← Clinical Trials
COPD Phase 3 Continuous Endpoint NCT02347761

Efficacy and Safety Trial of 12 Weeks of Treatment With Nebulized SUN-101 in Patients With COPD: Complete Statistical Analysis

This analysis examines the randomized, placebo-controlled GOLDEN-3 trial of nebulized SUN-101 for COPD, focusing on change in trough FEV1 at Week 12. It explains the reported repeated-measures results, unadjusted recalculations, secondary outcomes, precision, and safety figures.

Trial start: 2015-02  ·  Enrollment: 653  ·  Sponsor: Sunovion Respiratory Development Inc.
Scope of this record

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 Trial of 12 Weeks of Treatment With Nebulized SUN-101 in Patients With COPD (NCT02347761), a randomized phase 3 study. The primary outcome is Change From Baseline in Trough Forced Expiratory Volume in 1 Second (FEV1) at Week 12.

653
Enrollment
Phase 3
3
Arms
In the primary outcome
0.10
Mean difference
SUN-101 50 mcg BID eFlow (CS) Nebulizer
0.07–0.14
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT02347761
PhasePhase 3
ConditionCOPD
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment653
Arms in the primary outcome3
Lead sponsorSunovion Respiratory Development Inc.
Results postedYes

2. Clinical Question

Population

People with chronic obstructive pulmonary disease (COPD) were eligible under the trial’s stated GOLD 2014 guidelines. The primary analysis population was the Intent to Treat population: randomized subjects who received at least one dose of study medication, analyzed according to their randomized treatment. The registry record does not report further eligibility details in the listed primary-outcome description.

Intervention

The trial compared twice-daily nebulized SUN-101 at 50 mcg and 25 mcg, delivered with the eFlow Closed System nebulizer. Treatment lasted 12 weeks.

Comparator

The comparator was placebo, delivered twice daily with the eFlow Closed System nebulizer. This provides a control group receiving the same stated delivery schedule and device type.

Primary question

The primary question was whether change from baseline in trough forced expiratory volume in 1 second (FEV1) at Week 12 differed between either SUN-101 dose and placebo. The endpoint is expressed in liters, and the trial reports least-squares mean changes and between-group differences.

FEV1 is the volume of air exhaled during the first second of a forced expiration. Trough measurement is intended to assess lung function at the specified time near the end of the dosing interval. In this study, Week 12 trough FEV1 was the mean of measurements taken at two time points 30 minutes apart, approximately 24 hours after the previous morning dose. Change was calculated relative to the baseline morning trough, itself the mean of two pre-dose measurements.

The registry lists a randomized, double-blind, placebo-controlled, parallel-group, multicenter Phase 3 trial. It reports 653 enrolled participants and three treatment groups. The key statistical comparison is not simply whether each group’s mean changed from baseline; it is how much the mean change in each SUN-101 group differed from the placebo group, with uncertainty considered alongside the estimate.

3. Trial Design

GOLDEN-3 is registered as a Phase 3, randomized, quadruple-masked, parallel-group trial. Its official title describes a double-blind, placebo-controlled, multicenter study of 12 weeks of nebulized SUN-101 treatment in patients with COPD. The registry status is completed. The record lists 653 enrolled participants and three groups: SUN-101 50 mcg twice daily, SUN-101 25 mcg twice daily, and placebo twice daily, each using the eFlow Closed System nebulizer.

The primary outcome was change from baseline in trough FEV1 at Week 12. The listed analysis population included randomized participants who received at least one dose of study medication, with participants analyzed according to their randomized assignment. The primary endpoint description says all collected spirometry values were used, whether or not a participant remained on randomized treatment and whether or not other therapies might affect the values. It says missing values were assumed missing at random.

The treatment groups’ reported least-squares mean changes were 0.096 liters for 50 mcg, 0.089 liters for 25 mcg, and -0.007 liters for placebo. The reported between-group estimates came from a mixed model for repeated measurements. For the 50 mcg comparison, the registry reports a least-squares mean difference of 0.104 liters, with a 95% confidence interval from 0.066 to 0.141 and p < 0.001. For the 25 mcg comparison, the reported difference was 0.096 liters, with a 95% confidence interval from 0.059 to 0.133 and p < 0.001.

The registry record does not report the original sample-size justification, the detailed statistical analysis plan, or whether interim analyses were planned or conducted. Those details should not be inferred from the completed enrollment or the planning illustrations based on observed effects.

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.

All Collected

StageSUN-101 50 mcg BID eFlow (CS) NebulizerSUN-101 25 mcg BID eFlow (CS) NebulizerPlacebo BID eFlow (CS) Nebulizer
STARTED218217218
COMPLETED201203191
NOT COMPLETED171427

Reasons for not completing this period:

ReasonSUN-101 50 mcg BID eFlow (CS) NebulizerSUN-101 25 mcg BID eFlow (CS) NebulizerPlacebo BID eFlow (CS) Nebulizer
Death100
Lost to Follow-up323
Withdrawal by Subject111122
invetigator disretion200
instillation site pain001
exacerbation of COPD001
moved/travel010

On Study Treatment

StageSUN-101 50 mcg BID eFlow (CS) NebulizerSUN-101 25 mcg BID eFlow (CS) NebulizerPlacebo BID eFlow (CS) Nebulizer
STARTED218217218
COMPLETED191194176
NOT COMPLETED272342

Reasons for not completing this period:

ReasonSUN-101 50 mcg BID eFlow (CS) NebulizerSUN-101 25 mcg BID eFlow (CS) NebulizerPlacebo BID eFlow (CS) Nebulizer
Lack of Efficacy234
non-compliance with study medication002
Withdrawal by Subject735
move/travel265
dissastisfaction with device214
Lost to Follow-up211
investigator discretion200
durg not working011
Adverse Event10820

Analysis population for the primary outcome, as defined in the registry: Intent to Treat (ITT) Population: all subjects who were randomized to treatment and received at least one dose of study medication. Subjects were analyzed based on the treatment they were randomized to.

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.

CharacteristicUnitSUN-101 50 mcg BID eFlow (CS) NebulizerSUN-101 25 mcg BID eFlow (CS) NebulizerPlacebo BID eFlow (CS) NebulizerTotal
Participants analysed218217218653
Age, Categorical: <=18 yearsParticipants0000
Age, Categorical: Between 18 and 65 yearsParticipants135122109366
Age, Categorical: >=65 yearsParticipants8395109287
Age, Continuousyears62.5 (SD 8.09)63.1 (SD 8.78)63.7 (SD 8.37)63.1 (SD 8.42)
Sex: Female, Male: FemaleParticipants9899107304
Sex: Female, Male: MaleParticipants120118111349
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants67619
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants212210212634
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants0000
Race (NIH/OMB): American Indian or Alaska NativeParticipants1113
Race (NIH/OMB): AsianParticipants0112
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants1001
Race (NIH/OMB): Black or African AmericanParticipants18152053
Race (NIH/OMB): WhiteParticipants198200196594
Race (NIH/OMB): More than one raceParticipants0000
Race (NIH/OMB): Unknown or Not ReportedParticipants0000
Region of Enrollment: United StatesParticipants218217218653
cardiovascular risk (low/high) and categories for high caridovascular risk: low cardiovascular riskParticipants777876231
cardiovascular risk (low/high) and categories for high caridovascular risk: high cardiovascular riskParticipants141139142422
cardiovascular risk (low/high) and categories for high caridovascular risk: cerebrovascular diseaseParticipants10131437
cardiovascular risk (low/high) and categories for high caridovascular risk: peripheral arterial diseaseParticipants10131437
cardiovascular risk (low/high) and categories for high caridovascular risk: clinically significant arrhythmiaParticipants713222
cardiovascular risk (low/high) and categories for high caridovascular risk: heart failureParticipants97824
cardiovascular risk (low/high) and categories for high caridovascular risk: hyertensionParticipants127128138393
background long-acting beta(2) agonist (LABA) use: background LABA use =yesParticipants686663197
background long-acting beta(2) agonist (LABA) use: background LABA use =noParticipants150151155456
Forced expiratory volume in one second (FEV1)liters1.3745 (SD 0.52957)1.3108 (SD 0.50243)1.3122 (SD 0.47511)1.3325 (SD 0.50297)

6. Primary Endpoint

The registry lists the primary outcome as Change From Baseline in Trough Forced Expiratory Volume in 1 Second (FEV1) at Week 12, measured over Baseline and Week 12.

ElementRegistry entry
Result typeLeast Squares Mean
Measure of spreadStandard Error
Unitliters
Endpoint classificationContinuous Endpoint

The primary endpoint is change from baseline in trough forced expiratory volume in 1 second (FEV1) at Week 12, measured in liters. FEV1 records the amount of air exhaled during the first second of a forced expiration and is used as a continuous measure of lung function. A change score places the follow-up value in relation to the participant’s own baseline measurement.

In this trial, trough FEV1 at Week 12 was defined as the mean of two measurements taken 30 minutes apart, approximately 24 hours after the previous morning dose. Baseline morning trough FEV1 was the mean of values collected 45 and 15 minutes before the first dose. The endpoint is the Week 12 trough value minus that baseline value. The reported group values are least-squares means, which are model-based averages rather than simple arithmetic averages.

General: a trough assessment can characterize a measurement at a specified point near the end of a dosing interval, rather than at an unspecified time after treatment. Comparing change between randomized groups helps distinguish the observed treatment-group pattern from change also seen under placebo. The endpoint does not by itself describe every aspect of COPD, symptoms, daily functioning, or longer-term outcomes. The registry record lists several secondary outcomes addressing other measures, but the primary endpoint remains the specific lung-function measure defined above.

The primary outcome description states that all collected spirometry values were included, even if participants stopped randomized treatment or values might have been affected by other therapies. Missing values were assumed missing at random. That assumption is part of how the analysis handles unavailable measurements; the registry record does not establish whether it is fully realistic for every participant.

7. Results Posted in the Registry

Mean difference: SUN-101 50 mcg BID eFlow (CS) Nebulizer

0.10

95% CI: 0.07 to 0.14

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-0.1-0.00.00.10.10.1SUN-101 50 mcg BID eFlow (CS)… (n=218)SUN-101 25 mcg BID eFlow (CS)… (n=217)Placebo BID eFlow (CS) Nebuli… (n=218)liters (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)SUN-101 50 mcg BID eFlow (CS)…SUN-101 25 mcg BID eFlow (CS)…-0.010.020.050.090.120.15mean difference vs control (95% CI)

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 outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Standardized Change From Baseline at Week 12 in FEV1 Area Under the Curve (AUC) (0-12) in the Substudy PopulationContinuous EndpointMean difference0.12 (0.04 to 0.20)46 per arm
Standardized Change From Baseline at Week 12 in FEV1 Area Under the Curve (AUC) (0-12) in Substudy PopulationContinuous EndpointMean difference0.12 (0.04 to 0.21)51 per arm
Change From Baseline in Trough Forced Vital Capacity (FVC) at Week 12Continuous EndpointMean difference0.13 (-0.31 to 0.58)5,023 per arm

Standardized Change From Baseline at Week 12 in FEV1 Area Under the Curve (AUC) (0-12) in the Substudy Population

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)SUN-101 50 mcg BID eFlow (CS)…SUN-101 25 mcg BID eFlow (CS)…-0.58-0.31-0.030.240.520.79mean difference vs control (95% CI)

Standardized Change From Baseline at Week 12 in FEV1 Area Under the Curve (AUC) (0-12) in Substudy Population

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)SUN-101 50 mcg BID eFlow (CS)…SUN-101 25 mcg BID eFlow (CS)…-0.020.030.080.130.180.23mean difference vs control (95% CI)

Change From Baseline in Trough Forced Vital Capacity (FVC) at Week 12

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)SUN-101 50 mcg BID eFlow (CS)…SUN-101 25 mcg BID eFlow (CS)…-0.39-0.180.030.240.450.65mean difference vs control (95% CI)

Across the posted secondary outcomes, the overall pattern is mixed rather than uniformly precise. The two listed FEV1 area-under-the-curve outcomes in the substudy have positive estimated treatment-versus-placebo differences for both doses, but the estimates and uncertainty vary. One of the 25 mcg substudy recalculations is especially imprecise, with a confidence interval extending from -0.488 to 0.699 and p = 0.728. The other listed 25 mcg substudy recalculation has a positive interval from 0.009 to 0.196 and p = 0.032. These are unadjusted recalculations, not sponsor-reported analyses in the registry.

For trough FVC, the recalculated estimates are positive for both doses, but both confidence intervals include zero: -0.313 to 0.579 for 50 mcg and -0.309 to 0.583 for 25 mcg. The corresponding unadjusted p-values are 0.559 and 0.548. The posted summaries also contain comparatively large standard errors for the placebo FVC value, which contribute to the broad calculated intervals. The registry does not provide sponsor-reported analyses for these secondary outcomes in the listed results.

These outcomes address related but different measures from the primary trough FEV1 endpoint. They may add context, but do not replace the primary analysis. General: when many outcomes or comparisons are examined, some apparently notable results can arise by chance even if no underlying effect exists. The registry record does not report a multiplicity adjustment for the listed secondary results. Their unadjusted p-values should therefore carry less confirmatory weight than the primary analysis, especially where estimates are imprecise or results vary across related measures.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

9. Statistical Interpretation

Clinical Biostats interpretation

The registry’s formal primary analyses report positive differences in change from baseline in trough FEV1 for each SUN-101 dose compared with placebo. The estimated difference was 0.104 liters for SUN-101 50 mcg and 0.096 liters for SUN-101 25 mcg. Both reported 95% confidence intervals are above zero, and both reported p-values are < 0.001. These figures describe the model-based comparisons recorded by the trial sponsor.

The group-level least-squares mean changes put those contrasts in context: 0.096 liters for the 50 mcg group, 0.089 liters for the 25 mcg group, and -0.007 liters for placebo. The estimated differences therefore reflect the separation between each treatment group’s modeled change and the placebo group’s modeled change. They are not estimates of the difference between the two SUN-101 doses. The registry does not report a direct statistical comparison of the doses.

The unadjusted recalculations use posted group summary statistics and yield the same point estimates as the reported comparisons. Their confidence intervals and p-values differ somewhat from the sponsor’s mixed-model results: for 50 mcg, the recalculated interval is 0.065 to 0.142 and the recalculated p-value is < 0.001; for 25 mcg, the interval is 0.058 to 0.134 and the recalculated p-value is < 0.001. These recalculations are approximate, unadjusted comparisons, not reproductions of the repeated-measures model. The formal registry analyses are the mixed-model results.

General: an estimate describes the direction and magnitude of an observed group contrast, while a confidence interval communicates uncertainty around that estimate under the model and analysis assumptions. A p-value summarizes how compatible the observed data are with a specified null hypothesis under those assumptions; it is not the probability that the null hypothesis is true, nor a measure of clinical importance. Statistical evidence alone does not determine whether an effect is important to patients.

Because the trial randomized participants and included a placebo group, the comparisons are more informative than within-group change alone. Still, interpretation depends on how well the analysis assumptions fit the data, how missing measurements were handled, and how outcomes were selected and analyzed. The registry record does not report a multiplicity adjustment for the listed secondary outcomes, and their unadjusted findings should therefore be read as less confirmatory than the prespecified primary analysis. The primary result is specific to trough FEV1 at Week 12 and does not establish effects on every secondary outcome or over longer follow-up.

10. Statistical Methods Explained

What does a least-squares mean represent?

The primary outcome is reported as a least-squares mean (LS mean), with a standard error. General: a least-squares mean is an estimate from a statistical model, rather than necessarily the raw average of all observed values. It is useful when the analysis models repeated measurements or accounts for features of the data structure. The registry’s reported comparisons use a mixed model for repeated measurements. The full model specification, including all covariates and covariance choices, is not reported in the registry record.

The treatment-group LS mean changes were 0.096 liters for SUN-101 50 mcg, 0.089 liters for SUN-101 25 mcg, and -0.007 liters for placebo. A between-group mean difference expresses the estimated contrast between a treatment group and placebo. In the formal analyses, the differences were 0.104 liters and 0.096 liters, respectively. These are model-based contrasts; they are not the treatment groups’ individual changes and should not be read as direct comparisons between the two doses.

Why use a mixed model for repeated measurements?

General: repeated-measures models are designed for outcomes collected at multiple visits from the same participant. Measurements from one person are generally related to one another, so treating them as entirely independent observations can misrepresent uncertainty. A mixed model can account for this within-participant structure and use available repeated observations under its assumptions. The registry identifies the method as a mixed model for repeated measurements but does not report enough detail to reconstruct its exact specification.

The endpoint description states that all collected values were used, including values collected after a participant stopped randomized treatment if the participant remained in the study. It also says values not collected remained missing and were assumed missing at random. General: a missing-at-random assumption means that, conditional on the information represented in the analysis, the probability of a value being missing does not depend on its unobserved value. This assumption cannot be verified from the short registry description alone, and the record does not report sensitivity analyses for departures from it.

What do the p-values and confidence intervals convey?

The registry’s mixed-model analyses report a 95% confidence interval and p-value for each comparison. The 50 mcg difference is 0.104 liters, with a 95% confidence interval from 0.066 to 0.141 and p < 0.001. The 25 mcg difference is 0.096 liters, with a 95% confidence interval from 0.059 to 0.133 and p < 0.001. General: a confidence interval describes a range of values compatible with the data and model at its stated confidence level. A p-value describes evidence against a null hypothesis of no difference, conditional on the analysis assumptions. Neither statistic independently establishes clinical importance.

The separately calculated unadjusted comparisons are based on posted group summaries. They reproduce the point estimates but use an approximate standard deviation and do not implement the sponsor’s repeated-measures model. As a result, their intervals and p-values are not identical to the model-based results. Such recalculations can serve as a transparent check on the reported summaries, but they should not be treated as a replacement for the sponsor’s stated analysis.

Why can over-dispersion matter?

General: dispersion describes how variable individual measurements are around a group estimate. If variability is larger than a simple model assumes, standard errors can be too small, leading to confidence intervals that are too narrow and p-values that overstate precision. Conversely, a large standard error signals uncertainty even when the estimated mean difference is not small. The registry gives standard errors for the primary LS means, but the unadjusted recalculation uses an approximate standard deviation derived from the posted summaries. It is therefore important not to mistake the recalculated interval for the trial’s full model-based uncertainty.

The secondary results illustrate why data quality and dispersion deserve attention: some posted standard errors differ substantially between groups, including the 25 mcg substudy LS mean standard error of 0.301 liters and the placebo FVC standard error of 0.227 liters. Those entries are reported as recorded; the registry does not explain their pattern. The associated simple recalculations can consequently be highly imprecise and should not be treated as definitive confirmatory analyses.

What does the analysis population mean?

The primary endpoint description defines the Intent to Treat population as subjects randomized and given at least one dose of study medication, analyzed according to randomized treatment. General: retaining randomized assignment in analysis aims to preserve the comparability created by randomization. Here, the stated population is not every person enrolled regardless of treatment exposure; the registry definition requires at least one dose. The record does not provide further participant-flow detail in the primary-outcome description.

The registry does not report the original power calculation or the details needed to reproduce every element of the analysis plan. The sample-size illustrations associated with the observed effects are separate planning calculations and are not evidence about the trial’s original design choices or observed power.

11. Confidence Intervals and Precision

The sponsor-reported 95% confidence interval for the 50 mcg comparison runs from 0.066 to 0.141 liters around an estimated difference of 0.104 liters. For the 25 mcg comparison, the interval runs from 0.059 to 0.133 liters around an estimated difference of 0.096 liters. Both intervals lie above zero. These intervals convey the uncertainty in the model-based estimates under the analysis assumptions; they are not guarantees that the true difference lies within a fixed range.

The unadjusted recalculations give a 0.065 to 0.142 interval for 50 mcg and a 0.058 to 0.134 interval for 25 mcg. The point estimates match the reported model-based differences, but the bounds differ because the recalculations use posted summaries and approximate unadjusted methods rather than the repeated-measures model. The registry reports no discrepancy flag, but the two methods should still be distinguished by what they estimate and how they handle the data.

General: the width of a confidence interval reflects both the amount of information and the variability represented by the analysis. A narrower interval indicates greater statistical precision under the model; it does not establish that an effect is important in practice. A confidence interval that excludes zero is evidence against a zero difference in the corresponding analysis, but does not resolve questions about missing-data assumptions, multiplicity, or clinical relevance.

The registry reports standard errors for the LS means, but does not give a clinical threshold for interpreting the size of a trough FEV1 difference. Thus statistical precision can be described from the estimates and intervals, while the clinical importance of these particular differences cannot be determined from the registry record alone.

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 detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect6282
75% of the observed effect109146
50% of the observed effect245328
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect501002005001,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Standard deviation was approximated from model-based standard errors, so treat it as rough. Calculated for the comparison: SUN-101 50 mcg BID eFlow (CS) Nebulizer.

The sample-size illustrations are planning examples based on the observed effect, not the trial’s original design calculation. For these continuous outcomes, the figures are participants per arm, not total events. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each row changes the effect targeted: 100% of the observed effect, 75% of the observed effect, or 50% of the observed effect.

The 80% power column gives the illustrated number of participants per arm for a design with an 80% chance of detecting the stated effect under those assumptions, if that effect and model assumptions were true. The 90% power column gives the corresponding planning figure for a 90% chance. Higher target power generally calls for more participants. For a fixed power target, smaller effects require more participants because they are harder to distinguish from variability.

For the primary comparison against placebo, the illustrations use the observed comparisons and show the planning figures for each dose separately. The rows are scenarios, not a recommendation about an appropriate future trial, and they do not document the design choices made for GOLDEN-3. The registry record does not report the trial’s own original sample-size assumptions or justification. These calculations are not observed power: observed effects from a completed trial cannot establish the probability that the trial had to detect its true effect.

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 = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

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

Worked calculation for this trial

  1. Observed difference Δ = 0.104; pooled standard deviation σ = 0.204.
  2. n = 2 × (1.96 + 0.842)2 × 0.2042 / 0.1042 = 61.1, rounded up to 62 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 <- 0.1036                      # observed difference in means
sigma <- 0.204354165604717                     # 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(2347761)
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 = 62 (80% power), 82 (90% power)
 75% of observed effect: n per arm = 109 (80% power), 146 (90% power)
 50% of observed effect: n per arm = 245 (80% power), 328 (90% power)
power.t.test: 62.1 
Simulated power at n = 62 per arm: 0.795 (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

MethodEstimate95% CIP-value
MMixed Model Repeat MeasurementLeast Squares Mea Difference (SE) 0.10360.0663 to 0.1409< 0.001
Mixed Model Repeat MeasurementLeast Squares Mean Difference (SE) 0.09610.0589 to 0.1334< 0.001

The registry’s reported primary analyses use a mixed model for repeated measurements and give least-squares mean differences with 95% confidence intervals and p-values. For SUN-101 50 mcg, the reported difference is 0.104 liters, the interval is 0.066 to 0.141, and p < 0.001. For SUN-101 25 mcg, the reported difference is 0.096 liters, the interval is 0.059 to 0.133, and p < 0.001.

The unadjusted recalculations from the posted group summaries yield the same point estimates, but somewhat different intervals and p-values. Their method uses approximate variability from the summaries and does not recreate the sponsor’s repeated-measures model. For example, the recalculated p-values are < 0.001 for both comparisons, while the reported model-based p-values are < 0.001. The different precision reflects the different calculations, not a different point estimate.

The recalculations are best read as ancillary checks, while the registry’s formal reported analyses describe the sponsor’s stated primary method. The record does not provide sufficient model details to independently reproduce the mixed-model analyses. No discrepancy is flagged in the registry record.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary endpoint and multiple secondary outcomes, including lung-function measures, health status measured by the St. George’s Respiratory Questionnaire, rescue medication use, and major adverse cardiac events. It does not report a multiplicity adjustment for the secondary outcome analyses. Without information on the full testing strategy, a reader cannot determine whether the reported secondary comparisons were treated as confirmatory, exploratory, or part of a prespecified hierarchy.

General: testing many outcomes raises the chance of obtaining at least one apparently unusual result by chance. Multiplicity procedures control that risk by adjusting how evidence is evaluated across a family of tests. In the absence of a reported adjustment or testing hierarchy, individual unadjusted secondary p-values should not be interpreted as if they were the sole planned test. The registry record also does not report a detailed statistical analysis plan that would clarify the prespecification of the secondary tests.

Missing data are addressed in the primary endpoint description: values not collected remained missing and were assumed missing at random. All collected values were used, including measurements after discontinuation of randomized treatment when participants remained in the study. The description says that “ALL COLLECTED” and “ON TREATMENT” data are the same, with the difference being the visits included for participants who discontinued treatment but continued study participation. The registry does not report sensitivity analyses examining other missing-data assumptions.

The primary analysis population is defined as randomized subjects who received at least one dose of study medication, analyzed according to assigned group. The registry record does not provide additional detail about exclusions, missing-outcome counts, or participant flow by analysis population. The original sample-size justification, interim analyses, and complete statistical plan are also not reported in the registry record. Those absences limit assessment of how the reported analyses relate to the trial’s original design and decision rules.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
SUN-101 50 mcg BID eFlow (CS) Nebulizer102184.6%
SUN-101 25 mcg BID eFlow (CS) Nebulizer82173.7%
Placebo BID eFlow (CS) Nebulizer112185.0%
Participants with at least one serious adverse event
Serious adverse events by armSUN-101 50 mcg BID eFlow (CS)…4.6%SUN-101 25 mcg BID eFlow (CS)…3.7%Placebo BID eFlow (CS) Nebuli…5.0%% of participants with at least one serious adverse event

Other (non-serious) adverse events

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

ArmParticipants affected of at risk
SUN-101 50 mcg BID eFlow (CS) Nebulizer37 of 218
SUN-101 25 mcg BID eFlow (CS) Nebulizer23 of 217
Placebo BID eFlow (CS) Nebulizer38 of 218

Most frequent serious adverse event terms

Event termOrgan systemSUN-101 50 mcg BID eFlow (CS) NebulizerSUN-101 25 mcg BID eFlow (CS) NebulizerPlacebo BID eFlow (CS) Nebulizer
chronic obstructive pulmonary diseaseRespiratory, thoracic and mediastinal disorders4 of 2182 of 2172 of 218
angina unstableCardiac disorders1 of 2180 of 2171 of 218
pneumoniaImmune system disorders2 of 2180 of 2170 of 218
angina pectorisCardiac disorders0 of 2181 of 2170 of 218
coronary artery stenosisCardiac disorders0 of 2181 of 2170 of 218
diastolic dysfunctionCardiac disorders1 of 2180 of 2170 of 218
small intestinal obstructionGastrointestinal disorders0 of 2181 of 2170 of 218
chest painGeneral disorders1 of 2180 of 2170 of 218
gallbladder necrosisHepatobiliary disorders1 of 2180 of 2170 of 218
bronchitisInfections and infestations0 of 2180 of 2171 of 218

Most frequent non-serious adverse event terms

Event termOrgan systemSUN-101 50 mcg BID eFlow (CS) NebulizerSUN-101 25 mcg BID eFlow (CS) NebulizerPlacebo BID eFlow (CS) Nebulizer
coughRespiratory, thoracic and mediastinal disorders21 of 21816 of 21722 of 218
chronic obstructive ulmonary diseaseRespiratory, thoracic and mediastinal disorders19 of 2189 of 21717 of 218

Serious events with the highest arm-level rate: chronic obstructive pulmonary disease (1.8%), pneumonia (0.9%), angina pectoris (0.5%), coronary artery stenosis (0.5%), small intestinal obstruction (0.5%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The registry reports serious adverse event figures by group. Serious adverse events affected 10 participants among 218 at risk in the SUN-101 50 mcg group, 8 among 217 at risk in the SUN-101 25 mcg group, and 11 among 218 at risk in the placebo group. The figures for other adverse events are 37 among 218 at risk, 23 among 217 at risk, and 38 among 218 at risk, respectively. These counts describe the posted group-level safety data and are not calculations of comparative risk.

The most frequently listed serious-event terms include chronic obstructive pulmonary disease (1.8%), pneumonia (0.9%), angina pectoris (0.5%), coronary artery stenosis (0.5%), small intestinal obstruction (0.5%), and pyelonephritis (0.5%). The registry record does not report death counts in the available safety fields. It also does not provide a comparative statistical analysis of serious adverse events in the information.

General: safety counts should be considered alongside the period of observation, definitions, severity, and participant characteristics. These figures alone do not establish that a treatment caused or prevented an event, and they should not be interpreted as a complete assessment of safety.

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

The primary registry analyses show positive model-based differences in change from baseline in trough FEV1 at Week 12 for each SUN-101 dose compared with placebo. The reported estimates are 0.104 liters for 50 mcg and 0.096 liters for 25 mcg, with both 95% confidence intervals above zero and both p-values < 0.001. The result is a comparison of group-level changes for this defined endpoint and follow-up time.

This does not show that one SUN-101 dose is superior to the other: the reported primary comparisons are each against placebo, and the registry record does not report a direct test between doses. Nor do these results by themselves establish the size of any benefit that patients would notice. The registry does not give a clinical-importance threshold for the endpoint, and statistical significance is not a substitute for one.

The outcome is trough FEV1, not every dimension of COPD. Secondary outcomes include FEV1 area under the curve, trough FVC, health status, rescue medication use, and cardiac events, but the listed results do not provide uniform evidence across all measures. Several secondary recalculations are imprecise, and the registry does not report a multiplicity adjustment for them. The primary finding should not be extended to unreported outcomes, different populations, or longer-term follow-up.

Interpretation also depends on the model and missing-data assumptions. The registry states that the primary analysis used all collected values and assumed missingness at random, but does not report sensitivity analyses or enough detail to reconstruct the mixed model. The endpoint results describe what the posted analysis estimated under its methods; they do not remove uncertainty related to missing data or establish that the same pattern would occur in other settings.

The safety figures provide counts of participants with serious and other adverse events in the trial groups. They do not, on their own, establish causation or provide a complete comparative safety assessment. Overall, the results are specific to the randomized 12-week trial and its posted analyses.

18. Why This Trial Matters Statistically

This trial is a useful statistical example of why the comparison method matters. The primary outcome was measured repeatedly, and the sponsor reported a mixed model for repeated measurements rather than a simple comparison of group summaries. The model-based estimates and unadjusted recalculations have matching point estimates but different confidence limits and p-values. Readers can see why a transparent calculation from summary data is informative as a check, yet cannot replace the analysis that accounts for the trial’s repeated measurements.

The study also illustrates the distinction between an estimate and its precision. The primary differences are accompanied by confidence intervals that quantify uncertainty under the reported model. Secondary outcomes have more variable precision, including broad intervals in some recalculations. A result’s direction alone does not show how precisely it is estimated, while an interval alone does not determine whether the effect matters clinically.

It is also important that the registry’s primary analysis population and missing-data approach are stated. Participants were analyzed according to randomized assignment after receiving at least one dose, and all collected spirometry values were included under the stated missing-at-random assumption. Such details help define what the estimate represents, while the absence of a reported sensitivity analysis or full model specification leaves questions that cannot be resolved from this record.

Finally, the range of secondary outcomes makes multiplicity relevant. Without a reported adjustment or testing hierarchy, secondary p-values should be treated cautiously. The trial is therefore a practical illustration of how study design, analysis populations, repeated-measures methods, missingness, and outcome multiplicity all shape the interpretation of clinical-trial results.

19. Limitations

Several trial-specific limitations are apparent from the registry record. The primary outcome is defined for Week 12, so these results do not describe longer-term change. The registry’s endpoint description specifies that all collected values were analyzed and missing values were assumed missing at random, but it does not report a sensitivity analysis under alternative assumptions. The impact of missing data therefore cannot be assessed from the listed information.

The registry identifies a mixed model for repeated measurements but does not provide its full specification. Details such as the model terms and covariance structure are not reported in the registry record, limiting independent reproduction of the formal analysis. The unadjusted recalculations use approximate dispersion from group summaries and should not be mistaken for the sponsor’s model-based analysis.

Some secondary summary statistics have unusually large reported standard errors relative to other group entries, including 0.301 liters for one substudy estimate and 0.227 liters for the placebo FVC estimate. The registry does not explain these entries. The resulting unadjusted comparisons can be imprecise, and the record does not provide sponsor-reported analyses for the secondary outcomes listed in the calculations.

The registry record does not report a multiplicity adjustment for secondary outcomes, a complete statistical analysis plan, the original sample-size justification, or interim-analysis details. It also does not report a clinical-importance threshold for the primary FEV1 difference. These omissions restrict judgments about confirmatory status, design assumptions, clinical relevance, and robustness beyond the analyses described.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

Continue through the Clinical Biostats statistical pathway

Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.

23. Record Summary

GOLDEN-3 (NCT02347761) is a completed, randomized, quadruple-masked, parallel-group, placebo-controlled Phase 3 trial of 12 weeks of twice-daily nebulized SUN-101 in COPD. The registry lists 653 enrolled participants and three groups: 50 mcg SUN-101, 25 mcg SUN-101, and placebo, delivered with the eFlow Closed System nebulizer.

The primary endpoint was change from baseline in trough FEV1 at Week 12. The registry reports mixed-model differences versus placebo of 0.104 liters for 50 mcg and 0.096 liters for 25 mcg, with 95% confidence intervals of 0.066 to 0.141 and 0.059 to 0.133, respectively; both p-values are < 0.001. The secondary outcomes show varying precision, and multiplicity handling is not reported in the registry record.

The primary analysis included randomized participants who received at least one dose, analyzed as randomized. The outcome description states that missing values were assumed missing at random. Important details, including the original sample-size justification, full statistical plan, and sensitivity analyses for missing data, are not reported in the registry record.

Clinical Biostats