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Mild, Allergic Asthma Phase 1, Phase 2 Continuous Endpoint NCT02104505

Effect of Gamma Tocopherol Enriched Supplementation on Response to Inhaled LPS: Complete Statistical Analysis

This randomized crossover trial examined gamma tocopherol supplementation and responses to inhaled endotoxin in people with mild, allergic asthma. The primary outcome was change in sputum neutrophils; the registry also reports three secondary outcomes and sponsor analyses.

Trial start: 2015-11  ·  Enrollment: 23  ·  Sponsor: University of North Carolina, Chapel Hill
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 Effect of Gamma Tocopherol Enriched Supplementation on Response to Inhaled LPS (NCT02104505), a randomized phase 1, phase 2 study. The primary outcome is Comparison of Change in Sputum Percent Neutrophils (PMN)s Following Inhaled Clinical Center Reference Endotoxin (CCRE) Challenge as Affected by Gamma Tocopherol.

23
Enrollment
Phase 1, Phase 2
2
Arms
In the primary outcome
-8.40
Mean difference
Gamma Tocopherol
-21.80–5.00
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT02104505
PhasePhase 1, Phase 2
ConditionMild, Allergic Asthma
AllocationRandomized
Design modelCrossover
MaskingDouble
Enrollment23
Arms in the primary outcome2
Lead sponsorUniversity of North Carolina, Chapel Hill
Results postedYes

2. Clinical Question

Population

Participants with mild, allergic asthma. The primary analysis was restricted to participants who completed both treatment arms of the crossover study.

Intervention

Gamma tocopherol, described as 700 mg daily for 14 days.

Comparator

Placebo, described as safflower oil capsules.

Primary question

After an inhaled Clinical Center Reference Endotoxin challenge, how did change in sputum neutrophils compare following gamma tocopherol versus placebo treatment?

The trial was designed to test the hypothesis that gamma tocopherol supplementation inhibits endotoxin-induced airway inflammation in allergic asthma. In the registry description, the challenge was expected to increase sputum PMNs. The outcome compares the change from baseline to the post-treatment measurement following the challenge, rather than simply comparing a single post-treatment value.

This is a question about a short-term measured response under the study conditions. The registry record describes measurement after 14 days of treatment, with the post-treatment sputum measurement taken approximately 8 hours after the final dose. It does not establish how the results apply beyond the participants, treatment schedule, challenge, and outcome measurements described in the record.

3. Trial Design

The registry classifies the study as randomized, double-masked, and crossover, with Phase 1 and Phase 2 listed. It reports an enrollment of 23 and a completed status. The study was sponsored by the University of North Carolina, Chapel Hill. The recorded start is 2015-11 and primary completion is 2016-09.

In a crossover design, participants receive more than one treatment condition, so the comparison can use measurements from the same participants under different conditions. That general feature distinguishes this design from a simple parallel-group trial. The registry explicitly says that only participants who completed both arms were included in the primary analysis. The arm summaries each report 15 participants; the record does not explain the relationship between those counts and the overall enrollment of 23.

The intervention descriptions identify gamma tocopherol capsules and placebo, with the placebo described as safflower oil capsules. Gamma tocopherol is listed as 700 mg daily for 14 days. The primary outcome description places measurements at baseline and on day 14, with the latter approximately 8 hours after the final dose and following CCRE exposure.

Further operational details—including treatment sequence, any washout period, and how masking was implemented—are not reported in the registry record. The trial's original sample-size justification and design assumptions are also not reported in the registry record. The planning illustrations associated with the results are separate calculations and should not be read as evidence of what guided the original design.

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: There was no wash out or run-in phase prior to treatment assignment. No enrolled participants were excluded prior to treatment assignment.

First Intervention (14 Days)

StageGamma Tocopherol (14 Days) Then Placebo (14 Days)Placebo (14 Days) Then Gamma Tocopherol (14 Days)
STARTED1211
COMPLETED108
NOT COMPLETED23

Reasons for not completing this period:

ReasonGamma Tocopherol (14 Days) Then Placebo (14 Days)Placebo (14 Days) Then Gamma Tocopherol (14 Days)
Adverse Event20
Withdrawal by Subject01
Lost to Follow-up01
exclusionary condition01

Washout (Minimum 3 Weeks)

StageGamma Tocopherol (14 Days) Then Placebo (14 Days)Placebo (14 Days) Then Gamma Tocopherol (14 Days)
STARTED108
COMPLETED108
NOT COMPLETED00

Second Intervention (14 Days)

StageGamma Tocopherol (14 Days) Then Placebo (14 Days)Placebo (14 Days) Then Gamma Tocopherol (14 Days)
STARTED108
COMPLETED87
NOT COMPLETED21

Reasons for not completing this period:

ReasonGamma Tocopherol (14 Days) Then Placebo (14 Days)Placebo (14 Days) Then Gamma Tocopherol (14 Days)
Withdrawal by Subject01
Adverse Event20

Analysis population for the primary outcome, as defined in the registry: Since this study employed a crossover design, only participants who completed both arms of the study were included in the analysis.

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.

CharacteristicUnitGamma Tocopherol (14 Days) Then Placebo (14 Days)Placebo (14 Days) Then Gamma Tocopherol (14 Days)Total
Participants analysed121123
Age, Categorical: <=18 yearsParticipants000
Age, Categorical: Between 18 and 65 yearsParticipants121123
Age, Categorical: >=65 yearsParticipants000
Age, Continuousyears23.5 (20 to 42)30 (21 to 47)26 (20 to 47)
Sex: Female, Male: FemaleParticipants10919
Sex: Female, Male: MaleParticipants224
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants101
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants111122
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants000
Race (NIH/OMB): American Indian or Alaska NativeParticipants112
Race (NIH/OMB): AsianParticipants112
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants000
Race (NIH/OMB): Black or African AmericanParticipants224
Race (NIH/OMB): WhiteParticipants8715
Race (NIH/OMB): More than one raceParticipants000
Race (NIH/OMB): Unknown or Not ReportedParticipants000
Region of Enrollment: United StatesParticipants121123
AtopyParticipants9817
Body Mass Index (BMI)kg/m227.1 (20.5 to 34.8)25.2 (20.2 to 41.7)26 (20.2 to 41.7)
Forced expiratory volume in 1 second (FEV1) (%predicted)percent predicted102.5 (89 to 109)90 (83 to 108)97 (83 to 109)

6. Primary Endpoint

The registry lists the primary outcome as Comparison of Change in Sputum Percent Neutrophils (PMN)s Following Inhaled Clinical Center Reference Endotoxin (CCRE) Challenge as Affected by Gamma Tocopherol, measured over after 14 days of gamma tocopherol or placebo treatment.

ElementRegistry entry
Result typeMean
Measure of spreadStandard Deviation
Unitchange in percentage of PMNs in sputum
Endpoint classificationContinuous Endpoint

The primary endpoint is the change in the percentage of sputum PMNs from baseline to the post-treatment measurement following an inhaled CCRE challenge. PMNs are neutrophils, a type of white blood cell. The registry describes measuring sputum at baseline immediately before dosing and again on day 14, approximately 8 hours after the final dose. The comparison is between the change after gamma tocopherol and the change after placebo.

The endpoint is used to assess an airway inflammatory response in the setting of the endotoxin challenge. The registry states that exposure to CCRE was expected to increase sputum PMNs in asthmatic individuals, and the study hypothesis concerned whether gamma tocopherol inhibits endotoxin-induced airway inflammation. In that context, a change score represents movement from each treatment period's baseline rather than a post-treatment level alone.

This is a continuous outcome, summarized in the registry as a mean with a standard deviation. The posted arm summaries report mean changes of 11.7 for gamma tocopherol and 20.1 for placebo. A simple unadjusted comparison of those summaries estimates a mean difference of -8.4, with a confidence interval from -21.8 to approximately 5.0. Because the confidence interval includes zero, the recalculation does not precisely distinguish the treatment conditions at the conventional two-sided 0.05 level. The sponsor's mixed-model analysis is reported separately and takes precedence over this simple recalculation.

7. Results Posted in the Registry

Mean difference: Gamma Tocopherol

-8.40

95% CI: -21.80 to 5.00

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-1.55.011.618.124.631.2Gamma Tocopherol (n=15)Placebo (n=15)change in percentage of PMNs in sputum (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Gamma Tocopherol-24-18-12-5.290.927.14mean 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
Chronic Eosinophilic Airway Inflammation as Affected by Gamma TocopherolContinuous EndpointMean difference-6.90 (-14.46 to 0.66)37 per arm
Mucociliary Clearance (MCC) Associated With CCRE Challenge as Affected by Gamma TocopherolContinuous EndpointMean difference3.90 (-2.31 to 10.11)78 per arm
Mucociliary Clearance as Affected by Gamma TocopherolContinuous EndpointMean difference0.00 (-6.02 to 6.02)n/a

Chronic Eosinophilic Airway Inflammation as Affected by Gamma Tocopherol

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Gamma Tocopherol-16-12-8.65-5.15-1.641.87mean difference vs control (95% CI)

Mucociliary Clearance (MCC) Associated With CCRE Challenge as Affected by Gamma Tocopherol

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Gamma Tocopherol-3.30-0.422.465.348.2211mean difference vs control (95% CI)

Mucociliary Clearance as Affected by Gamma Tocopherol

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Gamma Tocopherol-6.99-4.19-1.401.404.196.99mean difference vs control (95% CI)

The secondary outcomes cover chronic eosinophilic airway inflammation and mucociliary clearance, including clearance associated with CCRE challenge. Across these measures, the sponsor's reported p-values are mixed rather than uniformly pointing to the same pattern. The secondary findings therefore do not form a consistent statistical signal across all measured outcomes.

Taken together, the secondary outcomes offer additional perspectives on airway inflammation and clearance, but they do not resolve the uncertainty in the primary summary-statistic contrast. Nor should they be interpreted as independent confirmation of the primary result: the outcomes were measured within the same study and may be related. The record does not report whether or how these endpoints were prioritized or adjusted for multiple testing.

Unadjusted secondary results carry less weight because evaluating several outcomes creates more opportunities for apparently noteworthy results to arise by chance. This is a general statistical concern, not a claim that any particular result is false. Without a stated multiplicity plan or a complete analysis description, the reported secondary p-values should be treated as exploratory context rather than as a set of definitive tests.

The registry posts three secondary outcomes, but details about the original hierarchy, prespecified hypotheses, and any corrections for multiplicity are not reported in the registry record. Sponsor analyses and simple recalculations are also not always aligned. Those features call for cautious synthesis across endpoints instead of selecting one result in isolation.

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

9. Statistical Interpretation

Clinical Biostats interpretation

The registry's primary arm summaries report mean changes in sputum PMNs of 11.7 after gamma tocopherol and 20.1 after placebo, with standard deviations of 20.7 and 16.5. The simple unadjusted recalculation gives a mean difference of -8.4, defined as gamma tocopherol minus placebo, and an unadjusted p-value of 0.219. Its confidence interval extends from -21.8 to approximately 5.0 and includes zero. These results indicate substantial uncertainty in the recalculated contrast: the data are compatible with differences in either direction as well as little difference.

The record also reports a sponsor mixed-model analysis for the primary outcome: a net mean difference of 0.41 and p = 0.04. This result does not numerically align with the simple comparison of the posted arm means. The record does not give enough detail about the model's estimand, coding, or other specifications to reconcile the difference. Because the record contains a discrepancy, the sponsor's own analysis takes precedence; the unadjusted recalculation is a descriptive check, not a replacement for that analysis. The sponsor result should be read using its own reported model and outcome definition, and not treated as interchangeable with the recalculated mean difference.

There are three posted secondary outcomes. Across their sponsor analyses, reported p-values are 0.01, 0.6, and 0.34. Their simple unadjusted recalculations do not all reproduce the sponsor estimates or p-values. This makes the distinctions between model-based and summary-statistic comparisons important. The secondary outcomes add context about eosinophilic airway inflammation and mucociliary clearance, but should not be treated as independent confirmation of the primary finding without a stated multiplicity plan.

The overall interpretation is constrained by the small analyzed arm summaries and the uncertainty around the simple primary contrast. The registry's participant restriction to those completing both arms also means the posted primary population is not necessarily everyone enrolled. How missing measurements, treatment sequence, and period effects were handled is not reported in the registry record. These omissions limit independent assessment of the crossover analysis. Neither the sponsor p-value nor the simple recalculation alone describes the size, precision, and design context of the result in full.

10. Statistical Methods Explained

What does a mean difference describe?

The primary measure is continuous, and the arm summaries are means with standard deviations. A mean describes the average observed change in each treatment condition. The simple mean difference subtracts the placebo mean from the gamma tocopherol mean. With this direction, a negative estimate indicates a lower mean change in the gamma tocopherol summaries than in the placebo summaries. The recalculated estimate is -8.4. This is an unadjusted comparison derived from the posted summaries, not the result of the sponsor's mixed model.

Standard deviation describes how dispersed individual measurements are around their group mean. It is not the same as the standard error, which describes uncertainty in an estimated mean. Greater variability relative to the observed contrast generally makes an estimate less precise. Here the posted standard deviations are large in relation to the estimated mean difference, and the confidence interval is broad enough to include zero.

What does the p-value tell the reader?

The simple recalculation reports an unadjusted p-value of 0.219 for the primary comparison. In general, a p-value measures how incompatible the observed data are with a specified null model, assuming the model's assumptions hold. It is not the probability that the null hypothesis is true, and it does not measure the size or importance of an effect. An unadjusted p-value also does not account for testing multiple outcomes unless an adjustment is explicitly made. The registry's adjustment approach is not reported.

The sponsor reports a mixed-model p-value of 0.04 for the primary analysis. A mixed model is a general approach that can account for structured or repeated observations, depending on how the model is specified. The registry names the method but does not report sufficient model details to establish exactly which repeated-measure, sequence, period, or other terms were included. The p-value therefore should be understood as the value reported for the sponsor's analysis, not as a p-value reconstructed from the two posted arm means.

Why does a crossover design matter?

Generally, crossover studies measure participants under more than one condition. Analyses can account for within-participant relationships, which may improve precision compared with treating all observations as unrelated. That benefit depends on appropriate design and analysis. Treatment sequence, period effects, carryover, and the handling of incomplete crossover data can matter. Specific handling of these issues is not reported in the registry record, so the mixed-model label alone does not reveal how they were addressed.

The registry says that only participants completing both arms were included in the primary analysis. This defines the stated analysis population but does not tell readers how many enrolled participants lacked complete data, why any data were missing, or whether any additional analyses used a different population. Those details are not reported in the registry record.

What is the role of recalculation?

A recalculation from summary statistics is a simple, unadjusted way to check the direction and approximate precision of a comparison. It uses the posted arm means and variability, rather than the participant-level data or a fitted crossover model. It cannot reproduce adjustments, covariance structures, or other model features that may be part of the sponsor analysis. When the recalculation and sponsor result differ, as they do for the primary outcome, the sponsor's own analysis takes precedence. The difference should be described transparently rather than resolved by assuming an unreported model specification.

Confidence intervals complement p-values by giving a range of estimates compatible with the data and the method used. General interpretation depends on the model and interval construction. The recalculated primary interval includes zero, which means it does not exclude no difference under that calculation. It does not establish that the true contrast is zero. The sponsor analysis has no confidence limits reported in the registry record, so its precision cannot be assessed from a sponsor interval.

Why distinguish statistical from clinical interpretation?

Statistical summaries describe estimated differences and uncertainty under particular methods. They do not by themselves establish clinical importance. The registry does not report a threshold for a meaningful change in sputum PMNs, nor does it report a clinical interpretation tied to such a threshold. Statistical significance, even when reported by a model, is not equivalent to evidence about the practical importance or broader effects of a treatment. The trial's measured challenge response and short treatment period also define the scope of what these outcomes address.

11. Confidence Intervals and Precision

The recalculated primary mean difference is -8.4, with a confidence interval from -21.8 to approximately 5.0. A confidence interval is a range of values compatible with the data and the assumptions of the calculation. In general, a narrower interval indicates greater precision, while a wider interval leaves more uncertainty about the size and direction of the contrast.

This interval includes zero. It therefore does not rule out no difference under the simple unadjusted calculation. It also covers values on either side of zero, so the direction of the primary contrast is not sharply determined by these summaries. The upper endpoint is approximately 5.0 because the registry's recalculated endpoint is reported with more than three decimal places, which is not reproduced at greater precision.

The sponsor's primary mixed-model result is reported as a net mean difference of 0.41 and p = 0.04, but its confidence limits are not reported in the registry record. Without an interval, readers cannot assess the sponsor estimate's precision from the registry entry. In addition, the sponsor estimate and p-value differ from the simple unadjusted recalculation, and the model details needed to explain that discrepancy are not reported.

Standard deviations in the primary arm summaries are 20.7 and 16.5. In general, substantial variability relative to the estimated difference can leave a comparison imprecise, especially when the analyzed sample is limited. The reported arm counts are 15 in each treatment condition, and the registry says the primary analysis included participants completing both arms. The confidence interval summarizes uncertainty under the recalculation; it does not capture every limitation arising from unreported design or analysis details.

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 effect78105
75% of the observed effect139186
50% of the observed effect312418
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect501002005001,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
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: Gamma Tocopherol.

The sample-size figures are planning illustrations, not counts of participants observed in the trial. For the continuous outcomes, the figures are participants per arm, not a total number of events. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each row uses a stated fraction of the observed effect as the effect to detect.

The 80% power column gives the illustrative number of participants per arm for a design with an 80% chance of detecting the assumed effect under those planning assumptions, if that effect and the assumptions are correct. The 90% power column describes the corresponding design target with a 90% chance. These are prospective planning quantities: they describe what a hypothetical study might require under the stated assumptions, not the probability that the completed trial found an effect.

The rows consider planning for 100%, 75%, and 50% of the observed effect. Smaller assumed effects require more participants to detect under the same assumptions. This reflects the general relationship between effect size and precision: when a difference is smaller relative to variability, more observations are generally needed to distinguish it from random variation.

The calculations use the observed effect as their starting point, so they should not be treated as a fresh, independent estimate of a realistic target effect. The trial's original sample-size justification and design assumptions are not reported in the registry record. These planning figures are not observed power.

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 = -8.400; pooled standard deviation σ = 18.718.
  2. n = 2 × (1.96 + 0.842)2 × 18.7182 / -8.4002 = 77.9, rounded up to 78 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 <- -8.4                      # observed difference in means
sigma <- 18.7181729877678                     # 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(2104505)
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 = 78 (80% power), 105 (90% power)
 75% of observed effect: n per arm = 139 (80% power), 186 (90% power)
 50% of observed effect: n per arm = 312 (80% power), 418 (90% power)
power.t.test: 78.9 
Simulated power at n = 78 per arm: 0.793 (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
Mixed Models AnalysisMean Difference (Net) 0.41not reported0.040
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 sponsor analysis is reported as a mixed-model net mean difference of 0.41 with p = 0.04. A simple unadjusted recalculation from the posted primary arm summaries gives a mean difference of -8.4 and p = 0.219, with a confidence interval that includes zero. These are not numerically concordant summaries of the comparison.

The registry identifies the sponsor method as Mixed Models Analysis but does not report the model specification or enough information about its estimand to determine why its estimate differs from the summary-statistic recalculation. In particular, the model's treatment coding and handling of crossover structure are not described in the available record. No explanation for the discrepancy should be inferred.

When the sponsor analysis and a simple recalculation disagree, the sponsor's own analysis takes precedence. The recalculation remains useful as a transparent comparison based on the posted means and standard deviations, but it is not a substitute for the sponsor's model-based analysis. The sponsor's confidence interval is not reported in the registry record, which limits assessment of precision for that analysis.

The same broad distinction applies to secondary outcomes: sponsor model results are posted alongside summary values, and the simple unadjusted comparisons do not uniformly match them. Readers should keep each method's result separate rather than combining them as if they were one estimate.

15. Multiplicity, Missing Data and Analysis Populations

The record lists one primary outcome and three secondary outcomes, and it reports analyses for these measures. It does not report a multiplicity adjustment or describe a testing hierarchy that would establish how the several statistical tests were intended to be interpreted together. Without that information, the posted p-values should not be treated as though they have automatically controlled the chance of a false-positive finding across all outcomes. This is a general issue when multiple endpoints are tested.

The primary analysis population is described as participants who completed both crossover arms. This makes completion of both conditions part of the stated analysis population. However, the registry record does not report how many participants had incomplete data for each outcome, the reasons for any missingness, or whether missing values were imputed. It also does not describe sensitivity analyses for missing data.

The overall enrollment is 23, while the primary arm summaries each report 15 participants. The registry does not explain how these counts relate to the full enrolled sample or provide a participant flow accounting for exclusions and incomplete follow-up. The record also does not state whether the same analysis population was used for every secondary endpoint.

For a crossover analysis, treatment sequence and period can be relevant, as can possible carryover between conditions. The registry describes a mixed-model analysis but does not report enough details to determine whether or how these features were addressed. The protocol's original analysis plan, interim analyses, and sample-size justification are not reported in the registry record. These absences limit independent evaluation of the statistical approach; they do not by themselves show that an issue occurred.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Gamma Tocopherol0170.0%
Placebo0200.0%

Deaths

ArmDeaths (participants affected of at risk)
Gamma Tocopherol0 of 17
Placebo0 of 20

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

ArmParticipants affected of at risk
Gamma Tocopherol11 of 17
Placebo14 of 20

Most frequent non-serious adverse event terms

Event termOrgan systemGamma TocopherolPlacebo
Cough during CCRE challengeRespiratory, thoracic and mediastinal disorders7 of 176 of 20
NauseaGastrointestinal disorders6 of 170 of 20
DiarrheaGastrointestinal disorders4 of 171 of 20
HeadacheNervous system disorders2 of 171 of 20
Abdominal bloatingGastrointestinal disorders2 of 170 of 20
Loose stoolsGastrointestinal disorders1 of 171 of 20
Chest tightnessRespiratory, thoracic and mediastinal disorders1 of 171 of 20
Diminished sense of tasteGastrointestinal disorders0 of 171 of 20
Skin rednessSkin and subcutaneous tissue disorders0 of 171 of 20
Vagal responseCardiac disorders1 of 170 of 20
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 serious adverse event entries report zero serious adverse events in both treatment groups: 0 among 17 at risk for gamma tocopherol and 0 among 20 at risk for placebo. The registry also reports zero deaths in both groups. No serious adverse-event terms are listed.

For other adverse events, the record reports 11 affected participants among 17 at risk in the gamma tocopherol group and 14 among 20 at risk in the placebo group. These are reported counts. The registry figures alone do not establish whether an event was caused by the assigned treatment, and they should not be interpreted as a comparison adjusted for the crossover design.

The at-risk counts differ between the safety groups and the primary outcome summaries. The record does not explain the relationship among these populations or provide details about event definitions, severity categories beyond the serious-event grouping, or event-level timing. Zero reported serious events is a description of the registry entries, not proof that a treatment is free of risk.

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

The results describe short-term measurements after gamma tocopherol or placebo treatment in a randomized, double-masked crossover study of people with mild, allergic asthma. The primary outcome concerns sputum neutrophil change following an inhaled endotoxin challenge. It is a focused experimental response, not a general measure of every aspect of asthma or airway health.

The posted arm summaries and simple recalculation show a negative mean difference, but the confidence interval includes zero and is broad. The sponsor's mixed-model analysis reports a different estimate and p-value, and its model details and confidence limits are not reported. The sponsor analysis takes precedence over the simple recalculation, while the discrepancy limits the extent to which the results can be independently reconciled from the registry record.

These results do not by themselves establish the practical importance of any difference. The registry does not report a threshold for a meaningful change in sputum PMNs. It also does not show whether the measured response persists beyond the reported treatment period or applies to people outside the study population and challenge conditions.

Likewise, secondary outcome results are not a standalone confirmation of the primary outcome. Several outcomes were assessed, and the record does not state how multiplicity was handled. The safest reading is descriptive: the registry reports sponsor model findings and arm summaries, with uncertainty and analysis details that matter for interpretation.

No medical decision should be based on these statistical summaries alone. They do not constitute individual treatment guidance, and they do not settle broader questions about benefits or harms. Their meaning is bounded by the enrolled study, its completed-both-arms analysis population, the recorded measurements, and the information available in the registry record.

18. Why This Trial Matters Statistically

This trial is statistically instructive because it combines a crossover design with a primary outcome that is a change from baseline. Such a design can use within-participant comparisons, but its interpretation depends on how repeated observations and crossover features are modeled. The registry identifies a mixed-model analysis, yet does not report the details needed to assess that model fully.

It also illustrates why arm summaries, recalculated contrasts, and sponsor analyses should not be collapsed into one result. The primary simple recalculation differs from the sponsor's reported analysis. A transparent account preserves both, explains their different basis, and gives precedence to the sponsor analysis when the record flags a discrepancy rather than inventing an explanation.

Precision matters as much as a point estimate or p-value. The simple primary confidence interval includes zero and spans estimates in both directions, while the sponsor's confidence limits are absent. That combination makes clear why statistical significance alone is not an adequate summary of evidence.

Finally, multiple outcome measures, a completers-only primary population, and unreported details about missing data and multiplicity affect how broadly results can be read. These are not reasons to assume that the analyses are invalid; they are boundaries on independent evaluation. The record provides a useful example of how design, analysis reporting, and uncertainty jointly shape statistical interpretation.

19. Limitations

Important design details for interpreting a crossover comparison are not reported in the registry record. These include treatment sequence and any washout period, as well as the model specification and whether period or carryover considerations were incorporated. The mixed-model label alone does not answer those questions.

The primary analysis includes only participants who completed both arms. The record does not provide a participant flow explanation for the difference between enrollment and arm summary counts, nor does it report reasons for non-completion or outcome-specific missingness. It is therefore not possible to assess from the record whether completion was related to treatment or outcome measurements.

The sponsor's primary model result differs from the simple recalculation of the arm summaries. The registry does not report enough detail to reconcile these analyses, and sponsor confidence limits are absent. The sponsor analysis takes precedence, but the discrepancy remains a limit on independent interpretation. Similar differences appear in secondary sponsor and recalculated results.

There are three secondary outcomes in addition to the primary endpoint. A multiplicity strategy and endpoint hierarchy are not reported. This limits interpretation of secondary p-values as confirmatory evidence. The original sample-size justification and interim-analysis plan are also not reported in the registry record.

Finally, the measured outcomes concern short-term responses after a specified challenge and treatment schedule. The record does not report a clinical threshold for meaningful change in the primary endpoint. These limitations constrain conclusions to the measurements and analyses recorded; they do not establish that unreported procedures were or were not used.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

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23. Record Summary

NCT02104505 is a completed randomized, double-masked crossover study listed as Phase 1 and Phase 2, with enrollment of 23. It examined gamma tocopherol supplementation versus safflower oil placebo in participants with mild, allergic asthma.

The primary endpoint was change in sputum PMNs after CCRE challenge following 14 days of treatment. The primary summaries report 15 participants per treatment condition. The sponsor reports a mixed-model net mean difference of 0.41 with p = 0.04; the simple unadjusted recalculation differs and has a confidence interval that includes zero. Because of this discrepancy, the sponsor's own analysis takes precedence.

Three secondary outcomes and safety counts are also reported. Details about multiplicity, missing-data handling, crossover model specifications, and the trial's original sample-size justification are not reported in the registry record.

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