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 Single Dose Study to Assess Efficacy and Safety of 4 Doses of LAS100977 in Chronic Obstructive Pulmonary Disease (COPD) Population (NCT01425814), a randomized phase 2 study. The primary outcome is Change From Baseline in Trough Forced Expiratory Volume in One Second (FEV1).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01425814 |
| Phase | Phase 2 |
| Condition | Chronic Obstructive Pulmonary Disease (COPD) |
| Allocation | Randomized |
| Design model | Crossover |
| Masking | Double |
| Enrollment | 87 |
| Arms in the primary outcome | 6 |
| Lead sponsor | AstraZeneca |
| Results posted | Yes |
2. Clinical Question
Population
Patients with stable moderate to severe chronic obstructive pulmonary disease (COPD). The primary analysis population was defined as patients who took at least one dose of investigational medicinal product and had at least a baseline and one post-dose FEV1 value from at least one treatment period.
Intervention
Single doses of inhaled LAS100977 at 0.625 μg, 2.5 μg, 5 μg, or 10 μg. The study assessed bronchodilation after dosing.
Comparator
Placebo was the control for the primary comparisons. The trial also included indacaterol 150 μg as an active comparator.
Primary question
How did change from baseline in trough forced expiratory volume in one second (FEV1) on Day 2 differ across the LAS100977 dose groups, placebo, and indacaterol?
The primary outcome is a continuous lung-function measure reported in liters. The registry record lists least-squares means for each treatment and sponsor-reported ANCOVA comparisons of four LAS100977 doses with placebo. The posted comparison estimates describe differences in the mean change from baseline; they do not by themselves describe individual responses, symptoms, or longer-term outcomes.
3. Trial Design
This was a Phase IIa, randomized, double-blind, double-dummy, placebo-controlled, six-way complete crossover trial. It evaluated single doses of four strengths of LAS100977, an active comparator, and placebo in patients with stable moderate to severe COPD. The registry record describes each arm as a single-dose, double-blind treatment period. It does not report the treatment sequence, washout duration, or other period details.
The registry record lists enrollment of 87 and a completed study. The recorded start was 2011-08 and primary completion was 2012-03. The primary analysis population was the ITT population as defined for this study: patients who took at least one dose of investigational medicinal product and had a baseline and at least one post-dose FEV1 value from at least one treatment period. The numbers contributing to the outcome vary by treatment, as indicated with the posted estimates.
A crossover design evaluates multiple treatments within a participant across treatment periods. This can make within-person comparisons informative, but interpretation also depends on treatment sequence, period effects, and how the analysis accounts for repeated measurements. The registry record identifies ANCOVA for the sponsor-reported primary comparisons, but the model details, sequence allocation, handling of period effects, and carryover assessment are not reported in the registry record. The posted summary statistics do not provide participant-level data with which to assess these issues independently.
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: Screening took place 14±2 days before randomization. After screening, eligible patients entered a run-in period to assess clinical stability. A total of 87 patients were screened, of whom 70 patients were assessed as eligible and randomized; 17 were not randomized due to screening failure (primarily non-fulfillment of inclusion/exclusion criteria)
Period 1
| Stage | Sequence A | Sequence B | Sequence C | Sequence D | Sequence E | Sequence F |
|---|---|---|---|---|---|---|
| STARTED | 12 | 11 | 12 | 10 | 12 | 13 |
| COMPLETED | 12 | 10 | 12 | 10 | 12 | 13 |
| NOT COMPLETED | 0 | 1 | 0 | 0 | 0 | 0 |
Reasons for not completing this period:
| Reason | Sequence A | Sequence B | Sequence C | Sequence D | Sequence E | Sequence F |
|---|---|---|---|---|---|---|
| Stability criteria not fulfilled | 0 | 1 | 0 | 0 | 0 | 0 |
Period 2
| Stage | Sequence A | Sequence B | Sequence C | Sequence D | Sequence E | Sequence F |
|---|---|---|---|---|---|---|
| STARTED | 12 | 10 | 12 | 10 | 12 | 13 |
| COMPLETED | 12 | 9 | 12 | 10 | 12 | 13 |
| NOT COMPLETED | 0 | 1 | 0 | 0 | 0 | 0 |
Reasons for not completing this period:
| Reason | Sequence A | Sequence B | Sequence C | Sequence D | Sequence E | Sequence F |
|---|---|---|---|---|---|---|
| Stability criteria not fulfilled | 0 | 1 | 0 | 0 | 0 | 0 |
Period 3
| Stage | Sequence A | Sequence B | Sequence C | Sequence D | Sequence E | Sequence F |
|---|---|---|---|---|---|---|
| STARTED | 12 | 9 | 12 | 10 | 12 | 13 |
| COMPLETED | 12 | 9 | 12 | 10 | 12 | 12 |
| NOT COMPLETED | 0 | 0 | 0 | 0 | 0 | 1 |
Reasons for not completing this period:
| Reason | Sequence A | Sequence B | Sequence C | Sequence D | Sequence E | Sequence F |
|---|---|---|---|---|---|---|
| Adverse Event | 0 | 0 | 0 | 0 | 0 | 1 |
Period 4
| Stage | Sequence A | Sequence B | Sequence C | Sequence D | Sequence E | Sequence F |
|---|---|---|---|---|---|---|
| STARTED | 12 | 9 | 12 | 10 | 12 | 12 |
| COMPLETED | 11 | 9 | 11 | 10 | 12 | 12 |
| NOT COMPLETED | 1 | 0 | 1 | 0 | 0 | 0 |
Reasons for not completing this period:
| Reason | Sequence A | Sequence B | Sequence C | Sequence D | Sequence E | Sequence F |
|---|---|---|---|---|---|---|
| Adverse Event | 1 | 0 | 1 | 0 | 0 | 0 |
Analysis population for the primary outcome, as defined in the registry: ITT population defined as patients who took at least one dose of investigational medicinal product and had at least a baseline and one post-dose value of FEV1 from at least one treatment period
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 | Overall Population |
|---|---|---|
| Participants analysed | 70 | |
| Age, Continuous | Years | 61.2 (SD 7.7) |
| Sex: Female, Male: Female | Participants | 26 |
| Sex: Female, Male: Male | Participants | 44 |
6. Primary Endpoint
The registry lists the primary outcome as Change From Baseline in Trough Forced Expiratory Volume in One Second (FEV1), measured over Day 2.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | Liters |
| Endpoint classification | Continuous Endpoint |
The primary endpoint was change from baseline in trough forced expiratory volume in one second (FEV1), measured in liters at Day 2. FEV1 is the volume of air exhaled in the first second of a forced breath; trough measurement assesses lung function at the specified late time point after dosing. In this trial, the Day 2 trough value was calculated as the average of measurements at 23 and 24 hours after the morning dose on Day 1.
Baseline was the average of the measurements taken 45 minutes and 15 minutes before dosing at Day 1 of each visit. At each time point, spirometry included three technically adequate lung-function measurements according to the acceptability and repeatability criteria of the ATS/ERS, and the highest FEV1 and FVC values were selected. The endpoint therefore describes the change from a visit-specific pre-dose reference to the defined Day 2 trough measure.
FEV1 was used to assess the study’s stated pharmacodynamic question: bronchodilation after a single dose. A continuous outcome preserves information about the magnitude of measured change rather than reducing it to a threshold category. It is a physiological measure, however, and does not alone establish effects on symptoms, daily functioning, exacerbations over time, or other outcomes. Those questions are not answered by this primary endpoint.
7. Results Posted in the Registry
- LAS100977 0.625 μg: mean 0.07 versus -0.04 on control; difference 0.10 (95% CI 0.03 to 0.17), standardized effect d = 0.51; z-test p = 0.003.
- LAS100977 2.5 μg: mean 0.17 versus -0.04 on control; difference 0.20 (95% CI 0.14 to 0.27), standardized effect d = 1.03; z-test p = <0.001.
- LAS100977 5 μg: mean 0.20 versus -0.04 on control; difference 0.23 (95% CI 0.17 to 0.30), standardized effect d = 1.19; z-test p = <0.001.
- LAS100977 10 μg: mean 0.22 versus -0.04 on control; difference 0.26 (95% CI 0.19 to 0.32), standardized effect d = 1.31; z-test p = <0.001.
Mean difference: LAS100977 0.625 μg
95% CI: 0.03 to 0.17
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 |
|---|---|---|---|---|
| Change From Baseline in Peak Forced Expiratory Volume in One Second (FEV1) | Continuous Endpoint | Mean difference | 0.19 (0.13 to 0.25) | 13 per arm |
| Time to Peak Forced Expiratory Volume in One Second (FEV1) | Continuous Endpoint | Mean difference | 0.90 (0.35 to 1.45) | 53 per arm |
| Change From Baseline in Trough Forced Vital Capacity (FVC) | Continuous Endpoint | Mean difference | 0.15 (0.02 to 0.27) | 97 per arm |
Change From Baseline in Peak Forced Expiratory Volume in One Second (FEV1)
- 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:
- LAS100977 0.625 μg: mean 0.29 versus 0.10 on control; difference 0.19 (95% CI 0.13 to 0.25), standardized effect d = 1.12; z-test p = <0.001.
- LAS100977 2.5 μg: mean 0.35 versus 0.10 on control; difference 0.25 (95% CI 0.20 to 0.31), standardized effect d = 1.61; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for LAS100977 0.625 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 LAS100977 2.5 μg than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Time to Peak Forced Expiratory Volume in One Second (FEV1)
- 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:
- LAS100977 0.625 μg: mean 3.40 versus 2.50 on control; difference 0.90 (95% CI 0.35 to 1.45), standardized effect d = 0.55; z-test p = 0.001.
- LAS100977 2.5 μg: mean 3.50 versus 2.50 on control; difference 1.00 (95% CI 0.45 to 1.55), standardized effect d = 0.61; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for LAS100977 0.625 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 LAS100977 2.5 μg than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Change From Baseline in Trough Forced Vital Capacity (FVC)
- 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:
- LAS100977 0.625 μg: mean 0.07 versus -0.08 on control; difference 0.15 (95% CI 0.02 to 0.27), standardized effect d = 0.40; z-test p = 0.019.
- LAS100977 2.5 μg: mean 0.18 versus -0.08 on control; difference 0.26 (95% CI 0.14 to 0.38), standardized effect d = 0.72; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for LAS100977 0.625 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 LAS100977 2.5 μg than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The posted secondary outcomes cover additional FEV1 measures, including peak response, time to peak, absolute values, and normalized area-under-the-curve measures. They also include FVC outcomes, which assess a different spirometric measure. Across the secondary summaries that are posted, treatment means generally show positive changes from baseline for LAS100977, with placebo values lower on several of the reported change measures. The active comparator is also reported for these measures.
This broad pattern is directionally consistent with the primary endpoint summaries, in which the LAS100977 treatment means are above the placebo mean. The secondary outcomes address different time points and measurement summaries, however, and they should not be treated as interchangeable replications of the primary endpoint. Peak response and time to peak, for example, describe aspects of the response that are distinct from Day 2 trough FEV1. The registry record also does not report sponsor analyses for the posted secondary comparisons, so the simple recalculations do not represent the sponsor’s fitted analyses.
Secondary findings generally carry less inferential weight when many outcomes or comparisons are examined without a reported multiplicity adjustment. Repeated testing increases the chance of at least one apparently notable result arising by chance. The registry record lists multiple secondary outcomes and does not report an adjustment strategy or a hierarchy for interpreting them. Their summaries are therefore best treated as supportive descriptive context, rather than as a separate confirmatory conclusion. The endpoints that are not posted with numerical results are not reported in the registry record.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Change From Baseline in Normalised Forced Expiratory Volume in One Second (FEV1) Area Under the Curve
- Change From Baseline in Forced Expiratory Volume in One Second (FEV1)
- Absolute Forced Expiratory Volume in One Second (FEV1) Values
- Change From Baseline in Peak Forced Expiratory Volume in One Second (FEV1)
- Time to Peak Forced Expiratory Volume in One Second (FEV1)
- Change From Baseline in Trough Forced Vital Capacity (FVC)
- Change From Baseline in Normalised Forced Vital Capacity (FVC) Area Under the Curve
- Change From Baseline in Forced Vital Capacity (FVC)
9. Statistical Interpretation
The posted primary endpoint means are least-squares mean changes from baseline at Day 2. Placebo was reported as -0.035 liters, while the LAS100977 means were 0.066 liters at 0.625 μg, 0.168 liters at 2.5 μg, 0.198 liters at 5 μg, and 0.223 liters at 10 μg. The indacaterol 150 μg mean was 0.076 liters. These are treatment-period summaries; in a crossover trial, they should not be read as separate parallel groups of unrelated participants.
The registry’s sponsor-reported ANCOVA comparisons give least-squares mean differences versus placebo. The estimates were 0.102 liters for 0.625 μg, 0.203 liters for 2.5 μg, 0.233 liters for 5 μg, and 0.259 liters for 10 μg. Each reported 95% confidence interval is above zero, and each sponsor-reported p-value is < 0.001. These results describe the recorded analyses for this endpoint and time point; they do not establish effects on outcomes not measured by the endpoint.
The posted summaries show a pattern of larger mean change at higher LAS100977 strengths, with the reported placebo mean below zero. This is a pattern in the group summaries, not proof of a dose-response relationship. The registry record does not report a formal dose-response test. Nor does it report a direct statistical comparison between LAS100977 doses or between LAS100977 and indacaterol. The indacaterol value is an active-comparator summary, not evidence from a reported head-to-head analysis.
Simple unadjusted recalculations from the posted summary statistics give mean differences of 0.101 liters, 0.203 liters, 0.233 liters, and 0.258 liters for the four LAS100977 doses versus placebo, respectively. Their approximate confidence intervals and unadjusted p-values are displayed with the posted comparisons. These recalculations are not the sponsor’s crossover ANCOVA analysis and do not use the individual participant-level information needed to reproduce it. The registry’s own analysis is the primary reference for its planned comparisons.
Precision is relevant alongside the point estimates. The sponsor-reported intervals convey a range of values compatible with the fitted model under its assumptions; they are not a guarantee that the true difference lies within that range. The unadjusted recalculated intervals use summary statistics and should be read as a separate approximation. The registry record does not report whether multiplicity adjustments were applied across the primary dose comparisons. As a result, the individual p-values should not be treated as an overall error-controlled conclusion across all comparisons.
10. Statistical Methods Explained
The registry record reports least-squares means for the primary continuous endpoint and ANCOVA for the sponsor’s comparisons. The following concepts are general explanations of these methods; details of the trial’s exact fitted model beyond the reported analysis are not reported in the registry record.
What does a least-squares mean represent?
A least-squares mean is a model-based mean, often adjusted for terms included in the statistical model. It is not necessarily the raw arithmetic average of the observed values. The registry record does not identify all covariates or other terms included in the primary ANCOVA, so the exact adjustment behind these values cannot be reconstructed from the posted results alone. The reported estimates should therefore be read as the sponsor’s model-based summaries, rather than assumed to be unadjusted sample means.
What does ANCOVA do?
Analysis of covariance (ANCOVA) estimates differences between treatment means while accounting for specified variables in a model. In clinical trials, baseline measurements may be included to improve precision or account for baseline differences. The registry record names ANCOVA and reports least-squares mean differences, but does not report the full model specification, covariates, assumptions, or handling of the crossover structure. It is not possible to infer those details from the method label alone.
Why does the crossover structure matter?
In a crossover trial, participants receive treatments across periods, so measurements from one participant are related rather than independent. General crossover analyses can account for this correlation and may include treatment, period, sequence, or participant terms, depending on the design and analysis plan. A simple recalculation from arm-level means and standard errors cannot recover the within-person covariance or fully reproduce such a model. The registry record does not report enough model detail or individual data to verify how those features were handled.
What do the recalculated comparisons represent?
The recalculated mean differences are simple, unadjusted comparisons derived from posted treatment and placebo summaries. Their standard deviations are approximate where indicated in the calculation inputs, because they are inferred from reported standard errors and group sizes rather than recovered from participant-level observations. The resulting intervals and p-values are useful as a transparent arithmetic check on the summary values, but they are not substitutes for the sponsor’s ANCOVA results. Where the two sets of estimates differ slightly, the registry’s sponsor-reported analysis takes precedence as the trial’s own analysis.
A p-value describes how incompatible the observed data are with a specified null hypothesis under a statistical model, assuming that model and its assumptions apply. It is not the probability that the null hypothesis is true, and it does not measure clinical importance. The reported p-values concern individual comparisons with placebo. The registry record does not report a multiplicity procedure for the set of dose comparisons, so the p-values should be interpreted as reported rather than as a family-wise adjusted set.
A confidence interval gives a range of values compatible with the data and analysis assumptions at a stated confidence level. A narrower interval indicates greater precision on that scale, while a wider interval indicates more uncertainty. Confidence intervals do not account for unreported sources of bias or uncertainty, and a 95% interval does not mean that 95% of participants’ responses fall inside it.
The posted results are continuous measures, with least-squares means and standard errors. Standard error describes uncertainty in an estimated mean, not the spread of individual participant measurements. General distinction matters: a small standard error can coexist with substantial variation among individuals. The registry record does not report standard deviations for the primary treatment means or individual measurements, so the spread of participant responses cannot be read directly from the reported standard errors.
The recalculated planning illustrations use the observed comparison effects and the assumptions listed with those illustrations. They are not the trial’s original design calculations, and the registry record does not report the original sample-size justification. Planning values describe the sample size a hypothetical future study might require under stated assumptions; they are not evidence that the current trial had a particular probability of detecting an effect.
11. Confidence Intervals and Precision
The sponsor-reported primary comparisons include 95% confidence intervals for the least-squares mean difference versus placebo. For 0.625 μg, the estimate was 0.102 liters, with an interval from 0.062 to 0.141. For 2.5 μg, it was 0.203 liters, with an interval from 0.164 to 0.242. For 5 μg, it was 0.233 liters, with an interval from 0.194 to 0.273. For 10 μg, it was 0.259 liters, with an interval from 0.219 to 0.298.
These intervals communicate uncertainty around the model-based differences. All four intervals are on the positive side of zero, and the associated sponsor-reported p-values are < 0.001. The interval widths also show that the estimates are not exact: plausible values under the model span a range rather than a single point. The interval should be interpreted with the assumptions of the ANCOVA and the trial design in mind.
The simple recalculated comparisons have somewhat different estimates and intervals. For example, the recalculated mean difference for 10 μg was 0.258 liters, with an approximate interval from 0.192 to 0.325. The sponsor’s model-based estimate and interval are the appropriate reference for its reported analysis; the recalculated interval is a separate unadjusted approximation based on posted summaries. It does not capture all features of the crossover analysis.
Precision is not the same as clinical importance. The registry record does not report a threshold for a clinically meaningful difference on this endpoint, nor does it give participant-level response distributions. Consequently, these intervals describe statistical uncertainty in group estimates, but they do not indicate the proportion of patients who experienced a particular degree of change or whether an observed difference is meaningful to patients.
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 | 60 | 81 |
| 75% of the observed effect | 107 | 143 |
| 50% of the observed effect | 240 | 321 |
The sample-size illustrations are planning estimates based on the observed effect, not the trial’s original design assumptions. The stated assumptions are a two-sided significance level of 0.05, equal allocation between two arms, a normal approximation, and an effect to detect set to the stated fraction of the observed effect. For these continuous outcomes, the figures are participants per arm. The special total-events convention for time-to-event outcomes does not apply to this endpoint.
The 80% power column gives the planned participants per arm under which a study would have an 80% chance of detecting the specified effect at the stated significance level, if the assumptions and effect were correct. The 90% power column represents a higher chance of detecting that same specified effect, and therefore generally calls for more participants per arm. Each row changes the target effect: planning for 75% or 50% of the observed effect means targeting a smaller difference than planning for 100% of the observed effect. Smaller effects need more participants to detect with the same power.
These figures are planning illustrations, not observed power. They are sensitive to the observed effect used as their starting point and to the simplifying assumptions, including equal allocation and the normal approximation. They do not reproduce the crossover model, account for unreported design features, or demonstrate how likely the current trial was to detect an effect. The registry record does not report the original sample-size justification or its design assumptions.
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 = 0.101; pooled standard deviation σ = 0.197.
- n = 2 × (1.96 + 0.842)2 × 0.1972 / 0.1012 = 59.8, rounded up to 60 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 <- 0.101 # observed difference in means
sigma <- 0.197185611578365 # 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(1425814)
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 = 60 (80% power), 81 (90% power)
75% of observed effect: n per arm = 107 (80% power), 143 (90% power)
50% of observed effect: n per arm = 240 (80% power), 321 (90% power)
power.t.test: 60.8
Simulated power at n = 60 per arm: 0.800 (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 | Least Squares Mean Difference 0.259 | 0.219 to 0.298 | < 0.001 |
| ANCOVA | Least Squares Mean Difference 0.233 | 0.194 to 0.273 | < 0.001 |
| ANCOVA | Least Squares Mean Difference 0.203 | 0.164 to 0.242 | < 0.001 |
| ANCOVA | Least Squares Mean Difference 0.102 | 0.062 to 0.141 | < 0.001 |
The sponsor-reported primary analysis used ANCOVA and reported least-squares mean differences with 95% confidence intervals. The comparisons were placebo versus LAS100977 0.625 μg, 2.5 μg, 5 μg, and 10 μg. The sponsor’s estimates were 0.102, 0.203, 0.233, and 0.259 liters, respectively, and each reported p-value was < 0.001.
The posted recalculations are simple unadjusted comparisons derived from treatment and placebo summary statistics. They give estimates of 0.101, 0.203, 0.233, and 0.258 liters, respectively, with approximate intervals and unadjusted p-values. Small differences between these recalculations and the sponsor estimates are expected when the calculations use different information or methods. The recalculations do not reproduce the sponsor’s ANCOVA, and the summary data do not provide the participant-level crossover information needed to do so.
There is no reported discrepancy flag for these results. The sponsor’s own ANCOVA is therefore the primary reference for the trial’s reported comparisons, while the unadjusted recalculations serve as a separate check based on posted summary statistics. The registry record does not report the full ANCOVA specification, so the model cannot be independently reconstructed from the information reported.
15. Multiplicity, Missing Data and Analysis Populations
The registry record reports four sponsor ANCOVA comparisons of LAS100977 doses with placebo for the primary endpoint. Each has a reported p-value of < 0.001 and a 95% confidence interval. The record does not report whether those comparisons were adjusted for multiplicity, whether one comparison was designated as the primary dose contrast, or whether a testing hierarchy was used. Without that information, the individual p-values should not be interpreted as an overall multiplicity-controlled test across the dose comparisons.
The record also lists multiple secondary outcomes. A prespecified strategy for controlling the chance of false-positive findings across those outcomes is not reported in the registry record. This matters because interpreting many unadjusted tests as if each were the only test can overstate the strength of the overall evidence. The secondary estimates are useful descriptions of the posted data, but formal confirmatory claims across the full set of outcomes cannot be assessed from the reported information.
The primary population is described as patients who took at least one dose and had baseline and at least one post-dose FEV1 value from at least one treatment period. This definition is reported, but the registry record does not give details of missing-data handling, exclusions after randomization, or sensitivity analyses. It also does not report how incomplete treatment periods were handled in the crossover analysis. These omissions limit assessment of whether missing observations or incomplete follow-up could have affected the estimates.
The full statistical analysis plan, detailed model specification, and interim-analysis information are not reported in the registry record. It is therefore not possible to determine from the record whether additional prespecified analyses were conducted or how all analysis decisions were made. These reporting gaps are reasons to interpret the posted estimates within their stated scope, rather than to assume unreported procedures.
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 | 0 | 68 | 0.0% |
| LAS100977 0.625 μg | 0 | 67 | 0.0% |
| LAS100977 2.5 μg | 0 | 66 | 0.0% |
| LAS100977 5 μg | 1 | 66 | 1.5% |
| LAS100977 10 μg | 1 | 67 | 1.5% |
| Indacaterol 150 μg | 0 | 68 | 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 |
|---|---|
| Placebo | 2 of 68 |
| LAS100977 0.625 μg | 4 of 67 |
| LAS100977 2.5 μg | 1 of 66 |
| LAS100977 5 μg | 1 of 66 |
| LAS100977 10 μg | 2 of 67 |
| Indacaterol 150 μg | 5 of 68 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo | LAS100977 0.625 μg | LAS100977 2.5 μg | LAS100977 5 μg | LAS100977 10 μg | Indacaterol 150 μg |
|---|---|---|---|---|---|---|---|
| COPD exacerbation | Respiratory, thoracic and mediastinal disorders | 0 of 68 | 0 of 67 | 0 of 66 | 1 of 66 | 0 of 67 | 0 of 68 |
| Dizziness | Nervous system disorders | 0 of 68 | 0 of 67 | 0 of 66 | 0 of 66 | 1 of 67 | 0 of 68 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo | LAS100977 0.625 μg | LAS100977 2.5 μg | LAS100977 5 μg | LAS100977 10 μg | Indacaterol 150 μg |
|---|---|---|---|---|---|---|---|
| Nasopharyngitis | Infections and infestations | 2 of 68 | 4 of 67 | 1 of 66 | 1 of 66 | 2 of 67 | 5 of 68 |
Serious events with the highest arm-level rate: copd exacerbation (1.5%), dizziness (1.5%).
The serious adverse event summaries are reported by treatment period. No serious adverse events were reported for placebo, LAS100977 0.625 μg, LAS100977 2.5 μg, or indacaterol 150 μg. One serious adverse event was reported for LAS100977 5 μg, and one for LAS100977 10 μg. The registry lists COPD exacerbation and dizziness as the top serious event terms, each at 1.5%.
These figures describe reported events in the safety summaries; they do not establish that an event was caused by a treatment. The record does not provide a causal assessment or detailed participant-level event narratives. Deaths are not reported in the registry record. As this was a single-dose study with treatment periods, the summaries also do not characterize longer-term safety or outcomes beyond the recorded reporting period.
Small event counts provide limited precision for comparing safety between treatments. The absence of a reported serious event in a treatment summary is not proof that the risk is zero, and comparisons across treatment periods should account for the crossover design. These descriptive data should be read as a safety snapshot, not as a complete estimate of uncommon or delayed risks.
17. What the Result Does, and Does Not, Mean
The primary results describe differences in a specific measure of lung function after single doses in patients with stable moderate to severe COPD. The sponsor-reported ANCOVA estimates for the four LAS100977 doses were positive versus placebo, with 95% confidence intervals above zero and reported p-values of < 0.001. The posted means also show a larger mean change at the higher LAS100977 strengths. These findings characterize the trial’s reported Day 2 trough FEV1 results.
They do not by themselves establish that LAS100977 improves how patients feel or function, reduces exacerbations, or changes the course of COPD. The primary outcome is a physiological measurement at a specified time, and this trial evaluated single doses. Longer-term effects and outcomes not included in the posted results are not reported in the registry record. Nor does a difference from placebo alone establish how the study treatments compare directly with one another.
The findings also should not be generalized automatically to all people with COPD. The enrolled population was described as having stable moderate to severe disease, and the registry record does not provide enough detail to assess applicability to other groups. The study was randomized and double-blind, but details needed to evaluate every potential source of bias—such as sequence allocation, period handling, and missing-data methods—are not reported.
The estimates and confidence intervals express statistical results under the analyses and assumptions used. They do not determine clinical importance; the registry record does not report a threshold for a clinically meaningful FEV1 difference. The safety summaries are limited and do not establish causality. Overall, the results are specific to the measured endpoint, dose periods, analysis population, and timeframe reported.
18. Why This Trial Matters Statistically
This trial is statistically informative because it uses a randomized crossover design to compare several single-dose strengths with placebo and an active comparator. Such a design can make within-person treatment contrasts useful by reducing the influence of stable differences between participants, when the analysis appropriately accounts for the repeated measures. The registry record reports the crossover structure and sponsor ANCOVA comparisons, but not enough model detail to verify how the design features were handled.
The outcome is continuous, and the reported mean differences retain information about the size and uncertainty of the estimated contrast. The sponsor’s confidence intervals allow readers to consider precision rather than relying only on p-values. The distinction between sponsor-reported model results and simple unadjusted recalculations is also important: the recalculations provide a summary-statistic check, but cannot recreate the trial’s full analysis.
The study also illustrates why statistical evidence needs context. Several doses and multiple secondary outcomes were examined, while multiplicity handling is not reported. The endpoint is a short-term physiological measure after single dosing, so its results do not answer longer-term clinical questions. Safety events were few in the posted summaries, limiting comparisons. These features make clear both what the design can estimate and what cannot be inferred from its numerical results.
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 posted record does not report the treatment sequence, washout periods, or complete crossover analysis specification. These are relevant to interpreting repeated treatment periods, period effects, and possible carryover. The ANCOVA method is identified, but its covariates and handling of within-participant correlation are not reported. Without individual data, the sponsor analysis cannot be independently reconstructed.
The reported primary population definition requires at least one post-dose FEV1 value from at least one treatment period, but details of missing-data handling and incomplete periods are not reported. The record also does not report a missing-data sensitivity analysis. The number of observations differs across treatment summaries, so the results should not be assumed to represent complete data from every participant at every period.
Multiplicity procedures are not reported despite multiple dose comparisons and secondary outcomes. The registry record does not provide the original sample-size rationale, full statistical analysis plan, or details about interim analyses. It also does not state a clinically meaningful threshold for the primary endpoint. The planning illustrations are based on the observed effects and simplifying assumptions, not on the trial’s original design.
Finally, this was a single-dose pharmacodynamic study with a Day 2 primary measurement. It does not establish the longer-term pattern of lung function, patient-centered outcomes, or uncommon and delayed safety events. The adverse-event summaries are descriptive and do not establish causality.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Single Dose Study to Assess Efficacy and Safety of 4 Doses of LAS100977 in Chronic Obstructive Pulmonary Disease (COPD) Population — NCT01425814.
- Registry record last updated 2017-04-10; status last verified 2017-02.
- Results first posted 2017-04-10.
- 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
This completed Phase IIa randomized, double-blind, double-dummy, six-way crossover study evaluated single doses of four LAS100977 strengths, placebo, and indacaterol in stable moderate to severe COPD. Enrollment was 87; the recorded study start was 2011-08 and primary completion was 2012-03.
The primary endpoint was change from baseline in trough FEV1 on Day 2, reported in liters as least-squares means. Sponsor-reported ANCOVA comparisons versus placebo had positive estimates for all four LAS100977 doses, with 95% confidence intervals above zero and p-values of < 0.001. The registry record does not report multiplicity handling or the full model specification. Safety summaries report few serious adverse events and do not provide a basis for causal conclusions.