromide in Patients With Chronic Obstructive Pulmonary Disease ( COPD) — NCT00696020.
- Registry record last updated 2015-08-13; status last verified 2015-07.
- Results first posted 2015-08-13.
- 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
NCT00696020 is a completed randomized, double-blind, parallel-group phase 2 study in patients with COPD. It compared once-daily low-, medium-, and high-dose BI 1744 CL fixed-dose combinations with tiotropium bromide against tiotropium bromide alone over 4 weeks. Enrollment was 360.
The primary endpoint was change from baseline in trough FEV1 response in liters. The registry reports adjusted means from ANCOVA and sponsor-reported comparisons against tiotropium alone. The sponsor’s analysis takes precedence over the approximate unadjusted recalculations, which differ. The record also lists secondary lung-function outcomes and serious adverse event counts.
The registry record does not report the original sample-size justification, multiplicity strategy, missing-data handling, or full statistical analysis plan. These gaps limit interpretation of the analysis strategy and the broader meaning of multiple endpoint results.