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 Efficacy and Safety of 2 Doses of Tiotropium Via Respimat in Adult Patients With Mild Persistent Asthma (NCT01316380), a randomized phase 3 study. The primary outcome is Peak Forced Expiratory Volume in 1 Second (FEV1) Response Within 3 Hours Post Dosing (0-3h) After a Treatment Period of 12 Weeks..
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01316380 |
| Phase | Phase 3 |
| Condition | Asthma |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 465 |
| Arms in the primary outcome | 3 |
| Lead sponsor | Boehringer Ingelheim |
| Results posted | Yes |
2. Clinical Question
Population
Adults with mild persistent asthma receiving maintenance inhaled corticosteroid treatment. The registry describes the primary analysis population as the Full Analysis Set: treated participants who received at least one dose of randomized trial medication.
Intervention
Tiotropium inhalation solution delivered by Respimat inhaler once daily, at either 2.5 mcg or 5 mcg, for the 12-week treatment period.
Comparator
Placebo delivered once daily by Respimat inhaler. The trial used a parallel-group design, so participants were assigned to one of the three groups.
Primary question
How did peak FEV1 response within 3 hours after dosing, measured after 12 weeks, compare between each tiotropium group and placebo? The registry defines response as the difference between the maximum FEV1 measured in that post-dose window and the baseline measurement.
The trial was designed to evaluate efficacy and safety in mild persistent asthma, with treatment given on top of maintenance inhaled corticosteroid treatment. The primary endpoint was a lung-function measure. The registry also lists outcomes concerning other lung-function measures, asthma control, exacerbations, and rescue medication use. These outcomes address different aspects of the trial question and should not be treated as interchangeable with the primary endpoint.
The posted primary results report adjusted mean responses for placebo and each tiotropium dose, alongside comparisons with placebo. Those estimates describe the recorded group results under the trial’s analysis. They do not by themselves establish how an individual participant would respond, nor do they determine the importance of any observed difference for patients. The registry record does not report a threshold for a clinically important difference.
3. Trial Design
This was a Phase III, randomized, double-blind, placebo-controlled, parallel-group trial. The registry lists 465 participants enrolled. Participants were assigned to placebo, tiotropium 2.5 mcg, or tiotropium 5 mcg; each treatment was administered once daily via Respimat inhaler. The treatment period was 12 weeks. The trial evaluated tiotropium on top of maintenance inhaled corticosteroid treatment in adults with mild persistent asthma.
For the primary outcome, the posted results include 154 participants in the placebo group, 151 in the 2.5 mcg group, and 152 in the 5 mcg group. These are the group counts associated with the endpoint results, not a statement that every enrolled participant contributed to every outcome. The primary analysis population is described as the Full Analysis Set, defined in the registry record as all patients in the treated set who received at least one dose of randomized trial medication.
The primary endpoint was peak FEV1 response within 3 hours after dosing, assessed after a treatment period of 12 weeks. The registry describes the analysis as a mixed model repeated-measures analysis, with means adjusted for treatment, pooled centre, visit, baseline, treatment-by-visit, and baseline-by-visit. The registry also lists 11 outcome measures and 20 analyses overall. The reported secondary outcomes include lung-function measures, an asthma control questionnaire responder outcome, time to asthma exacerbation outcomes, and rescue medication use.
The registry record gives the sponsor as Boehringer Ingelheim and the study status as completed. It records the study start as 2011-03 and primary completion as 2012-04. The original trial’s sample-size justification, intended allocation proportions, and detailed statistical analysis plan 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.
Overall Study
| Stage | Placebo | Tio R2.5 | Tio R5 |
|---|---|---|---|
| STARTED | 156 | 154 | 155 |
| COMPLETED | 154 | 149 | 152 |
| NOT COMPLETED | 2 | 5 | 3 |
Reasons for not completing this period:
| Reason | Placebo | Tio R2.5 | Tio R5 |
|---|---|---|---|
| Adverse Event | 0 | 2 | 1 |
| Protocol Violation | 0 | 0 | 1 |
| Withdrawal by Subject | 1 | 2 | 0 |
| Other | 0 | 1 | 1 |
| Not treated | 1 | 0 | 0 |
Analysis population for the primary outcome, as defined in the registry: All patients from Full Analysis Set (FAS) FAS is defined as all patients in the treated set who received at least one dose of randomized trial medication.
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 | Tio R2.5 | Tio R5 | Total |
|---|---|---|---|---|---|
| Participants analysed | 155 | 154 | 155 | 464 | |
| Age, Continuous | Years | 42.8 (SD 12.1) | 43.8 (SD 14.0) | 41.9 (SD 13.0) | 42.9 (SD 13) |
| Sex: Female, Male: Female | Participants | 103 | 82 | 96 | 281 |
| Sex: Female, Male: Male | Participants | 52 | 72 | 59 | 183 |
6. Primary Endpoint
The registry lists the primary outcome as Peak Forced Expiratory Volume in 1 Second (FEV1) Response Within 3 Hours Post Dosing (0-3h) After a Treatment Period of 12 Weeks., measured over Baseline and 12 weeks.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | Liter |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is peak forced expiratory volume in 1 second (FEV1) response within 3 hours after dosing, measured after a 12-week treatment period. FEV1 is the volume of air a person can forcibly exhale in the first second of a breath. The registry records the outcome in liters and defines the response as the maximum FEV1 measured during the first 3 hours after dosing minus the baseline FEV1 measurement. Baseline was measured 10 minutes before the first dose of trial medication.
The endpoint is a change-from-baseline measure rather than a single follow-up value. Comparing that response between a randomized treatment group and placebo can help describe whether the groups’ recorded lung-function changes differed during the trial. The endpoint is described as a least-squares mean, which is a model-adjusted group mean rather than a simple arithmetic average. The model included treatment, pooled centre, visit, baseline, treatment-by-visit, and baseline-by-visit terms.
General statistical context: a continuous lung-function measure retains information about the size of observed values, rather than reducing them to categories such as responder or non-responder. That can make it useful for comparing group averages. However, a group-average change does not convey the full spread of individual responses, and an endpoint estimate alone does not establish whether a difference is clinically important. The registry record does not report a clinical-importance threshold for this endpoint.
7. Results Posted in the Registry
- Tio R2.5: mean 0.29 versus 0.13 on control; difference 0.16 (95% CI 0.09 to 0.23), standardized effect d = 0.50; z-test p = <0.001.
- Tio R5: mean 0.26 versus 0.13 on control; difference 0.13 (95% CI 0.06 to 0.20), standardized effect d = 0.40; z-test p = <0.001.
Mean difference: Tio R2.5
95% CI: 0.09 to 0.23
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 |
|---|---|---|---|---|
| Trough FEV1 Response Determined After a Treatment Period of 12 Weeks. | Continuous Endpoint | Mean difference | 0.11 (0.04 to 0.18) | 134 per arm |
| Peak (Within 3 Hours Post-dosing) Forced Vital Capacity (FVC) Response at the End of the 12-week Treatment Period. | Continuous Endpoint | Mean difference | 0.11 (0.02 to 0.19) | 196 per arm |
| FEV1 Area Under the Curve (AUC0-3h) Response at the End of the 12-week Treatment Period. | Continuous Endpoint | Mean difference | 0.15 (0.08 to 0.22) | 62 per arm |
Trough FEV1 Response Determined After a Treatment Period of 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:
- Tio R2.5: mean 0.12 versus 0.01 on control; difference 0.11 (95% CI 0.04 to 0.18), standardized effect d = 0.34; z-test p = 0.003.
- Tio R5: mean 0.14 versus 0.01 on control; difference 0.12 (95% CI 0.05 to 0.20), standardized effect d = 0.37; z-test p = 0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Tio R2.5 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 Tio R5 than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Peak (Within 3 Hours Post-dosing) Forced Vital Capacity (FVC) Response at the End of the 12-week Treatment Period.
- 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:
- Tio R2.5: mean 0.23 versus 0.13 on control; difference 0.11 (95% CI 0.02 to 0.19), standardized effect d = 0.28; z-test p = 0.013.
- Tio R5: mean 0.18 versus 0.13 on control; difference 0.06 (95% CI -0.03 to 0.14), standardized effect d = 0.15; z-test p = 0.179.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Tio R2.5 than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Tio R5 and the control. The interval gives the range of effects that remain compatible with the data.
FEV1 Area Under the Curve (AUC0-3h) Response at the End of the 12-week Treatment Period.
- 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:
- Tio R2.5: mean 0.20 versus 0.05 on control; difference 0.15 (95% CI 0.08 to 0.22), standardized effect d = 0.51; z-test p = <0.001.
- Tio R5: mean 0.17 versus 0.05 on control; difference 0.13 (95% CI 0.06 to 0.19), standardized effect d = 0.42; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Tio R2.5 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 Tio R5 than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary outcomes cover several related but distinct domains: trough and peak lung-function responses, area-under-the-curve lung-function measures, asthma control, time to asthma exacerbation, and rescue medication use. The posted continuous lung-function results generally show higher adjusted mean responses in one or both tiotropium groups than in the placebo group. The pattern is not uniform across all outcomes or doses; for example, the reported peak FVC comparison for the 5 mcg group has a confidence interval spanning zero. The registry record also lists responder and time-to-event outcomes, but detailed posted numerical results for all secondary outcomes are not included in the endpoint summaries.
Broadly, the lung-function pattern is compatible with the direction of the primary peak FEV1 comparisons, but the secondary endpoints measure different quantities and time points. Agreement across related measures can add context; it does not make the endpoints interchangeable or independently establish clinical importance. The registry record lists 11 outcome measures and 20 analyses overall, so the secondary findings represent multiple opportunities to observe differences.
Unless an analysis plan specifies otherwise, unadjusted secondary p-values should be interpreted cautiously. General statistical context: when many outcomes or comparisons are tested, the chance of at least one small p-value arising by chance increases. A prespecified multiplicity strategy can address that concern, but it is not reported in the registry record. Consequently, the secondary results are best treated as supportive and exploratory rather than as definitive evidence in isolation. The registry record does not report which secondary outcomes were designated confirmatory, how their testing was ordered, or whether any multiplicity adjustment was applied.
For individual secondary estimates, the endpoint-specific posted results and sponsor analyses carry more detail than an overall pattern description. The main statistical point is that the secondary outcomes broaden the scope of measurement, while also increasing the need to account for multiple comparisons and to distinguish planned tests from exploratory analyses.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Trough FEV1 Response Determined After a Treatment Period of 12 Weeks.
- Peak (Within 3 Hours Post-dosing) Forced Vital Capacity (FVC) Response at the End of the 12-week Treatment Period.
- FEV1 Area Under the Curve (AUC0-3h) Response at the End of the 12-week Treatment Period.
- FVC (AUC0-3h) Response at the End of the 12-week Treatment Period.
- Asthma Control Questionnaire (ACQ) Responder After 12 Weeks of Treatment
- Time to First Severe Asthma Exacerbation During the 12-week Treatment.
- Time to First Asthma Exacerbation During the 12-week Treatment.
- Use of Rescue Medication During 24h Period
9. Statistical Interpretation
In the posted primary results, the adjusted mean peak FEV1 response was 0.134 liters for placebo, 0.293 liters for tiotropium 2.5 mcg, and 0.262 liters for tiotropium 5 mcg. The registry’s reported mixed-model comparison with placebo estimated a mean difference of 0.159 liters for the 2.5 mcg group, with a 95% confidence interval from 0.088 to 0.230 and p < 0.001. For the 5 mcg group, the reported mean difference was 0.128 liters, with a 95% confidence interval from 0.057 to 0.199 and p < 0.001.
These are group-level estimates for the defined primary outcome and analysis population. Both reported confidence intervals lie above zero, and the sponsor’s reported p-values are small under the fitted model’s comparison. This describes statistical evidence of between-group differences in the endpoint within the posted analysis. It does not establish the size of benefit for any particular participant, the clinical importance of the differences, or what would happen beyond the 12-week treatment period.
The registry’s arm-level values are adjusted means with standard errors. A standard error describes uncertainty in estimating a group mean; it is not the range of individual participant responses. The sponsor-reported confidence intervals provide a range of estimates compatible with the analysis and its assumptions. Their width matters alongside the point estimates: the point estimate alone does not communicate the uncertainty around it.
The recalculated comparisons use unadjusted calculations from the posted summary statistics, rather than reproducing the sponsor’s mixed-model analysis. For tiotropium 2.5 mcg, the recalculated mean difference is 0.159 liters, with an approximate 95% confidence interval from 0.087 to 0.231 and p <0.001. For tiotropium 5 mcg, the recalculated mean difference is 0.128 liters, with an approximate 95% confidence interval from 0.056 to 0.200 and p <0.001. These calculations are useful as a transparent cross-check, but they are not a substitute for the sponsor’s model-based results. The registry record does not flag a discrepancy.
The primary result should be read in the context of the trial’s design and limitations. Randomization and double masking are features of the trial design, but the registry record does not provide details about sequence generation, concealment, adherence, or missing outcome data. It also does not report the trial’s prespecified analysis plan or the clinical-importance threshold for peak FEV1. Those absences limit what can be concluded from the posted result alone.
10. Statistical Methods Explained
The primary outcome is continuous: it is a change in FEV1 measured in liters. The registry reports adjusted least-squares means and standard errors for the three groups, and describes the primary analysis as a mixed model repeated-measures analysis. General statistical context: a continuous outcome retains information about the magnitude of measurements. Its analysis can compare group averages while accounting for selected model terms, but interpretation depends on how those terms and the repeated observations are handled.
What does the mixed model describe?
The registry says that the primary means were adjusted for treatment, pooled centre, visit, baseline, treatment-by-visit, and baseline-by-visit. General explanation: adjustment means the model estimates group results while incorporating the listed factors rather than simply comparing raw averages. A treatment-by-visit term allows the modeled treatment contrast to vary by visit. A baseline-by-visit term allows the relationship between baseline measurement and outcome to vary across visits. The registry does not describe the full model specification, covariance structure, estimation details, or missing-data assumptions, so those aspects are not reported in the registry record.
The primary description calls the model a repeated-measures model, while the displayed endpoint is a response after 12 weeks. General statistical context: repeated-measures analyses can use information from measurements made at more than one visit and account for the fact that measurements from the same participant are related. The registry does not identify the exact set of observations included in the fitted model or explain how incomplete follow-up was treated. It is therefore not possible to assess from the registry record whether or how the analysis used every available post-baseline observation.
What is an adjusted mean difference?
The posted arm values are least-squares means. The comparison estimates are the modeled mean difference between a tiotropium group and placebo. General explanation: the difference is a contrast between the two group estimates, expressed in the outcome’s units. It is not a percentage change and does not describe the distribution of responses within either group. The reported contrasts are consistent with the direction of the displayed arm means, but they should be understood as model-based comparisons under the sponsor’s stated approach.
The sponsor reports mixed-model comparisons with 95% confidence intervals and p-values. General explanation: a confidence interval conveys uncertainty around an estimated contrast under the model; a p-value describes how compatible the observed data are with a specified null hypothesis, given the analysis assumptions. Neither statistic measures clinical importance. The registry record does not report whether the primary test was part of a multiplicity-controlled testing hierarchy or whether any alpha adjustment was used.
How do the recalculated results differ?
The recalculated results are simple, unadjusted comparisons based on the posted summary statistics. They use the reported group means and standard errors to produce approximate comparisons; they do not reproduce the repeated-measures model or its covariate adjustment. The recalculated confidence intervals are therefore approximate and may differ from the sponsor’s model-based intervals. They are presented as a check on the scale and direction of the posted contrast, not as a replacement analysis. The registry record does not flag a discrepancy, and the sponsor’s reported analysis remains the primary account of the trial’s modeled results.
General statistical context: standard errors quantify uncertainty in an estimated mean, while standard deviations describe variability among individual observations. The posted arm values give standard errors, not standard deviations. The recalculation uses an approximate pooled standard deviation inferred from the reported standard errors and group counts; that approximation does not recover the original participant-level variability or model. The recalculated effect-size and planning illustrations should consequently be interpreted as analytical aids, not as additional outcomes observed in the trial.
Why can over-dispersion matter?
General explanation: for continuous outcomes, variability affects how precisely group means and differences can be estimated. For count outcomes, over-dispersion means that observed variation exceeds what a simple count model expects; an analysis that ignores it can understate uncertainty. The primary outcome is continuous, and the registry does not report an over-dispersion assessment for it. The registry’s listed time-to-event outcomes are different types of outcomes and require methods suited to event timing. The posted sample-size assumptions identify a Schoenfeld approach for time-to-event planning illustrations; that does not establish which full analysis method or assumptions were used for those trial outcomes.
General statistical context: models are only as informative as their assumptions and the data available for analysis. Randomization supports comparisons between assigned groups, while masking can reduce some sources of differential assessment or behavior. Neither feature eliminates uncertainty from missing observations, nonadherence, measurement error, or incomplete reporting. Detailed information on these matters is not reported in the registry record.
11. Confidence Intervals and Precision
The sponsor’s primary comparison for tiotropium 2.5 mcg is 0.159 liters, with a 95% confidence interval from 0.088 to 0.230. The comparison for tiotropium 5 mcg is 0.128 liters, with a 95% confidence interval from 0.057 to 0.199. These intervals quantify uncertainty around the estimated group contrasts under the sponsor’s mixed-model analysis. Both intervals are above zero, while their widths show that the estimates are not exact values.
General explanation: a confidence interval is a range produced by a method that, under its assumptions, has a stated long-run coverage property. It does not mean that there is a 95% probability that the particular interval contains the true value. Nor does it include every possible source of uncertainty, such as bias from missing data or model misspecification. The registry record does not provide enough detail to evaluate all such sources.
The recalculated intervals are 0.087 to 0.231 liters for 2.5 mcg and 0.056 to 0.200 liters for 5 mcg. They are approximate intervals from unadjusted calculations, not the sponsor’s model-based intervals. The small differences between the posted intervals and the sponsor’s intervals reflect that the methods are not identical; the registry record does not flag a discrepancy.
Precision should be considered together with the estimated contrast and its units. A confidence interval that excludes zero addresses compatibility with a zero contrast under the analysis, but it does not answer whether the contrast is large enough to matter clinically. The clinical-importance threshold for peak FEV1 is not reported in the registry record. The reported standard errors for the group means also do not describe individual-level variation, so they should not be read as ranges of likely participant responses.
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 | 65 | 86 |
| 75% of the observed effect | 114 | 153 |
| 50% of the observed effect | 257 | 343 |
The sample-size figures are planning illustrations derived from the observed effect, not the trial’s original design assumptions. For these continuous-outcome comparisons, the figures refer to participants per arm, not total events. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set at the stated fraction of the observed effect. The original trial’s own sample-size justification and design assumptions are not reported in the registry record.
The 80% power column indicates the number of participants per arm that the planning calculation estimates would be needed for an 80% chance of detecting the selected effect under those assumptions, if that effect were the true one. The 90% power column uses a higher target chance of detecting the selected effect and therefore generally requires more participants per arm. These are prospective planning quantities, not descriptions of the trial’s realized probability of finding a result.
The rows planning for 100%, 75%, and 50% of the observed effect explore how the required group size changes when the target difference is smaller than the observed estimate. Smaller effects need more participants to distinguish them from random variation with the same target power and significance level. The curve is a visual representation of the same relationship between a chosen effect size and the planning requirement; it is not a separate trial result.
This is not observed power. Because the calculations start with an effect estimate from the trial, they are illustrations for designing future research and can be unstable when the observed estimate is imprecise. They do not show whether the completed trial was adequately powered according to its original plan, which is not reported in the registry record.
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 = 0.159; pooled standard deviation σ = 0.321.
- n = 2 × (1.96 + 0.842)2 × 0.3212 / 0.1592 = 64.0, rounded up to 65 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 <- 0.159 # observed difference in means
sigma <- 0.321091948830799 # 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(1316380)
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 = 65 (80% power), 86 (90% power)
75% of observed effect: n per arm = 114 (80% power), 153 (90% power)
50% of observed effect: n per arm = 257 (80% power), 343 (90% power)
power.t.test: 65
Simulated power at n = 65 per arm: 0.804 (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) 0.128 | 0.057 to 0.199 | < 0.001 |
| Mixed Models Analysis | Mean Difference (Final Values) 0.159 | 0.088 to 0.230 | < 0.001 |
The sponsor’s primary analysis is reported as a mixed-model analysis of mean differences, with 95% confidence intervals and p-values. For the 2.5 mcg comparison, the reported difference is 0.159 liters, the interval is 0.088 to 0.230, and p < 0.001. For the 5 mcg comparison, the reported difference is 0.128 liters, the interval is 0.057 to 0.199, and p < 0.001.
The recalculated values use unadjusted calculations from the posted group summary statistics. They give the same displayed mean differences to the reported precision as the sponsor’s estimates, while their approximate confidence intervals and p-values are not identical to the sponsor’s model-based results. That is expected because the recalculation does not reproduce the mixed model and its adjustments. The registry record does not flag a discrepancy. Accordingly, the sponsor’s own reported analysis is the principal source for interpreting the trial’s primary comparison; the recalculation is a transparent check, not a competing analysis.
For secondary outcomes, the same distinction applies: the registry reports sponsor analyses, while the accompanying recalculations are unadjusted approximations. Where estimates or p-values differ, the methods and rounding can account for differences; those calculations should not replace the sponsor’s reported analyses. The registry record does not provide participant-level data or a full analysis plan that would permit an independent reproduction of the model.
15. Multiplicity, Missing Data and Analysis Populations
The registry record lists multiple outcomes and analyses, but it does not report a multiplicity strategy for the primary and secondary comparisons. It is not reported in the registry record whether the primary endpoint was tested within a formal hierarchy, whether secondary tests were adjusted, or whether a family-wise error or false-discovery approach was used. This matters because interpreting each p-value as if it were the only test can overstate the strength of evidence when many outcomes and contrasts are considered.
The sponsor reports primary comparisons for both tiotropium doses against placebo, alongside secondary analyses across additional lung-function, asthma-control, exacerbation, and rescue-medication outcomes. Without the prespecified testing structure, the role of each p-value cannot be fully assessed. The primary outcome remains the clearest focal comparison, but the registry record does not establish whether the two dose comparisons were jointly controlled or how the secondary tests were handled.
The registry identifies the Full Analysis Set as the primary analysis population: treated participants who received at least one dose of randomized trial medication. The primary outcome group counts are 154 for placebo, 151 for tiotropium 2.5 mcg, and 152 for tiotropium 5 mcg. The record does not provide a participant flow account, the number with missing primary endpoint measurements, reasons for missingness, or the exact method used to handle missing observations. Those details are not reported in the registry record.
General statistical context: missing outcome data can affect precision and, depending on why data are missing and how the analysis handles them, can also affect the estimated comparison. The registry’s description of a repeated-measures model does not by itself specify the missing-data assumptions or establish that missingness had no effect. The record also does not describe adherence, protocol deviations, imputation, sensitivity analyses, or analyses in populations other than the stated Full Analysis Set. These omissions limit independent assessment of robustness.
The registry record describes randomization and double masking, but detailed procedures for sequence generation, allocation concealment, and maintenance of masking are not reported. The original sample-size justification and the complete statistical analysis plan are also not reported in the registry record. These gaps prevent a full assessment of prespecification and selective reporting from the posted record alone.
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 | 1 | 155 | 0.6% |
| Tio R2.5 | 0 | 154 | 0.0% |
| Tio R5 | 1 | 155 | 0.6% |
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 | 25 of 155 |
| Tio R2.5 | 30 of 154 |
| Tio R5 | 21 of 155 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo | Tio R2.5 | Tio R5 |
|---|---|---|---|---|
| Breast cancer in situ | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 0 of 155 | 0 of 154 | 1 of 155 |
| Asthma | Respiratory, thoracic and mediastinal disorders | 1 of 155 | 0 of 154 | 0 of 155 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo | Tio R2.5 | Tio R5 |
|---|---|---|---|---|
| Asthma | Respiratory, thoracic and mediastinal disorders | 19 of 155 | 24 of 154 | 17 of 155 |
| Peak expiratory flow rate decreased | Investigations | 6 of 155 | 9 of 154 | 6 of 155 |
Serious events with the highest arm-level rate: breast cancer in situ (0.6%), asthma (0.6%).
The registry reports serious adverse events in 1 participant at risk in the placebo group, 0 in the tiotropium 2.5 mcg group, and 1 in the tiotropium 5 mcg group. The corresponding at-risk counts were 155, 154, and 155. These are reported participant counts, not estimates of comparative risk adjusted for follow-up or other factors. The registry record also lists breast cancer in situ and asthma among the top serious-event terms, each at 0.6%; the listed terms are not assigned to a specific treatment group in the available record.
The registry reports other adverse events affecting 25 participants in the placebo group, 30 in the 2.5 mcg group, and 21 in the 5 mcg group, with at-risk counts of 155, 154, and 155, respectively. These figures describe the posted counts; they do not establish that the groups had comparable exposure, ascertainment, or event severity. Deaths are not reported in the registry record.
General statistical context: safety counts are most informative when considered with consistent definitions, follow-up time, and complete event reporting. Small differences in counts alone do not establish a treatment-related cause or a reliable between-group difference. The 12-week trial record offers a limited observation period, and the registry does not provide detailed event narratives or a full breakdown of all adverse-event categories.
17. What the Result Does, and Does Not, Mean
The posted results describe estimated differences in a specific lung-function response after 12 weeks among randomized groups of adults with mild persistent asthma receiving maintenance inhaled corticosteroid treatment. The primary sponsor-reported comparisons favor higher peak FEV1 response estimates in both tiotropium groups than in placebo, and their 95% confidence intervals exclude zero. That is a statistical description of the recorded endpoint under the stated analysis, not a conclusion about an individual participant or a guarantee of a particular response.
The results do not establish clinical importance because the registry record does not report a threshold for a meaningful change in peak FEV1. Nor do they establish effects beyond the trial’s 12-week treatment period. The primary outcome is one measure of lung function; it does not by itself summarize asthma control, exacerbation experience, rescue medication use, or safety. Those outcomes require their own results and interpretation.
The trial included placebo and two tiotropium doses, but the presented primary comparisons are each against placebo. The registry results do not establish that one dose is superior to the other. Comparing the two point estimates directly would require an appropriate analysis, which is not reported as a trial comparison in the registry record.
The findings also do not remove uncertainty from incomplete reporting. The record does not report the original sample-size justification, the full statistical analysis plan, missing-data details, or a multiplicity strategy. These omissions mean that the precision and nominal p-values should be read within the limits of the registry’s reporting. The trial results are not a recommendation for treatment, and they do not determine what is suitable for any individual. They describe the posted group-level evidence for this particular population, treatment context, endpoint, and follow-up period.
18. Why This Trial Matters Statistically
This trial illustrates several central issues in clinical biostatistics. First, the primary endpoint is a continuous change-from-baseline measure, analyzed as an adjusted mean. Readers need to distinguish that model-based estimate from a raw average and from the individual responses that the group mean represents. The registry’s description of the adjustment terms provides useful information, while the absence of a full model specification limits independent replication.
Second, the sponsor’s comparisons and the recalculated comparisons answer related but not identical analytical questions. The sponsor used a mixed model repeated-measures analysis with specified adjustment terms; the recalculations are unadjusted approximations from summary statistics. Their closeness offers a useful check on the reported scale and direction, but the recalculation cannot reproduce the underlying model or replace the sponsor’s analysis.
Third, the registry lists many outcomes and analyses. This makes multiplicity, prespecification, and the distinction between primary and secondary evidence important. A set of related results may provide context, but multiple unadjusted tests should not be interpreted as independent confirmation without knowing the testing plan.
Finally, precision and clinical importance are separate questions. The confidence intervals describe uncertainty around estimated contrasts, but the record does not give a threshold for a clinically important difference. The sample-size illustrations demonstrate how assumed effect size affects planning, while not revealing the original trial’s design justification or the probability that the completed trial would detect an effect. Together, these features make the record a useful example of how statistical estimates, methods, reporting completeness, and clinical interpretation must be read together.
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.
Several limitations are specific to the information reported for this trial. The primary endpoint is a lung-function measure assessed over a 12-week treatment period; the registry record does not report longer-term outcomes. It also does not state a clinical-importance threshold for peak FEV1, limiting interpretation of the practical meaning of the estimated differences.
The primary analysis is described as a mixed model repeated-measures analysis with adjustment for treatment, pooled centre, visit, baseline, treatment-by-visit, and baseline-by-visit. The complete model specification, covariance structure, handling of missing observations, and sensitivity analyses are not reported in the registry record. These details would be needed to fully evaluate the assumptions underlying the reported estimates and confidence intervals.
The record does not report the original sample-size justification, the complete statistical analysis plan, a multiplicity procedure, or the hierarchy among the numerous listed outcomes and analyses. Without those details, it is difficult to determine which secondary findings were confirmatory and how the reported p-values were intended to be interpreted. The sample-size illustrations based on observed effects cannot fill this gap.
The registry lists enrolled and endpoint analysis counts, but a detailed participant flow, reasons for non-inclusion, missing endpoint counts, adherence, and protocol deviations are not reported. The record also does not provide detailed randomization and masking procedures. For safety, adverse-event counts are posted, but full descriptions and participant-level event details are not reported, and deaths are not reported in the registry record.
Finally, the posted results concern adults with mild persistent asthma treated on top of maintenance inhaled corticosteroid treatment. The registry record alone does not establish how the findings apply outside that population, treatment context, endpoint, or follow-up period.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Efficacy and Safety of 2 Doses of Tiotropium Via Respimat in Adult Patients With Mild Persistent Asthma — NCT01316380.
- Registry record last updated 2015-04-15; status last verified 2015-03.
- Results first posted 2013-07-31.
- 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 Phase III, randomized, double-blind, placebo-controlled, parallel-group trial of once-daily tiotropium 2.5 mcg or 5 mcg delivered by Respimat inhaler, compared with placebo, over 12 weeks. It enrolled 465 adults with mild persistent asthma receiving maintenance inhaled corticosteroid treatment. The primary endpoint was peak FEV1 response within 3 hours after dosing at 12 weeks, analyzed in the Full Analysis Set using a mixed model repeated-measures approach.
The sponsor reported mean differences versus placebo of 0.159 liters for 2.5 mcg and 0.128 liters for 5 mcg, with 95% confidence intervals of 0.088 to 0.230 and 0.057 to 0.199, respectively. Recalculated comparisons are approximate unadjusted checks and do not replace the sponsor’s model-based results. The record lists additional lung-function, asthma-control, exacerbation, rescue-medication, and safety outcomes.
The registry does not report the original sample-size justification, full analysis plan, multiplicity approach, missing-data details, or a clinical-importance threshold for the primary endpoint. The posted estimates therefore describe the recorded group comparisons, while these unreported details limit a fuller assessment of their interpretation.