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COPD Phase 3 Continuous Endpoint NCT02465567

Study to Assess the Efficacy and Safety of PT010 Relative to PT003 and PT009 in Subjects With Moderate to Very Severe COPD (Ethos): Complete Statistical Analysis

This analysis examines the randomized ETHOS trial of four inhaled treatment regimens in people with moderate to very severe COPD. It focuses on the adjusted rate of moderate or severe exacerbations over the 52-week treatment period, the registry’s comparative analyses, and the precision and limits of the posted results.

Trial start: 2015-06-30  ·  Enrollment: 8588  ·  Sponsor: Pearl Therapeutics, 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 Study to Assess the Efficacy and Safety of PT010 Relative to PT003 and PT009 in Subjects With Moderate to Very Severe COPD (Ethos) (NCT02465567), a randomized phase 3 study. The primary outcome is Adjusted Rate of Moderate or Severe Exacerbations.

8588
Enrollment
Phase 3
4
Arms
In the primary outcome
-0.01
Mean difference
BGF MDI 160/14.4/9.6 μg
-0.12–0.10
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT02465567
PhasePhase 3
ConditionCOPD
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment8588
Arms in the primary outcome4
Lead sponsorPearl Therapeutics, Inc.
Results postedYes

2. Clinical Question

Population

People with moderate to very severe chronic obstructive pulmonary disease (COPD) were eligible for this phase 3 study. The primary outcome was analyzed in the modified intention-to-treat (mITT) population. The registry record lists an enrollment of 8588.

Intervention

The intervention of interest was BGF MDI 320/14.4/9.6 μg, a regimen containing budesonide, glycopyrronium, and formoterol fumarate. A second BGF regimen, at 160/14.4/9.6 μg, was also studied.

Comparator

The two other groups received GFF MDI 14.4/9.6 μg or BFF MDI 320/9.6 μg. These are the comparator regimens in the posted primary analyses. The registry describes the study as randomized, double-blind, multicenter, and parallel-group.

Primary question

Over a 52-week treatment period, how did the adjusted rate of moderate or severe COPD exacerbations compare among the treatment groups? The registry reports adjusted rate ratios from negative binomial regression for selected comparisons. These are the sponsor’s analyses of the primary outcome.

The primary endpoint concerns the frequency of exacerbations rather than simply whether a participant experienced at least one. That distinction matters: a rate analysis can reflect repeated events, whereas a time-to-first-event outcome considers only the timing of the first qualifying event. The registry also lists time to first moderate or severe exacerbation as a secondary outcome.

The posted results include all four treatment groups, but the registry’s reported primary comparisons pair each BGF group with GFF and BFF. The posted adjusted rate ratios compare BGF MDI 320/14.4/9.6 μg with each of those regimens, and do the same for BGF MDI 160/14.4/9.6 μg. The primary question is therefore addressed through multiple pairwise comparisons, not through a single overall test across all four groups.

The question is about the relative event rates observed during the specified trial period and in the analyzed population. It does not, by itself, establish what would happen outside the trial population or treatment period. Nor does an endpoint focused on exacerbations summarize every outcome relevant to COPD. The registry separately lists secondary outcomes concerning time to first exacerbation, rescue medication use, respiratory health status, death, and severe exacerbations.

3. Trial Design

ETHOS is identified in the registry as a phase 3, randomized, quadruple-masked, parallel-group trial. The official title describes a double-blind, multicenter study designed to assess the efficacy and safety of PT010 relative to PT003 and PT009 on COPD exacerbations over a 52-week treatment period. The trial status is completed. Its registry dates are a start date of 2015-06-30 and a primary completion date of 2019-07-26.

The four groups received BGF MDI 320/14.4/9.6 μg, BGF MDI 160/14.4/9.6 μg, GFF MDI 14.4/9.6 μg, or BFF MDI 320/9.6 μg. The posted primary outcome uses the mITT population. The arm counts for that outcome are 2137, 2121, 2120, and 2131, respectively. These outcome-specific counts need not be interpreted as the total number enrolled in the study.

Randomization is intended to make treatment groups comparable, on average, with respect to measured and unmeasured baseline characteristics. Masking is intended to limit the influence of treatment knowledge on participant behavior, clinical care, and outcome assessment. These are general design principles; the registry record does not detail the exact procedures used to implement allocation concealment or masking.

The parallel-group structure means that participants were assigned to a treatment group rather than being described as crossing between treatments. The registry identifies multiple intervention products and reports group-level outcomes. It does not report the original sample-size justification, the detailed randomization procedure, the planned interim analyses, or the complete statistical analysis plan. Those details should not be inferred from the final enrollment or the observed results.

The primary endpoint is a count-based event rate, and the reported sponsor analyses use negative binomial regression. A rate-based model is suitable for analyzing repeated events when participants can experience more than one qualifying exacerbation. The trial also reports selected secondary outcomes using other methods, including Cox regression for time-to-event outcomes and logistic regression for a binary health-status outcome.

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: Subjects who successfully complete the Screening Period will then be randomized in a 1:1:1:1 scheme to BGF MDI 320/14.4/9.6 μg BID, BGF MDI 160/14.4/9.6 μg BID, BFF MDI 320/9.6 μg BID, or GFF MDI 14.4/9.6 μg BID, respectively.

Overall Study

StageBGF MDI 320/14.4/9.6 μgBGF MDI 160/14.4/9.6 μgGFF MDI 14.4/9.6 μgBFF MDI 320/9.6 μg
STARTED2157213721432151
COMPLETED1708171315801643
NOT COMPLETED449424563508

Reasons for not completing this period:

ReasonBGF MDI 320/14.4/9.6 μgBGF MDI 160/14.4/9.6 μgGFF MDI 14.4/9.6 μgBFF MDI 320/9.6 μg
Adverse Event118113147138
Lack of Efficacy103102171135
Withdrawal by Subject10494123130
Physician Decision23333828
Major Protocol Deviation24262225
Lost to Follow-up25211915
Protocol Specified Criteria2010912
Administrative Reasons129115
Randomized but not treated1545
enrolled in >1 studies18111915
missing PI Signature1000

Analysis population for the primary outcome, as defined in the registry: mITT Population

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

Population: mITT population

CharacteristicUnitBGF MDI 320/14.4/9.6 μgBGF MDI 160/14.4/9.6 μgGFF MDI 14.4/9.6 μgBFF MDI 320/9.6 μgTotal
Participants analysed21372121212021318509
Age, ContinuousYears64.6 (SD 7.6)64.6 (SD 7.6)64.8 (SD 7.6)64.6 (SD 7.6)64.7 (SD 7.6)
Sex: Female, Male: FemaleParticipants8778238768523428
Sex: Female, Male: MaleParticipants12601298124412795081
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants4003934264011620
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants16901680164916836702
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants47484547187
Race (NIH/OMB): American Indian or Alaska NativeParticipants33403039142
Race (NIH/OMB): AsianParticipants162166157166651
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants20002
Race (NIH/OMB): Black or African AmericanParticipants78887564305
Race (NIH/OMB): WhiteParticipants18191783180818167226
Race (NIH/OMB): More than one raceParticipants00000
Race (NIH/OMB): Unknown or Not ReportedParticipants43445046183

6. Primary Endpoint

The registry lists the primary outcome as Adjusted Rate of Moderate or Severe Exacerbations, measured over 52-week treatment period.

ElementRegistry entry
Result typeLeast Squares Mean
Measure of spreadStandard Error
UnitModerate or Severe Exacerbations
Endpoint classificationContinuous Endpoint

The primary endpoint is the adjusted rate of moderate or severe COPD exacerbations during the 52-week treatment period, measured in the mITT population. An exacerbation is counted as an event, so a participant may contribute more than one event to a rate analysis. This differs from an endpoint that records only whether a participant had any event or the time until the first event.

Rates are useful when repeated episodes are clinically and analytically relevant. A comparison of rates can incorporate the frequency of events across the group, rather than reducing each participant’s experience to a yes-or-no indicator. The registry’s primary outcome is described as an adjusted rate, and the sponsor’s reported comparisons use negative binomial regression to estimate rate ratios. Adjustment means the reported model incorporates covariates, but the specific covariates are not reported in the registry record.

General statistical context: recurrent-event counts often vary more across participants than a simple Poisson model assumes. This extra variability is called over-dispersion. A negative binomial model can accommodate over-dispersion, making it a commonly used approach for count outcomes when variation exceeds the Poisson model’s assumptions. The registry identifies the model used but does not report diagnostic checks or details of how over-dispersion was assessed.

The event-rate endpoint is not interchangeable with time to first exacerbation, severe exacerbation rate, symptoms, or health status. Each addresses a different aspect of the trial question. The primary result should therefore be read as a comparison of adjusted moderate-or-severe exacerbation rates, not as a comprehensive summary of every potential benefit or harm.

7. Results Posted in the Registry

Mean difference: BGF MDI 160/14.4/9.6 μg

-0.01

95% CI: -0.12 to 0.10

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals0.91.11.21.31.41.6BGF MDI 320/14.4/9.6 μg (n=2137)BGF MDI 160/14.4/9.6 μg (n=2121)GFF MDI 14.4/9.6 μg (n=2120)BFF MDI 320/9.6 μg (n=2131)Moderate or Severe Exacerbations (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)BGF MDI 160/14.4/9.6 μgGFF MDI 14.4/9.6 μgBFF MDI 320/9.6 μg-0.17-0.030.100.240.380.51mean 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
Time to First Moderate or Severe COPD ExacerbationBinary EndpointRisk difference-0.3 pts (-3.3 to 2.8)623,091 per arm
Percentage of Subjects Achieving a MCID of 4 Units or More in SGRQ Total ScoreBinary EndpointRisk difference-1.7 pts (-4.7 to 1.3)13,810 per arm
Time to Death (All Cause)Binary EndpointRisk difference+0.5 pts (-0.2 to 1.3)8,709 per arm

Time to First Moderate or Severe COPD Exacerbation

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)BGF MDI 160/14.4/9.6 μgGFF MDI 14.4/9.6 μg-3.90-2.03-0.161.713.585.45risk difference (percentage points) vs control (95% CI)

Percentage of Subjects Achieving a MCID of 4 Units or More in SGRQ Total Score

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)BGF MDI 160/14.4/9.6 μgGFF MDI 14.4/9.6 μg-12-8.95-6.14-3.33-0.512.30risk difference (percentage points) vs control (95% CI)

Time to Death (All Cause)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)BGF MDI 160/14.4/9.6 μgGFF MDI 14.4/9.6 μg-0.380.090.561.031.491.96risk difference (percentage points) vs control (95% CI)

The registry posts secondary outcomes covering time to first moderate or severe exacerbation, rescue Ventolin HFA use over 24 weeks, SGRQ response at Week 24, time to death from any cause, and severe COPD exacerbation rate. The reported analyses use different outcome scales and methods. Some comparisons are available for only selected treatment pairs, so the secondary evidence is not a complete set of all possible contrasts across all four groups.

At a broad level, the secondary results are not uniformly conclusive across outcomes and comparisons. Some sponsor-reported time-to-event or health-status comparisons have intervals excluding the relevant null value, while other contrasts have intervals that include it. This variation is compatible with the fact that the outcomes measure distinct aspects of the trial and use different models. Secondary results can provide context for the primary exacerbation-rate finding, but they are not interchangeable confirmations of it.

General statistical context: when many outcomes and comparisons are examined, the chance of at least one apparently notable result can increase even if no underlying effect exists. A multiplicity procedure can control or otherwise address that issue, but the registry record does not report the complete procedure used across secondary endpoints. The unadjusted secondary results should therefore carry less weight than a clearly prespecified primary analysis with a documented testing strategy.

The secondary results are also subject to their own uncertainty, population definitions, and missing-data considerations. A time-to-first-event analysis discards information about later recurrent events; a binary health-status response reduces a continuous score to a threshold-based outcome; and a death analysis addresses a different event from COPD exacerbations. The overall pattern should be considered complementary and exploratory in emphasis unless the trial’s full analysis plan establishes a stronger inferential role.

Because the registry record does not provide a full account of multiplicity control, these secondary findings should not be combined into a single claim of consistency or inconsistency. Their role is to broaden the description of outcomes while leaving the primary adjusted rate analysis as the central result for the stated endpoint.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The registry reports adjusted rate ratios from negative binomial regression for four primary comparisons. For BGF MDI 320/14.4/9.6 μg versus GFF MDI 14.4/9.6 μg, the rate ratio is 0.76, with a 95% confidence interval from 0.69 to 0.83 and p < 0.001. For BGF MDI 320/14.4/9.6 μg versus BFF MDI 320/9.6 μg, the rate ratio is 0.87, with a 95% confidence interval from 0.79 to 0.95 and p = 0.003.

For BGF MDI 160/14.4/9.6 μg versus GFF MDI 14.4/9.6 μg, the rate ratio is 0.75, with a 95% confidence interval from 0.69 to 0.83 and p < 0.001. For BGF MDI 160/14.4/9.6 μg versus BFF MDI 320/9.6 μg, the rate ratio is 0.86, with a 95% confidence interval from 0.79 to 0.95 and p = 0.002. The registry classifies each comparison as a superiority analysis.

General interpretation: a rate ratio below 1 indicates a lower modeled event rate in the first group named in the comparison relative to the second group. The reported confidence intervals for these four comparisons do not include 1, and the posted p-values are below 0.05. This describes the sponsor’s reported model results; it is not a statement about whether any treatment should be used.

Group-level adjusted rates were 1.08 for BGF MDI 320/14.4/9.6 μg, 1.07 for BGF MDI 160/14.4/9.6 μg, 1.42 for GFF MDI 14.4/9.6 μg, and 1.24 for BFF MDI 320/9.6 μg. The registry reports standard errors of 0.04, 0.04, 0.05, and 0.04, respectively. These are model-based adjusted summaries and should not be confused with unadjusted participant-level event counts.

Separate unadjusted recalculations based on posted summary statistics are not the same analysis as the sponsor’s adjusted negative binomial models. The registry record flags a discrepancy between the recalculated comparisons and the sponsor’s reported analyses. Accordingly, the sponsor’s own analysis takes precedence for interpretation of the primary endpoint. The recalculations are useful only as a transparent, simplified comparison of the posted group summaries, not as a replacement for the trial’s reported model.

The primary findings describe the relative rates during the trial’s 52-week treatment period in the stated population. They do not establish that the same rate ratios would apply to other populations, settings, or follow-up periods. The registry record does not report all details needed to independently reproduce the adjusted analysis, including the full covariate specification and complete handling of missing outcome data.

10. Statistical Methods Explained

The central primary analysis is negative binomial regression. The endpoint is a rate of recurrent exacerbations, so a participant can contribute more than one event. General statistical explanation: a count model estimates how the expected event count changes between groups while accounting for the observation period. A negative binomial model allows more variability in event counts than a basic Poisson model. That flexibility is relevant when some participants have substantially more events than others, although the registry does not report the model diagnostics used in this trial.

The primary reported effect measure is a rate ratio. General interpretation: a ratio of 1 represents equal modeled rates; a value below 1 represents a lower modeled rate in the numerator group, and a value above 1 represents a higher modeled rate. The registry’s reported rate ratios are adjusted. This means the estimates come from a statistical model rather than a direct division of the displayed adjusted group means. The adjustment variables and their specification are not reported in the registry record.

A confidence interval expresses uncertainty around an estimated effect under the statistical model. General explanation: a 95% confidence interval is a range generated by a method that, across repeated samples under the method’s assumptions, would contain the underlying parameter in 95% of those samples. It does not mean there is a 95% probability that this particular interval contains the parameter. For the primary comparisons, the reported 95% intervals accompany the adjusted rate ratios and provide information about both the direction and precision of the estimates.

The p-value measures how incompatible the observed data are with a specified null model, under the assumptions of the analysis. It is not the probability that the null hypothesis is true, nor a measure of clinical importance. The sponsor reports p-values for each primary contrast and labels those analyses as superiority tests. The registry record does not report the complete multiplicity procedure, so the displayed p-values should be read with that limitation in mind.

The posted recalculations are unadjusted re-calculations from summary statistics. They compare group means using a simple mean-difference framework, with standard deviations approximated from the posted standard errors. General explanation: an unadjusted comparison does not reproduce a model that adjusts for covariates or uses a count-distribution likelihood. For a recurrent-event endpoint, that distinction is important. A mean difference from group summaries and a negative binomial rate ratio answer related but not identical statistical questions.

The recalculated results are flagged as discrepant from the sponsor’s analyses. The sponsor’s own analysis takes precedence. The recalculations can help readers see how simple comparisons of group-level summaries behave, but they should not be used to overrule the prespecified or sponsor-reported model. The registry record does not contain enough detail to determine the exact source of the discrepancy.

Other posted analyses illustrate different outcome types. Time to first moderate or severe exacerbation and time to death are reported using Cox regression and hazard ratios. General explanation: a hazard ratio compares the instantaneous event rates over follow-up, conditional on remaining event-free up to a given time, under the model’s assumptions. It is not the same quantity as a risk ratio or a rate ratio. The secondary SGRQ outcome is reported using logistic regression and an odds ratio; an odds ratio compares odds, not probabilities or risk differences.

For count and continuous-style outcomes, the accompanying sample-size illustrations use the observed effect or a stated fraction of it. These are planning calculations based on a normal approximation, equal allocation, and a two-sided significance level of 0.05. The planning assumptions are not the original trial design assumptions, and the registry record does not report the original sample-size justification. Sample-size illustrations describe hypothetical study requirements under their assumptions; they do not reveal the power achieved by the completed trial.

The methods listed in the registry identify broad model families, but not every analytical decision. The record does not report the complete model formula, exact covariates, detailed missing-data procedures, all analysis-population definitions beyond the stated mITT primary population, or the complete approach to multiplicity. These omissions constrain independent reproduction and make it important to distinguish reported sponsor analyses from simple recalculations.

11. Confidence Intervals and Precision

The primary comparisons are reported with 95% confidence intervals. For BGF MDI 320/14.4/9.6 μg versus GFF MDI 14.4/9.6 μg, the rate ratio is 0.76 and the interval is 0.69 to 0.83. The comparison with BFF MDI 320/9.6 μg has a rate ratio of 0.87 and an interval of 0.79 to 0.95. For BGF MDI 160/14.4/9.6 μg, the corresponding rate ratios are 0.75 versus GFF, with an interval of 0.69 to 0.83, and 0.86 versus BFF, with an interval of 0.79 to 0.95.

General interpretation: narrower confidence intervals indicate more precise estimates under the model, while wider intervals indicate greater uncertainty. The four primary intervals are entirely below 1, consistent with the direction of the reported rate ratios. The interval boundaries also show that the estimates are not exact; a range of values remains compatible with the data and model.

The group-level adjusted rates are reported with standard errors rather than confidence intervals. The standard errors are 0.04 for each BGF group, 0.05 for GFF, and 0.04 for BFF. Standard errors describe the estimated sampling variability of the group summaries, but they are not themselves ranges of plausible values. They also do not provide the full uncertainty for a contrast between groups.

Precision depends on the outcome, model, number of observed events, variability, and assumptions. The registry record gives outcome-specific group sizes and the reported intervals, but does not provide all event-count distribution details or model diagnostics. The displayed estimates should therefore be interpreted as precise to the reported interval, not as exact underlying treatment effects. The recalculated intervals are distinct from the sponsor’s adjusted intervals, and the flagged discrepancy means the sponsor’s analysis is the appropriate primary result to emphasize.

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 effect534,737715,860
75% of the observed effect950,6421,272,640
50% of the observed effect2,138,9452,863,440
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect500,0001,000,0002,000,0005,000,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
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: BGF MDI 160/14.4/9.6 μg.

The sample-size illustrations are planning calculations based on the observed effect, with additional rows showing planning for 75% or 50% of the observed effect. They assume a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. For outcomes other than time-to-event endpoints, the figures are participants per arm. For time-to-event calculations, the figures are total numbers of events. The trial’s own original design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the number of participants per arm, or total events for a time-to-event calculation, that the planning method estimates would be needed to detect the stated effect with 80% power under its assumptions. The 90% power column gives the corresponding requirement for 90% power. General explanation: power is the probability of detecting an effect of the specified size when that effect is present, given the assumptions of the calculation. These figures are hypothetical planning requirements, not descriptions of the completed trial’s achieved power.

The rows that plan for smaller fractions of the observed effect require larger sample sizes. This is expected: smaller differences are harder to distinguish from random variation, so more information is generally needed. The illustrations are sensitive to the observed effect used as their starting point, and a small observed effect can produce very large planning numbers. They should not be treated as a recommendation for a future trial without additional design work.

These calculations are not observed power. They do not change the interpretation of the registry’s estimated effects, confidence intervals, or p-values, and they do not establish whether the trial was adequately designed. The original trial’s sample-size rationale 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 = 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 = -0.010; pooled standard deviation σ = 1.846.
  2. n = 2 × (1.96 + 0.842)2 × 1.8462 / -0.0102 = 534,736.0, rounded up to 534,737 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 <- -0.01                      # observed difference in means
sigma <- 1.84565655534846                     # 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(2465567)
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 = 534,737 (80% power), 715,860 (90% power)
 75% of observed effect: n per arm = 950,642 (80% power), 1,272,640 (90% power)
 50% of observed effect: n per arm = 2,138,945 (80% power), 2,863,440 (90% power)
power.t.test: 534737 
Simulated power at n = 534,737 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

MethodEstimate95% CIP-value
Negative Binomial RegressionRate Ratio 0.760.69 to 0.83< 0.001
Negative Binomial RegressionRate Ratio 0.870.79 to 0.950.003
Negative Binomial RegressionRate Ratio 0.750.69 to 0.83< 0.001
Negative Binomial RegressionRate Ratio 0.860.79 to 0.950.002
Where the two analyses differ, rely on the sponsor's. The simple re-calculation above reaches a different conclusion from the sponsor's analysis, usually because the sponsor adjusts for covariates, stratification or repeated measures, or (for event rates) uses a negative binomial model that allows for over-dispersion and so gives wider intervals.

The primary results reported by the sponsor use negative binomial regression and present adjusted rate ratios, 95% confidence intervals, and p-values. Those analyses compare the BGF groups with GFF and BFF. The separately calculated comparisons use posted summary statistics and are unadjusted. They are not equivalent to the sponsor’s count-model analyses.

The registry record flags a discrepancy between the recalculated results and the sponsor’s results. Under that circumstance, the sponsor’s own analysis takes precedence. The recalculations are best viewed as a simplified check based on the displayed group summaries, not as a competing estimate of the primary adjusted effect. Different estimands, adjustment, distributional assumptions, and summary-statistic approximations can yield results that do not match exactly.

The registry does not report enough detail to identify the cause of the discrepancy or fully reproduce the sponsor’s model. The primary interpretation should therefore rely on the sponsor-reported rate ratios and their intervals, while retaining the distinction between adjusted model results and unadjusted recalculations.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists multiple outcomes and multiple pairwise analyses. The primary endpoint itself has four reported comparisons: each BGF regimen against GFF and against BFF. Secondary outcomes add further comparisons and distinct hypotheses. When many hypotheses are tested, the probability of at least one small p-value by chance can rise. General statistical practice may address this through a prespecified hierarchy, family-wise error control, false-discovery procedures, or clearly exploratory labeling.

The registry record does not report the complete multiplicity strategy, including whether the primary comparisons were tested in a fixed sequence or whether any adjustment was applied across them. It also does not report a complete testing framework for the secondary outcomes. Consequently, the p-values should be interpreted in the context of the reported analyses, without assuming an unreported multiplicity adjustment.

The primary outcome is explicitly described as assessed in the mITT population. The registry record does not fully describe the mITT definition, the handling of participants with missing endpoint data, or the approach to incomplete follow-up. It does not report whether missingness was handled through imputation, likelihood-based methods, censoring rules, or another procedure. Such details can affect estimates and uncertainty, particularly if missingness differs by treatment group or relates to outcome risk.

The record also does not report the original sample-size justification, any interim analyses, or the complete statistical analysis plan. These omissions mean it is not possible to determine from the registry alone whether every displayed analysis follows the original prespecified hierarchy or how decisions were made before outcome data were examined. This is a limitation of the information available in the registry record, not evidence that a particular procedure was or was not used.

For a complete assessment, the adjusted model, analysis populations, missing-data procedures, and multiplicity plan would need to be documented in the trial’s fuller analysis materials. In their absence, the most defensible reading distinguishes the sponsor’s primary analyses from recalculations and gives less inferential weight to numerous secondary comparisons.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
BGF MDI 320/14.4/9.6 μg426214419.9%
BGF MDI 160/14.4/9.6 μg445212421.0%
GFF MDI 14.4/9.6 μg433212520.4%
BFF MDI 320/9.6 μg440213620.6%
Participants with at least one serious adverse event
Serious adverse events by armBGF MDI 320/14.4/9.6 μg19.9%BGF MDI 160/14.4/9.6 μg21.0%GFF MDI 14.4/9.6 μg20.4%BFF MDI 320/9.6 μg20.6%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
BGF MDI 320/14.4/9.6 μg27 of 2144
BGF MDI 160/14.4/9.6 μg42 of 2124
GFF MDI 14.4/9.6 μg47 of 2125
BFF MDI 320/9.6 μg35 of 2136

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
BGF MDI 320/14.4/9.6 μg337 of 2144
BGF MDI 160/14.4/9.6 μg361 of 2124
GFF MDI 14.4/9.6 μg292 of 2125
BFF MDI 320/9.6 μg336 of 2136

Most frequent serious adverse event terms

Event termOrgan systemBGF MDI 320/14.4/9.6 μgBGF MDI 160/14.4/9.6 μgGFF MDI 14.4/9.6 μgBFF MDI 320/9.6 μg
Chronic obstructive pulmonary diseaseRespiratory, thoracic and mediastinal disorders202 of 2144221 of 2124219 of 2125241 of 2136
PneumoniaInfections and infestations61 of 214459 of 212435 of 212555 of 2136
Acute respiratory failureRespiratory, thoracic and mediastinal disorders14 of 214420 of 212420 of 21257 of 2136
Acute myocardial infarctionCardiac disorders7 of 214410 of 212417 of 21257 of 2136
Atrial fibrilationCardiac disorders9 of 21448 of 212414 of 21253 of 2136
Respiratory failureRespiratory, thoracic and mediastinal disorders10 of 21449 of 21245 of 21259 of 2136
Myocardial infarctionCardiac disorders5 of 21445 of 21247 of 21254 of 2136
SepsisInfections and infestations7 of 21445 of 21245 of 21253 of 2136
Coronary artery diseaseCardiac disorders5 of 21445 of 21247 of 21251 of 2136
CellulitisInfections and infestations4 of 21446 of 21244 of 21253 of 2136

Most frequent non-serious adverse event terms

Event termOrgan systemBGF MDI 320/14.4/9.6 μgBGF MDI 160/14.4/9.6 μgGFF MDI 14.4/9.6 μgBFF MDI 320/9.6 μg
NasopharyngitisInfections and infestations227 of 2144239 of 2124199 of 2125234 of 2136
Upper respiratory tract infectionInfections and infestations123 of 2144137 of 2124102 of 2125115 of 2136

Serious events with the highest arm-level rate: chronic obstructive pulmonary disease (11.3%), pneumonia (2.8%), acute respiratory failure (0.9%), acute myocardial infarction (0.8%), atrial fibrilation (0.7%).

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 events affecting 426 of 2144 participants in the BGF MDI 320/14.4/9.6 μg group, 445 of 2124 in the BGF MDI 160/14.4/9.6 μg group, 433 of 2125 in the GFF MDI 14.4/9.6 μg group, and 440 of 2136 in the BFF MDI 320/9.6 μg group. The record also lists other adverse events affecting 337, 361, 292, and 336 participants in those groups, respectively. These are counts of participants, not measures of event severity beyond the registry’s serious-event classification.

Deaths listed for the groups are 27, 42, 47, and 35, respectively. The registry also identifies serious-event terms including chronic obstructive pulmonary disease at 11.3%, pneumonia at 2.8%, acute respiratory failure at 0.9%, acute myocardial infarction at 0.8%, atrial fibrilation at 0.7%, and respiratory failure at 0.5%.

These figures are descriptive. They do not by themselves establish comparative safety, because the record does not provide a complete adjusted safety analysis, uncertainty intervals, or detailed definitions and follow-up rules for each adverse-event measure. Event counts should be read alongside the trial’s clinical context and not as stand-alone causal comparisons.

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

The primary result describes adjusted moderate-or-severe COPD exacerbation rates during the 52-week treatment period among participants in the mITT population. The sponsor’s negative binomial analyses report rate ratios below 1 for the BGF comparisons with GFF and BFF, with the posted 95% confidence intervals entirely below 1. These estimates and intervals describe the direction and precision of the reported model contrasts.

The result does not mean that every participant in one group experienced fewer exacerbations than every participant in another group. Group-level rates summarize distributions of outcomes, and individual experiences vary. A rate ratio also does not reveal the full range of event histories, symptom burden, or patient priorities. The endpoint focuses on moderate or severe exacerbations and cannot stand in for all dimensions of COPD or treatment experience.

The result does not establish that the same estimates apply in populations not represented in the trial, beyond the trial’s 52-week treatment period, or under different care conditions. The registry record does not provide enough information to assess every source of uncertainty, including the complete handling of missing data and multiplicity. The discrepancy flag also means the unadjusted recalculations should not replace the sponsor’s own adjusted analysis.

Secondary outcomes provide additional but distinct information. Time to first exacerbation, rescue medication use, SGRQ response, all-cause death, and severe exacerbation rate address different questions. Their results should not be treated as direct substitutes for the primary rate comparison, and the incomplete reporting of multiplicity limits how strongly multiple secondary p-values can be interpreted together.

Finally, statistical evidence is not a treatment recommendation. The posted analyses describe observed trial data under specified models; decisions about care require considerations beyond this statistical summary. The trial record supports interpretation of the reported comparisons, not conclusions about an individual’s expected outcome.

18. Why This Trial Matters Statistically

This trial illustrates why endpoint choice and model choice matter in clinical research. The primary outcome counts recurrent moderate or severe exacerbations, so a rate model retains information about repeated events that a simple indicator of “any event” would discard. Negative binomial regression is a familiar approach for count outcomes when extra variability may be present, and the registry identifies it as the sponsor’s method.

The record also shows why effect measures must be distinguished. A rate ratio for recurrent events is not the same as a hazard ratio for time to an event, an odds ratio for a binary response, or a risk difference based on event proportions. The secondary endpoints use these different measures, each answering a different statistical question. Reading them as though they were interchangeable would blur the meaning of the results.

The discrepancy between the recalculations and the sponsor’s analysis is another important statistical lesson. Simple unadjusted comparisons of published group summaries can be informative, but they do not reproduce a covariate-adjusted model for a recurrent count endpoint. The sponsor’s reported analysis takes precedence, and the discrepancy emphasizes the need to report model specifications and analysis decisions transparently.

Finally, the registry’s missing information about multiplicity, missing data, and the original sample-size rationale limits independent evaluation. These are not merely technical details: they help readers understand which findings were confirmatory, how uncertainty was handled, and what the design was intended to detect. Clear reporting of these features is essential for careful interpretation of large, multi-outcome trials.

19. Limitations

The registry record provides the broad design, outcome summaries, and selected model results, but not the full statistical analysis plan. The exact covariates in the adjusted negative binomial models are not reported, so the primary results cannot be completely reproduced from the registry alone. Nor does the record provide the original sample-size justification or detailed design assumptions.

The record flags a discrepancy between unadjusted recalculations and the sponsor’s analyses. Because the primary endpoint is a recurrent-event rate and the sponsor used an adjusted negative binomial model, the recalculations are not an equivalent analysis. The sponsor’s own result takes precedence, but the registry information does not explain the discrepancy in detail.

Multiplicity control across primary and secondary analyses is not reported. The registry lists numerous outcomes and analyses, yet does not provide the complete inferential hierarchy or clarify how the family of comparisons was handled. This makes isolated secondary p-values harder to interpret as confirmatory evidence.

Details of missing-data handling, censoring, analysis-population definitions beyond the primary mITT label, model diagnostics, and treatment adherence are not reported in the registry record. The available serious-adverse-event summaries are descriptive and do not include a complete comparative safety analysis with uncertainty estimates in the posted information.

These limitations do not negate the reported results, but they restrict independent verification and the strength of conclusions that can be drawn from registry-level information alone. Interpretation should remain tied to the stated population, endpoints, treatment period, and sponsor-reported models.

20. Related Tutorials

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22. Sources

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23. Record Summary

ETHOS (NCT02465567) is a completed phase 3 randomized, quadruple-masked, parallel-group study in people with moderate to very severe COPD. The registry lists enrollment of 8588 and a 52-week treatment period. Four inhaled regimens were compared, and the primary endpoint was the adjusted rate of moderate or severe exacerbations in the mITT population.

The sponsor’s negative binomial analyses report four adjusted rate ratios comparing the two BGF regimens with GFF and BFF. All four reported 95% confidence intervals are below 1. The registry also posts secondary outcomes and descriptive adverse-event counts. The record does not report the complete statistical plan, original sample-size justification, multiplicity strategy, or detailed missing-data procedures. The primary interpretation should rely on the sponsor’s adjusted analyses, which take precedence over the flagged unadjusted recalculations.

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