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Rhinitis, Allergic, Seasonal Phase 3 Continuous Endpoint NCT01279057

A Study Comparing Two Fluticasone Furoate Nasal Sprays in the Relief of the Signs and Symptoms of Seasonal Allergic Rhinitis: Complete Statistical Analysis

This analysis examines a randomized, parallel-group study comparing a fluticasone furoate nasal spray from Lek Pharmaceuticals with Veramyst and placebo for seasonal allergic rhinitis. The primary result concerns change in reflective nasal symptom scores over 14 days, with equivalence assessed in the per-protocol population.

Trial start: 2010-12-27  ·  Enrollment: 727  ·  Sponsor: Sandoz
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 A Study Comparing Two Fluticasone Furoate Nasal Sprays in the Relief of the Signs and Symptoms of Seasonal Allergic Rhinitis (NCT01279057), a randomized phase 3 study. The primary outcome is PRIMARY: Mean Change From Baseline in Reflective Total Nasal Symptom Score (rTNSS) (Equivalence: Per-Protocol Population).

727
Enrollment
Phase 3
2
Arms
In the primary outcome
0.13
Mean difference
Test
-0.29–0.55
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01279057
PhasePhase 3
ConditionRhinitis, Allergic, Seasonal
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment727
Arms in the primary outcome2
Lead sponsorSandoz
Results postedYes

2. Clinical Question

Population

Participants with seasonal allergic rhinitis, listed in the registry record as rhinitis, allergic, seasonal. The primary endpoint analysis used the per-protocol population; its size is reflected in the reported treatment groups.

Intervention

Fluticasone furoate 27.5 mcg/actuation nasal spray from Lek Pharmaceuticals, administered once daily at a dose of 110 mcg (4 actuations) for 14 days.

Comparator

The reference fluticasone furoate nasal spray, Veramyst, at the same listed strength and daily dose for 14 days. Placebo was also included in the trial for comparisons against each active formulation.

Primary question

In the per-protocol population, how did mean change from baseline in reflective Total Nasal Symptom Score (rTNSS) compare between the test and reference sprays over 14 days, and did the registry analysis support clinical equivalence?

The primary comparison is between the Lek Pharmaceuticals test spray and the Veramyst reference spray, not between either active formulation and placebo. The registry record also describes planned superiority comparisons of the active formulations with placebo. Those are distinct questions: equivalence asks whether the test and reference formulations are sufficiently alike under a prespecified criterion, while superiority asks whether a treatment differs from placebo in a specified direction. The equivalence criterion and margin are not reported in the registry record, so the numerical results alone do not establish whether the criterion was met.

The primary measure summarizes four nasal symptoms: congestion, runny nose, sneezing, and itchy nose. Each symptom was scored from 0 (no symptom) to 3 (severe symptom); the summed score ranges from 0 to 12, with lower scores indicating less severe symptoms. For change from baseline, the registry defines baseline minus post-randomization score, so a positive change is favorable. The question is therefore about comparative change on a symptom scale during the stated treatment period, rather than about a diagnosis, a long-term outcome, or an individual participant's response.

3. Trial Design

The registry record describes a completed, randomized, quadruple-masked, parallel-group, multi-site phase 3 study sponsored by Sandoz. Enrollment was 727. The listed condition was seasonal allergic rhinitis. The study compared the test fluticasone furoate nasal spray with the reference product Veramyst and placebo. The test and reference arms were each dosed once daily at 110 mcg (4 actuations) for 14 days; placebo was administered once daily for 14 days.

Random allocation means treatment assignment was determined through a random process, rather than being selected by participants or investigators. Masking is intended to limit the influence of treatment knowledge on participants, clinical staff, and assessments. The record labels the masking quadruple but does not identify the specific roles covered by that label. A parallel-group design assigns participants to treatment groups that continue alongside one another, rather than crossing participants between treatments.

The study began on 2010-12-27, reached primary completion on 2011-02-08, and is listed as completed. These dates describe the registry record; they do not establish the length of follow-up for outcomes beyond the stated 14-day treatment period. The primary endpoint was mean change from baseline in rTNSS, analyzed for equivalence in the per-protocol population and using only the test and reference arms. The registry also lists superiority analyses in the intent-to-treat population and equivalence analyses in the per-protocol population for nasal and ocular symptom outcomes.

The registry record does not report the original sample-size justification, the intended allocation ratio, the detailed randomization method, the masking procedures, or the full statistical analysis plan. The enrolled total should not be taken as evidence of the assumptions used to design the study. Nor does the posted primary analysis alone explain how exclusions from the per-protocol population were determined.

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: Participants who met the inclusion/exclusion criteria entered a 7-day placebo lead-in period. Following this placebo lead-in period, on Day 1 participants who continued to meet eligibility criteria were randomly assigned in a 2:2:1 ratio to one of three treatment groups (Test Product:Reference Product:Placebo).

Overall Study

StageTestReferencePlacebo
STARTED288292147
Per-Protocol (PPP) Population257245126
Intent-to-Treat (ITT) Population284285144
COMPLETED282287144
NOT COMPLETED653

Reasons for not completing this period:

ReasonTestReferencePlacebo
Adverse Event101
Insufficient therapeutic response001
Restricted medication for seasonal allergic rhinitis010
Withdrew consent201
Pregnancy010
Other330

Analysis population for the primary outcome, as defined in the registry: Per-Protocol population was used in this analysis. To determine equivalence, only the test and reference treatment arms were analyzed.

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.

CharacteristicUnitTestReferencePlaceboTotal
Participants analysed288292147727
Age, Customized: < 18Participants17281762
Age, Customized: 18 - 40Participants13312265320
Age, Customized: 41 - 64Participants12213759318
Age, Customized: 65 - 75Participants154625
Age, Customized: > 75Participants1102
Sex: Female, Male: FemaleParticipants17419591460
Sex: Female, Male: MaleParticipants1149756267
Race/Ethnicity, Customized: WhiteParticipants233241126600
Race/Ethnicity, Customized: Black/African AmericanParticipants504019109
Race/Ethnicity, Customized: AsianParticipants2529
Race/Ethnicity, Customized: Native Hawaiian / Other Pacific IslanderParticipants0202
Race/Ethnicity, Customized: American Indian / Alaska NativeParticipants2002
Race/Ethnicity, Customized: OtherParticipants1405

6. Primary Endpoint

The registry lists the primary outcome as PRIMARY: Mean Change From Baseline in Reflective Total Nasal Symptom Score (rTNSS) (Equivalence: Per-Protocol Population), measured over Baseline, 14 days.

ElementRegistry entry
Result typeMean
Measure of spreadStandard Deviation
Unitscore on scale
Endpoint classificationContinuous Endpoint

The primary endpoint is mean change from baseline in reflective Total Nasal Symptom Score (rTNSS) over the randomized treatment period, reported at baseline and 14 days. Participants rated congestion, runny nose, sneezing, and itchy nose on a four-point scale from 0 (no symptom) to 3 (severe symptom). The four symptom ratings were combined into a score ranging from 0 to 12; lower scores indicate less severe symptoms.

For a reflective rating, participants looked back over the previous 12 hours. They were asked to record the score twice daily, approximately 12 hours apart, with the first daily rating taken before dosing. Baseline was calculated from scores recorded over the 72 hours before the randomized treatment period. The registry defines change as mean baseline rTNSS minus mean post-randomization rTNSS. Under that definition, a positive change indicates improvement in the score.

A symptom score condenses several related experiences into a repeatable measure that can be compared between groups. Repeated ratings across the treatment period contribute to the mean, reducing reliance on a single observation. In general, a continuous score can retain gradations of response that would be lost if outcomes were reduced to categories such as improved or not improved. The registry record does not report the smallest clinically important difference for rTNSS or explain how the equivalence margin was selected. Statistical differences in the score therefore need to be interpreted alongside the stated endpoint definition and the limits of the posted analysis.

7. Results Posted in the Registry

Mean difference: Test

0.13

95% CI: -0.29 to 0.55

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals1.51.71.92.12.22.4Test (n=257)Reference (n=245)score on scale (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Test-0.36-0.160.030.230.430.62mean 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
Mean Change From Baseline in Instantaneous Total Nasal Symptom Score (iTNSS) (Equivalence: Per-Protocol Population)Continuous EndpointMean difference0.16 (-0.26 to 0.59)3,476 per arm
Mean Change From Baseline in Instantaneous Total Nasal Symptom Score (iTNSS) (Superiority: Intent-to-Treat Population)Continuous EndpointMean difference0.19 (-0.21 to 0.58)2,528 per arm
Mean Change From Baseline in Reflective Total Ocular Symptom Score (rTOSS) (Equivalence: Per-Protocol Population)Continuous EndpointMean difference0.24 (-0.08 to 0.55)925 per arm

Mean Change From Baseline in Instantaneous Total Nasal Symptom Score (iTNSS) (Equivalence: Per-Protocol Population)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Test-0.33-0.130.060.260.460.66mean difference vs control (95% CI)

Mean Change From Baseline in Instantaneous Total Nasal Symptom Score (iTNSS) (Superiority: Intent-to-Treat Population)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)TestPlacebo-1.54-1.09-0.63-0.170.280.74mean difference vs control (95% CI)

Mean Change From Baseline in Reflective Total Ocular Symptom Score (rTOSS) (Equivalence: Per-Protocol Population)

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Test-0.130.020.160.310.460.60mean difference vs control (95% CI)

The registry lists six secondary outcomes spanning nasal and ocular symptoms, with both reflective and instantaneous scoring represented. The detailed results identify per-protocol equivalence analyses for instantaneous nasal and reflective ocular scores, and intent-to-treat superiority analyses for instantaneous nasal scores. These outcomes broaden the assessment beyond the primary reflective nasal score, but they are related symptom measures rather than independent confirmation of the primary equivalence question.

Across the detailed results, the sponsor-reported equivalence analyses are expressed as ratios of test to reference least-squares means with 90% confidence intervals. The registry record does not report the equivalence margins or the methods for these analyses, so the ratios and intervals cannot independently establish equivalence. The superiority analyses compare each active treatment with placebo and report ANCOVA p-values of < 0.001. Those findings concern active-treatment-versus-placebo comparisons and do not establish that the test and reference sprays are equivalent.

The primary result remains the central answer to the stated question because it is the designated endpoint and directly compares the test and reference formulations on reflective nasal symptoms in the per-protocol population. Secondary outcomes can indicate whether related measures were also examined, but they do not replace the primary analysis. The registry record lists the other ocular and nasal outcomes, but detailed numerical results for all six are not included in the record information; their direction and precision should not be inferred.

In general, multiple secondary comparisons raise the possibility of chance findings when each is interpreted separately. Unadjusted p-values do not account for the full number of analyses unless a multiplicity method is applied, and the registry record does not report whether such an adjustment was planned or used. Secondary results are consequently best treated as supporting context rather than as standalone confirmation. They should be considered alongside their endpoint definitions, populations, analysis methods, and the uncertainty about multiplicity.

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

9. Statistical Interpretation

Clinical Biostats interpretation

In the primary per-protocol comparison, the mean change was 2.036 for the test spray and 1.904 for the reference spray. Both group means are positive under the registry's change definition, where positive change is favorable. The unadjusted recalculation estimates the test-minus-reference mean difference as 0.132, with a 95% confidence interval from -0.290 to 0.554 and an unadjusted p-value of 0.54. This calculation uses the posted group summary statistics and is not the sponsor's adjusted equivalence analysis.

The sponsor-reported analysis is a ratio of test to reference least-squares means of 104.085, with a 90% confidence interval from 87.421 to 124.210. The registry classifies this as an equivalence analysis, but the equivalence margin and the method used to decide whether the interval satisfies that margin are not reported in the registry record. Without that criterion, the ratio and interval cannot by themselves establish whether the sponsor's prespecified equivalence standard was met. The registry record does not report a p-value for this primary equivalence result.

The confidence interval from the unadjusted recalculation includes zero. In general, that means the summary-statistic calculation is compatible with a range of differences that includes no average difference, as well as differences in either direction. It does not prove the groups are identical. Equivalence is not established merely because a conventional test fails to show a difference: it requires a prespecified acceptable range and an analysis that evaluates the estimate against that range. The posted equivalence analysis and the unadjusted mean-difference calculation also report results on different scales.

The secondary results include an equivalence analysis of instantaneous nasal symptoms in the per-protocol population and superiority analyses of instantaneous nasal symptoms in the intent-to-treat population. The registry reports ANCOVA p-values of < 0.001 for each active formulation compared with placebo in the latter analyses. Those findings address active-treatment-versus-placebo questions and do not answer the primary test-versus-reference equivalence question. The record also lists ocular symptom outcomes, but the pattern across symptom domains cannot resolve the unreported equivalence margin or missing details of the analysis plan.

The reported group summaries are averages. They do not describe how individual participants' scores changed, how many participants improved, or how variable their responses were beyond the reported standard deviations. The primary analysis was per-protocol, while some secondary comparisons used the intent-to-treat population. Those populations answer related but not identical analytic questions. The registry record does not describe missing-data handling, protocol deviations, or whether sensitivity analyses were conducted. These gaps limit how fully the posted results can be assessed.

Overall, the registry shows similar numerical average changes in the two active-treatment groups on the primary endpoint, alongside uncertainty in the unadjusted mean-difference estimate. Similar observed averages are not a formal demonstration of equivalence. Interpretation should give priority to the sponsor's reported analysis for its intended equivalence question, while recognizing that the margin and decision rule needed to interpret that analysis are not reported in the registry record.

10. Statistical Methods Explained

The primary outcome is continuous: it is a score summarized as a mean, with a standard deviation describing variation among participant scores. The registry defines the analysis as a comparison of mean change from baseline in rTNSS between the test and reference groups. Because the score is defined as baseline minus post-randomization, a positive change represents a favorable direction. The test and reference per-protocol group means were 2.036 and 1.904, respectively.

What does the recalculated mean difference represent?

The unadjusted recalculation compares the posted group means on the original score-change scale. It estimates a test-minus-reference mean difference of 0.132. The associated 95% confidence interval is -0.290 to 0.554, and the unadjusted p-value is 0.54. These are simple calculations from the posted summary statistics; they are not an adjusted model result and do not substitute for the sponsor's own analysis. The calculation does not use participant-level observations or account for covariates that may have been included in a model.

In general, an unadjusted mean difference is easy to interpret because it is expressed in the scale's units. It is also limited: summary statistics cannot reproduce analyses that rely on individual records, model adjustments, exclusions, or other features not present in the group summaries. A recalculated p-value tests a difference under its own assumptions. It is not, by itself, an equivalence test.

How does equivalence differ from testing for a difference?

In general, a conventional difference test asks whether the data are inconsistent with a specified null hypothesis of no difference. Equivalence instead asks whether the plausible treatment difference lies within a prespecified range considered acceptably small. That range is commonly expressed through an equivalence margin. The margin, the method used to construct the sponsor's interval, and the decision rule are not reported in the registry record. Consequently, the label “equivalence” identifies the analysis question but does not provide enough information to independently verify its conclusion.

The sponsor-reported primary quantity is the ratio of test to reference least-squares means: 104.085, with a 90% confidence interval from 87.421 to 124.210. Least-squares means are model-based estimates, rather than necessarily being the raw group averages. The registry does not report the method for this primary analysis, so the model specification and any adjustment cannot be described. The sponsor's ratio is on a relative scale, whereas the recalculated difference is on the score-change scale. They are not interchangeable estimates.

What does the confidence interval add?

In general, a confidence interval expresses uncertainty in an estimate under the assumptions of the analysis. Its endpoints show a range of values compatible with the observed data and method at the stated confidence level. A wider interval indicates less precision than a narrower interval on the same scale. The recalculated interval includes zero, but that does not prove the treatments are the same. For equivalence, the interval must be interpreted against the prespecified equivalence margin, which is not reported in the registry record. The sponsor's reported interval is at 90%, while the recalculated mean-difference interval is at 95%; they also concern different estimands and scales.

Why do the analysis populations matter?

The primary equivalence outcome used the per-protocol population, and only the test and reference groups were analyzed for that outcome. A per-protocol analysis generally focuses on participants who meet specified criteria for adherence or evaluability, but the registry record does not report the criteria or the reasons participants may have been excluded. The intent-to-treat population is used for the posted superiority comparisons of instantaneous nasal symptoms. In general, an intent-to-treat analysis retains participants in their randomized groups, although the precise population definition and missing-data approach still matter. The registry record does not provide enough detail to determine those implementation choices.

Using different populations for equivalence and superiority analyses may affect how their results relate. Equivalence analyses can be sensitive to nonadherence or exclusions, while retaining randomized participants can preserve the benefits of random allocation for treatment comparisons. These are general considerations, not claims about the conduct of this trial. The registry record does not describe sensitivity analyses comparing populations or approaches to missing observations.

What does the reported ANCOVA analysis tell readers?

The registry reports ANCOVA superiority analyses comparing each active formulation with placebo for instantaneous nasal symptoms in the intent-to-treat population, with p-values of < 0.001 for both comparisons. ANCOVA is a general linear-model approach that can compare groups while adjusting for covariates specified in the model. The registry does not identify the covariates, model details, multiplicity procedure, or missing-data handling for these analyses. The p-values are therefore reported as recorded, without inferring additional model details. They address superiority against placebo, not equivalence between the two active sprays.

In general, a p-value measures how incompatible the data are with a specified null model, given the analysis assumptions. It is not the probability that the null hypothesis is true, nor does it measure the size or clinical importance of an effect. A small p-value in a superiority comparison does not quantify equivalence between active treatments.

Why does over-dispersion matter in general?

For continuous outcomes, the standard deviation describes the spread of individual scores around the group mean. Greater spread relative to the difference in means generally makes the group contrast less precise. In other kinds of outcomes, over-dispersion refers to variability greater than a model assumes; ignoring it can make standard errors too small and confidence intervals too narrow. That is a general statistical issue, not a reported finding about this trial. The registry gives standard deviations for the continuous outcomes but does not report an over-dispersion assessment.

11. Confidence Intervals and Precision

The unadjusted primary mean-difference estimate is 0.132, with a 95% confidence interval from -0.290 to 0.554. The interval spans zero, so the posted summary-statistic calculation does not pin down the direction of the underlying average difference. Its endpoints also show that the estimate is not precise enough to narrow the plausible difference to a single value. This interval is specific to the unadjusted mean-difference calculation and its assumptions.

The sponsor-reported primary ratio of test to reference least-squares means is 104.085, with a 90% confidence interval from 87.421 to 124.210. This interval is on a relative scale and is not directly comparable to the recalculated interval on the score-change scale. The registry does not report the equivalence margin, so the interval cannot be judged against the range required for the sponsor's equivalence decision.

In general, a confidence interval represents uncertainty around an estimate under the analysis method. It does not guarantee that the true value falls within the interval, and it is not a range of individual participant outcomes. Precision depends on the data and analysis; the observed standard deviations indicate that individual scores varied around the group means. The registry reports standard deviations of 2.415 for the test group and 2.409 for the reference group in the primary analysis.

The size of the enrolled trial does not, on its own, determine whether an equivalence conclusion is adequately precise. That assessment depends in part on the target margin, analysis population, variability, and method. The original sample-size justification and the margin are not reported in the registry record. The confidence intervals therefore support a careful description of the estimates and uncertainty, but not an independent judgment that a prespecified equivalence standard was satisfied.

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 effect5,2427,018
75% of the observed effect9,31912,475
50% of the observed effect20,96728,069
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect5,00010,00020,00050,00040%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. Calculated for the comparison: Test.

The planning figures are illustrative calculations based on the observed effect, not the original design assumptions for the trial. The registry record does not report the trial's own sample-size justification. The listed planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. For continuous outcomes such as these score measures, the figures are participants per arm; for time-to-event outcomes, the convention is total events. These analyses concern continuous measures, so read the figures as participants per arm.

The 80% power column describes the number of participants per arm that a planning calculation estimates would be needed to have an 80% chance of detecting the selected effect, if the planning assumptions hold. The 90% power column describes the corresponding target for a 90% chance. These are design probabilities under specified assumptions, not guarantees about what a future trial will find. The planning estimates are not observed power.

The displayed scenarios use 100%, 75%, and 50% of the observed effect. Reducing the assumed effect means trying to detect a smaller difference; smaller effects generally require more participants to distinguish them from random variation under the same assumptions. For example, the primary endpoint planning illustration gives 5,242 participants per arm at 80% power for 100% of the observed effect, and 20,967 participants per arm for 50% of the observed effect. Those numbers are hypothetical planning outputs, not the number enrolled or a recommendation for a particular study.

Planning illustrations based on an observed effect should be treated cautiously. An observed estimate may be uncertain, and using it as the planning target does not demonstrate that the original study had a particular power. The values also do not incorporate design details that are absent from the registry record, such as the original equivalence margin or any adjustments beyond the stated planning 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 = 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 = 0.132; pooled standard deviation σ = 2.412.
  2. n = 2 × (1.96 + 0.842)2 × 2.4122 / 0.1322 = 5,241.7, rounded up to 5,242 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 <- 0.132                      # observed difference in means
sigma <- 2.41207386454064                     # 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(1279057)
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 = 5,242 (80% power), 7,018 (90% power)
 75% of observed effect: n per arm = 9,319 (80% power), 12,475 (90% power)
 50% of observed effect: n per arm = 20,967 (80% power), 28,069 (90% power)
power.t.test: 5242.6 
Simulated power at n = 5,242 per arm: 0.799 (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
not statedRatio Test/Ref. Least Squares (LS) Means 104.08587.421 to 124.210not reported

For the primary endpoint, the sponsor-reported analysis is a ratio of test to reference least-squares means of 104.085, with a 90% confidence interval from 87.421 to 124.210. The registry classifies this as an equivalence analysis. The method field is not reported, and the registry record does not give the equivalence margin or the detailed decision rule. Those missing details prevent an independent assessment of whether the reported interval met the intended criterion.

The recalculated result uses the posted per-protocol group means and standard deviations to estimate an unadjusted mean difference of 0.132, with a 95% confidence interval from -0.290 to 0.554 and an unadjusted p-value of 0.54. It is a simple comparison on the score-change scale, whereas the sponsor reports a least-squares mean ratio. The analyses therefore do not estimate the same quantity and their intervals should not be compared as if they were alternative versions of one result.

The registry lists no discrepancy between the sponsor's result and the recalculation. Even so, the sponsor's analysis is the relevant posted analysis for the stated equivalence question, while the recalculation offers a separate, unadjusted view of the group summaries. A nonsignificant unadjusted p-value does not establish equivalence. The record does not report enough detail to reconstruct the sponsor's model or independently reproduce its result.

15. Multiplicity, Missing Data and Analysis Populations

The registry record lists one primary outcome and multiple secondary outcomes, including several symptom measures and both equivalence and superiority questions. It reports 12 analyses overall. Conducting multiple analyses can increase the chance that at least one result appears statistically notable by chance. In general, multiplicity procedures can control this risk by adjusting significance thresholds or otherwise accounting for the analysis family. The registry record does not report whether any multiplicity adjustment was planned or used, how analyses were grouped into families, or whether the primary and secondary tests followed a hierarchy.

The reported ANCOVA p-values for active treatment versus placebo are both < 0.001, but the record does not state whether they are adjusted. The unadjusted recalculated p-values are not substitutes for the sponsor's statistical plan and do not resolve multiplicity. The equivalence analyses have a separate interpretive requirement: the registry record does not report their margins or decision rules. Thus, neither the presence of multiple comparisons nor the method for interpreting equivalence can be fully assessed from the registry information.

Population definitions also differ across outcomes. The primary endpoint and listed equivalence analyses use a per-protocol population, while the posted superiority analysis of instantaneous nasal symptoms uses an intent-to-treat population. The record does not describe how either population was defined in practice, how protocol deviations were handled, or whether participants were excluded from the per-protocol analyses. Those details matter because changing the analysis population can change the estimate and its uncertainty.

Missing-data methods are not reported in the registry record. It is not stated how missing symptom ratings were handled, whether the analysis required a minimum number of diary entries, or whether sensitivity analyses tested alternative assumptions. These are important considerations for repeated participant-reported measures. The registry record also does not report interim analyses, stopping rules, or the original sample-size justification. Their absence from the record should be read as information not reported, rather than as evidence that a particular procedure was or was not used.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Test02880.0%
Reference02920.0%
Placebo11470.7%
Participants with at least one serious adverse event
Serious adverse events by armTest0.0%Reference0.0%Placebo0.7%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Test0 of 288
Reference0 of 292
Placebo0 of 147

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 2% reporting threshold.

ArmParticipants affected of at risk
Test6 of 288
Reference4 of 292
Placebo4 of 147

Most frequent serious adverse event terms

Event termOrgan systemTestReferencePlacebo
Chest painRespiratory, thoracic and mediastinal disorders0 of 2880 of 2921 of 147

Most frequent non-serious adverse event terms

Event termOrgan systemTestReferencePlacebo
EpistaxisRespiratory, thoracic and mediastinal disorders6 of 2884 of 2924 of 147

Serious events with the highest arm-level rate: chest pain (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 no serious adverse events among 288 participants at risk in the test group and none among 292 participants at risk in the reference group. One serious adverse event was reported among 147 placebo participants at risk. The record identifies chest pain at 0.7% among the top serious terms. Deaths are reported as zero in each of the three groups.

The counts for other, non-serious adverse events are 6 among 288 participants in the test group, 4 among 292 in the reference group, and 4 among 147 in the placebo group. These are descriptive counts from the registry record. They do not establish that an event was caused by a treatment, and the record does not provide event-level detail, duration, severity beyond the serious/non-serious grouping, or a formal comparative safety analysis.

In general, safety counts should be interpreted in light of the number of participants observed, the length and completeness of follow-up, and how events were collected and classified. The registry describes treatment for 14 days but does not report all details needed to assess safety follow-up. The counts are therefore a limited description of reported events during the study, not a comprehensive comparison of longer-term risks.

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

The posted results describe average symptom-score changes over a 14-day treatment period in a study of seasonal allergic rhinitis. For the primary per-protocol outcome, the test and reference group means were 2.036 and 1.904, respectively. The unadjusted mean-difference estimate is 0.132, with a 95% confidence interval from -0.290 to 0.554. The sponsor reports a test-to-reference least-squares mean ratio of 104.085, with a 90% confidence interval from 87.421 to 124.210.

These results do not, on their own, establish that the formulations are equivalent. A formal equivalence conclusion depends on comparing an appropriate estimate and interval with a prespecified margin. That margin and the detailed decision rule are not reported in the registry record. Nor does a nonsignificant unadjusted p-value demonstrate that two treatments are the same. It indicates only that this recalculation did not provide strong evidence of a difference under its assumptions.

The results also do not determine how an individual participant will respond. Group means conceal variation among participants, and the registry does not report the distribution of individual changes or the proportion meeting a defined response threshold. The score is a measure of nasal symptoms, not a direct measure of every aspect of health or daily functioning. The reported data concern the stated outcomes and follow-up, not longer-term outcomes.

The secondary superiority analyses compare each active formulation with placebo for instantaneous nasal symptoms and report ANCOVA p-values of < 0.001. Those comparisons answer a different question from the primary comparison between the active formulations. They should not be used as evidence of equivalence between the test and reference products. The available record also leaves key statistical details unreported, including missing-data handling, multiplicity methods, and the equivalence margin.

In general, statistical evidence describes uncertainty about group-level outcomes under a particular design and analysis. It does not provide medical advice, guarantee outcomes for a particular person, or replace a complete evaluation of study conduct and clinical relevance. The registry supports a careful account of the numerical results and their limits, rather than a categorical conclusion beyond the information it records.

18. Why This Trial Matters Statistically

This trial is statistically interesting because its central question is equivalence, not simply whether one treatment differs from another. Equivalence requires a prespecified tolerance for differences that would be considered acceptably small. The registry labels the primary analysis as equivalence and reports a ratio with a 90% confidence interval, but does not report the margin or decision rule. This illustrates why a study label and a point estimate are not enough to evaluate an equivalence claim.

The record also makes clear that different statistical questions coexist within one trial. The primary comparison concerns the test spray versus the reference spray in a per-protocol population. The secondary superiority analyses compare each active formulation with placebo in an intent-to-treat population. A result from one comparison cannot be transferred to another: evidence about active treatment versus placebo does not establish equivalence between the active treatments.

Another useful distinction is between model-based sponsor results and simple recalculations from group summaries. The sponsor reports a ratio of least-squares means, while the recalculation gives an unadjusted mean difference. These estimates use different scales and may reflect different analysis methods. The recalculation is transparent and helpful for understanding the posted means, but it cannot reproduce a model whose specification is not reported.

Finally, the trial highlights how precision, analysis populations, and multiplicity affect interpretation. Confidence intervals describe uncertainty; a nonsignificant test does not prove equality. The per-protocol primary analysis and intent-to-treat secondary analyses use different populations, and the record does not detail missing-data or multiplicity procedures. Reading these features together is essential to distinguish what the registry reports from what remains uncertain.

19. Limitations

The registry record does not report the primary equivalence margin or the decision rule used to interpret it. Although a sponsor-reported ratio and 90% confidence interval are available, the equivalence conclusion cannot be independently checked against the intended criterion. The method for the primary sponsor analysis is also not identified, and the model specification for its least-squares means is not available.

The unadjusted recalculation is based on group-level means, standard deviations, and sample sizes. It does not use participant-level data, cannot account for model covariates or other adjustments, and is not a reconstruction of the sponsor's equivalence analysis. Its confidence interval and p-value should be treated as a complementary summary-statistic calculation, not a replacement for the reported analysis.

Some design and analysis details are not reported in the registry record. These include the original sample-size justification, the per-protocol criteria, the randomization procedure, the roles covered by quadruple masking, missing-data handling, multiplicity procedures, and interim analyses. Without the sample-size justification, the enrolled total cannot be linked to a stated target or equivalence margin. Without missing-data methods, it is difficult to assess the influence of incomplete symptom diaries.

The endpoint measures participant-reported nasal symptoms over a limited treatment period. The results do not provide individual response distributions or long-term outcome information. The registry lists six secondary outcomes, but the available detailed numerical results do not cover all six. Safety information is also descriptive and does not include a reported comparative analysis or extended follow-up. These limitations concern what can be established from the registry record, and do not imply that unreported procedures were not performed.

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23. Record Summary

The registry record describes a completed, randomized, quadruple-masked, parallel-group phase 3 study sponsored by Sandoz, with enrollment of 727. It compared a Lek Pharmaceuticals fluticasone furoate nasal spray, Veramyst, and placebo for seasonal allergic rhinitis. Active treatments were administered once daily at 110 mcg (4 actuations) for 14 days; placebo was given once daily for 14 days.

The primary outcome was mean change from baseline in reflective Total Nasal Symptom Score over 14 days, analyzed for equivalence between the active treatments in the per-protocol population. The sponsor reported a test-to-reference least-squares mean ratio of 104.085, with a 90% confidence interval from 87.421 to 124.210. The registry does not report the equivalence margin. An unadjusted recalculation gives a mean difference of 0.132, with a 95% confidence interval from -0.290 to 0.554 and an unadjusted p-value of 0.54.

The record also lists secondary nasal and ocular symptom outcomes and reports superiority p-values of < 0.001 for each active formulation versus placebo on instantaneous nasal symptoms. Missing-data and multiplicity methods, the original sample-size justification, and several details of the sponsor's statistical analysis are not reported in the registry record.

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