Response of FeNO, Small Airway Dysfunction and Lung Heterogeneity to 2-week Montelukast Treatment in Asthmatic Children.: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Response of FeNO, Small Airway Dysfunction and Lung Heterogeneity to 2-week Montelukast Treatment in Asthmatic Children. (NCT01581710), a randomized na study. The primary outcome is Baseline Lung Function of Rrs 5 With IOS Before the Bronchodilator (Pre-Rrs5).

2. Clinical Question

The clinical question concerns a short-term physiological measure, rather than a clinical event or a longer-term outcome. Resistance at 5 Hz is the primary measure named in the registry, and the study description also refers to airway inflammation, small-airway dysfunction, and lung heterogeneity. The posted primary result, however, is specifically pre-bronchodilator Rrs 5.

The registry lists two treatment sequences: montelukast followed by placebo, and placebo followed by montelukast. In a crossover design, participants receive both treatments in sequence, so the intended comparison can use measurements from the same people under each condition. The registry record does not report enough detail to establish how the posted comparison handled that within-participant structure.

The result therefore addresses the recorded lung-function measure over the reported treatment periods. It does not by itself answer broader questions about symptom relief, long-term asthma control, or outcomes beyond those recorded. Those outcomes are not reported in the registry record as the primary question.

3. Trial Design

This was a randomized, quadruple-masked, crossover study listed as completed. The registry identifies the population as children with mild persistent asthma and records enrollment of 32. The phase is listed as NA. CHA University is the named sponsor.

The two treatment sequences were montelukast followed by placebo and placebo followed by montelukast. Each treatment period is described as 14 days, with a 14-day washout listed between periods. The design allows each participant to receive both treatments, which can support a within-participant comparison when analysis accounts for repeated measurements and treatment sequence.

Randomization in a crossover study generally determines which treatment sequence a participant receives. Masking is listed as quadruple, but the registry record does not specify which groups were masked or how masking was maintained. Details such as sequence allocation, adherence, carryover assessment, and the analysis of period effects are not reported in the registry record.

The recorded study dates are 2012-05 for start and 2015-09 for primary completion. The primary outcome timeframe is listed as up to 2 weeks. The primary measurement is pre-bronchodilator resistance at 5 Hz, and a secondary outcome is relative change in FEV1 after bronchodilator. The registry lists 8 outcome measures, but only 1 secondary outcome appears in the posted secondary results. A complete account of the remaining outcomes and their results is not reported in the registry record.

Although the crossover structure is central to interpreting the comparison, the posted summary does not provide a participant-level analysis or a model description. It is therefore not possible to confirm from the record whether the displayed estimates account for the paired measurements, treatment sequence, or period. The registry also does not report its original sample-size assumptions or a detailed statistical analysis plan.

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.

First Intervention (14days)

Washout Period (14days)

Second Intervention (14days)

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: Measure Analysis Population Description: two participants did not complete the second set test due to symptom aggravation

6. Primary Endpoint

The registry lists the primary outcome as Baseline Lung Function of Rrs 5 With IOS Before the Bronchodilator (Pre-Rrs5), measured over up to 2 weeks.

The primary endpoint is pre-bronchodilator Rrs 5: resistance at 5 Hz measured with impulse oscillometry before administration of a bronchodilator. It is reported as a mean with standard deviation in kPa/L/s, with a timeframe of up to 2 weeks. The registry describes this measure as baseline lung function.

In general, respiratory resistance describes opposition to airflow in the respiratory system. The 5 Hz measurement is used as a physiological indicator of airway mechanics, and impulse oscillometry obtains respiratory measurements during breathing rather than relying on a forced expiratory maneuver. The particular rationale for selecting Rrs 5 as the primary endpoint is not reported in the registry record.

Measuring before bronchodilator administration distinguishes the recorded value from a post-bronchodilator response. This makes the endpoint a measure of lung function under the specified pre-bronchodilator condition, not a direct measure of how much lung function changes after bronchodilator. The registry lists relative change in FEV1 after bronchodilator as a secondary outcome, which addresses a different aspect of respiratory response.

The posted means are 0.73 kPa/L/s at baseline, 0.74 kPa/L/s after placebo, and 0.73 kPa/L/s after montelukast. The standard deviations are 0.15, 0.2, and 0.15, respectively. These summaries describe the observed values; they do not establish the reason for any individual participant's measurement or the clinical importance of a difference. A threshold for a clinically important change is not reported in the registry record.

7. Results Posted in the Registry

• Baseline Lung Function: mean 0.73 versus 0.74 on control; difference -0.01 (95% CI -0.10 to 0.08), standardized effect d = -0.06; z-test p = 0.825.
• 2 Weeks After Montelukast Administration: mean 0.73 versus 0.74 on control; difference -0.01 (95% CI -0.10 to 0.08), standardized effect d = -0.06; z-test p = 0.825.

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.

Relative Change (%) of FEV1 After the Bronchodilator

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • 2 Weeks After Montelukast Administration: mean 5.65 versus 9.68 on control; difference -4.03 (95% CI -9.99 to 1.93), standardized effect d = -0.34; z-test p = 0.185.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 2 Weeks After Montelukast Administration and the control. The interval gives the range of effects that remain compatible with the data.

The posted secondary results concern relative change in FEV1 after bronchodilator. The registry reports group summaries and an unadjusted comparison, but does not report a broader set of secondary analyses. The overall record lists 8 outcome measures and 1 posted secondary outcome, so the visible secondary evidence represents only part of the outcome set recorded for the study.

The secondary result does not provide a clear statistical contrast in the posted comparison: its unadjusted confidence interval spans zero and its unadjusted p-value is 0.185. This pattern is consistent with uncertainty about the direction and size of the difference. It should not be treated as confirmation of the primary result, nor as a contradiction of it, because the endpoints measure different aspects of lung function and are subject to their own variability.

In general, a secondary endpoint can add context by examining a different physiological response, but its interpretation depends on whether it was prespecified, how many other outcomes were tested, and whether the analysis accounted for multiple comparisons. Those details are not reported in the registry record. The unadjusted results consequently carry less weight as confirmatory evidence than a clearly prespecified primary comparison with a documented analysis plan.

The record does not provide a complete account of the other outcome measures, their results, or any multiplicity adjustment. That limits how confidently the set of findings can be viewed as a coherent pattern rather than as selected outcomes from a wider set of measurements. The secondary evidence is best read as exploratory context, not as an independent basis for a definitive conclusion.

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

• Relative Change (%) of FEV1 After the Bronchodilator

9. Statistical Interpretation

10. Statistical Methods Explained

The primary outcome is continuous and is summarized by a mean and standard deviation. In general, a mean describes the central value of a set of measurements, while a standard deviation describes their spread around that mean. Neither statistic, by itself, accounts for the crossover structure or describes uncertainty in the mean difference.

What does the mean difference represent?

The posted primary comparison gives a mean difference of -0.01 for the comparison of montelukast with placebo. The negative sign indicates that the value in the montelukast condition is lower according to the subtraction direction used for the comparison. The registry's displayed means are 0.73 after montelukast and 0.74 after placebo. The comparison is accompanied by an unadjusted p-value of 0.825 and a confidence interval that includes zero.

A mean difference is expressed in the outcome's original unit, so it retains a direct link to the measured quantity, kPa/L/s. This can be useful for clinical interpretation, but deciding whether a difference is important requires context, such as a clinically meaningful threshold. Such a threshold is not reported in the registry record.

What does the p-value say?

In general, a p-value describes how compatible the observed data are with a specified null model, under the assumptions of the calculation. It is not the probability that the null hypothesis is true, and it is not the probability that a result occurred by chance. The unadjusted p-value of 0.825 does not indicate a clear separation in the posted primary comparison. It does not demonstrate equivalence or prove the absence of an effect.

The p-value is labelled unadjusted. The registry record does not report a multiplicity procedure, so the value should not be read as accounting for testing across multiple outcomes or comparisons. The record also lists 8 outcome measures, while only 1 secondary outcome is posted. The full set of planned tests and their relationship to the reported result are not reported in the registry record.

Why does the crossover structure matter?

In general, crossover data contain repeated observations from the same participant under different treatment conditions. Measurements from one person may be more alike than measurements from different people. A paired analysis can use that within-person relationship and may differ in precision from an analysis that treats observations as independent.

The registry names a crossover design and two treatment sequences, but the comparison summaries list group sample sizes and pooled spread rather than a paired effect estimate. The registry record does not describe the analysis model, the within-participant correlation, or how period and sequence were handled. The comparison should therefore be understood as a simple unadjusted recalculation from posted summary statistics, not a confirmed analysis of the full crossover structure.

In general, crossover analyses may need to consider whether treatment effects differ by period and whether effects from an earlier treatment carry into a later period. The registry lists a washout period, but it does not report an assessment of carryover or a statistical method for period effects. No assumption about the adequacy of the washout or the absence of carryover can be established from the record alone.

How should the summaries be distinguished from an analysis?

The registry posts outcome means and standard deviations, as well as derived comparison summaries. It records zero reported analyses. This means a reader should distinguish the posted descriptive values and the unadjusted recalculation from a detailed, prespecified sponsor analysis. The registry record does not provide an analysis population, a model specification, or a detailed account of covariate adjustment.

In general, an analysis plan specifies how outcomes, missing measurements, repeated observations, and multiple comparisons will be handled. These choices can affect both estimates and uncertainty. The original statistical plan and sample-size justification are not reported in the registry record. Consequently, the posted summaries support a limited description of the recorded measurements, but do not resolve every design or analysis question relevant to a crossover trial.

11. Confidence Intervals and Precision

The primary estimate is a mean difference of -0.01, with a 95% confidence interval extending from a negative value to a positive value and therefore spanning zero. This indicates that the posted data do not locate the difference precisely enough to rule out values on either side of no difference under the calculation used. The unadjusted p-value is 0.825.

In general, a confidence interval is a range of values compatible with the data and the statistical method used, at the stated confidence level. It describes uncertainty about the estimated difference, not the range of individual participants' measurements. A wider interval indicates less precision than a narrower interval, but interpretation also depends on the scale and on what differences would matter clinically. The registry record does not report a clinically important threshold for Rrs 5.

The primary outcome standard deviations are 0.15 at baseline, 0.2 after placebo, and 0.15 after montelukast. These describe participant-level variability, not the uncertainty in the estimated treatment contrast. In a crossover study, the precision of a paired comparison also depends on how measurements within each participant relate to one another. That relationship is not reported in the registry record.

The comparison's precision should be considered alongside the missing analysis details. The record does not state whether the confidence interval accounts for paired measurements, treatment period, sequence, or missing observations. Thus, the interval communicates uncertainty for the displayed calculation, but the record does not establish how fully it reflects the crossover design.

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.

The planning values are expressed as participants per arm, not as total events. They are illustrations based on the observed effect, not the original trial's documented design assumptions; those original assumptions are not reported in the registry record. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The detectable effect is set to the stated fraction of the observed effect.

The 80% power column gives the number of participants per arm under those assumptions for a design intended to have an 80% chance of detecting the specified effect if that effect were the true one. The 90% power column gives the corresponding per-arm number for a 90% chance. These are design calculations, not estimates of what the completed trial achieved. They are not observed power.

Planning for 100% of the observed primary effect gives 4,860 participants per arm for 80% power and 6,506 participants per arm for 90% power. Planning for 75% of the observed effect gives 8,640 and 11,566 participants per arm, respectively. Planning for 50% of the observed effect gives 19,440 and 26,024 participants per arm, respectively. The secondary outcome's planning values are distinct and are based on its own observed effect.

Smaller effects require more participants to detect under the same assumptions, because a smaller separation is harder to distinguish from random variation. These calculations use an equal-allocation, two-arm normal approximation, whereas the trial itself is a crossover study. The planning illustration should not be taken as a reconstruction of the trial's original design or as a crossover-specific sample-size calculation.

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 z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

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

Worked calculation for this trial

1. Observed difference Δ = -0.010; pooled standard deviation σ = 0.176.
2. n = 2 × (1.96 + 0.842)² × 0.176² / -0.010² = 4,859.8, rounded up to 4,860 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 <- 0.175949803447839                     # 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(1581710)
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 = 4,860 (80% power), 6,506 (90% power)
 75% of observed effect: n per arm = 8,640 (80% power), 11,566 (90% power)
 50% of observed effect: n per arm = 19,440 (80% power), 26,024 (90% power)
power.t.test: 4860.7 
Simulated power at n = 4,860 per arm: 0.801 (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. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when a study evaluates multiple outcomes, time points, treatment contrasts, or statistical tests. In general, the more tests conducted, the greater the chance that at least one will appear notable by chance if no effects are present. A prespecified strategy can control or otherwise address this issue, but the registry record does not report a multiplicity plan or adjustment.

The registry lists 8 outcome measures and posts 1 secondary outcome. It records zero reported analyses, and the secondary results list no reported analyses. The record therefore does not establish which outcomes were prespecified for formal testing, how many comparisons were conducted, or whether results were selected for posting. The unadjusted p-values should be interpreted with that uncertainty in mind.

Missing-data handling is also not reported in the registry record. The primary summaries include 30 participants after placebo and 32 after montelukast, compared with enrollment of 32 and a baseline summary for 32. The record does not explain the difference in available observations, whether missingness occurred, or how any missing measurements were handled. It does not report whether participants were excluded from analyses or how incomplete crossover sequences were treated.

The analysis population is not reported in the registry record. There is no stated intention-to-treat, per-protocol, or other population definition, and no account of adherence or withdrawals. In a crossover study, the population contributing complete measurements to both treatment periods can matter for the paired comparison. Without these details, it is not possible to determine how the reported summaries relate to all randomized participants.

The statistical analysis plan, original sample-size justification, and interim-analysis approach are not reported in the registry record. These omissions do not show that any particular procedure was or was not used; they limit what can be verified from the posted information. The reported comparisons should therefore be read as unadjusted and incompletely documented rather than as a fully specified confirmatory analysis.

15. Safety Results

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

Other (non-serious) adverse events

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

Most frequent non-serious adverse event terms

The registry reports zero serious adverse events among 32 participants at baseline, zero among 30 after placebo, and zero among 32 after montelukast. These are counts of participants with serious adverse events in the listed groups. The record does not provide serious adverse-event terms, and the number of deaths is not reported in the registry record.

Other adverse events are listed for 7 of 30 participants after placebo and 1 of 32 after montelukast; none are listed at baseline among 32 participants. The registry does not provide the event terms in these summaries, so the counts do not describe what types of events occurred, their severity, timing, or relationship to treatment.

In general, an absence of reported serious events in a small study does not establish that a treatment has no safety risks. These counts describe the registry entries for the study groups and should not be interpreted as a complete assessment of safety or as evidence that one treatment is safer. The record does not report additional detail needed to interpret event collection and attribution.

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

The posted primary result shows similar group means for pre-bronchodilator Rrs 5 after placebo and montelukast. The estimated mean difference is -0.01, the 95% confidence interval spans zero, and the unadjusted p-value is 0.825. Taken together, these statistics do not provide a clear separation between the displayed conditions for this endpoint.

That finding is not the same as proving the treatments are equivalent or that there is no effect. Equivalence requires a prespecified margin and an analysis designed to assess whether the uncertainty lies within that margin. Neither an equivalence margin nor a non-inferiority margin is reported in the registry record. The confidence interval also leaves uncertainty about the size and direction of the underlying difference.

The outcome is a short-term physiological measure. The result does not directly establish effects on symptoms, exacerbations, quality of life, or long-term asthma control; these are not the primary endpoint reported in the registry record. The secondary FEV1 measure is another physiological outcome and does not substitute for outcomes that were not reported.

The design is a randomized crossover, but the registry does not describe how the reported comparison accounts for the repeated observations, sequence, period, or missing data. The displayed summaries thus cannot be interpreted as a fully documented crossover model. The record also does not provide a full statistical analysis plan or a complete set of results across the listed outcome measures.

The appropriate interpretation is narrow: the posted summaries do not show a clear difference in the named primary measure during the recorded treatment periods, while leaving meaningful uncertainty about the estimate and the analysis. They are not a basis for medical advice or a general conclusion about whether montelukast works. Clinical importance, longer-term effects, and the relationship to other outcomes remain unestablished by these summaries.

17. Why This Trial Matters Statistically

This study illustrates why the design and analysis need to be read together. A crossover trial exposes participants to both treatment conditions, creating the potential for a within-person comparison. That structure can be informative, but interpreting the result depends on how repeated measurements, period, sequence, and possible carryover are handled. Those analytical details are not reported in the registry record.

The primary outcome is a continuous physiological measurement with group means and standard deviations. The posted treatment means are close, and the unadjusted comparison has a confidence interval that spans zero. This combination shows why an estimate, its uncertainty, and its design assumptions all matter: a p-value alone cannot establish equivalence, and a point estimate alone cannot express precision.

The sample-size illustrations also demonstrate that planning depends strongly on the effect size chosen for detection. Smaller target effects require substantially more participants per arm under the stated assumptions. These are planning calculations based on observed effects, not a report of the study's original design or an assessment of its achieved power.

Finally, the registry record lists more outcome measures than are represented in the posted secondary results, and it does not document a multiplicity approach or analysis population. These features highlight the value of complete outcome reporting and transparent analysis methods. The study is statistically instructive because it connects a randomized crossover design, continuous outcomes, uncertainty, and incomplete reporting without allowing any one summary statistic to stand in for the full evidence.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

Several limitations are specific to interpreting this record. First, the design is crossover, but the posted comparisons do not describe a paired model or explain how treatment sequence and period were handled. The registry lists a washout period but does not report an assessment of carryover. These gaps make it difficult to determine whether the displayed uncertainty fully reflects the trial design.

Second, the primary summaries do not have identical numbers of observations across conditions: 30 after placebo and 32 after montelukast, while the baseline summary includes 32. The reason for this difference and the handling of incomplete data are not reported in the registry record. The analysis population and participant flow are also not reported.

Third, the registry lists 8 outcome measures, but only 1 secondary result is posted, and it records zero reported analyses. A complete statistical analysis plan, outcome hierarchy, and multiplicity strategy are not reported. This limits assessment of whether the posted outcomes and analyses represent the full planned set.

Fourth, the sample-size figures are planning illustrations based on observed effects and specified assumptions; they are not the original design justification. The trial's own sample-size assumptions are not reported in the registry record. The planning assumptions also use equal allocation between two arms and a normal approximation, without a reported adjustment for crossover features.

Finally, the primary endpoint is a short-term lung-function measure, and no clinically important threshold is reported. The record does not provide enough detail to connect the observed measurement contrast to patient-experienced outcomes or longer-term effects. These limitations constrain interpretation of the posted statistics; they do not establish that unreported methods or outcomes were absent from the conduct of the study.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Response of FeNO, Small Airway Dysfunction and Lung Heterogeneity to 2-week Montelukast Treatment in Asthmatic Children. — NCT01581710.
• Registry record last updated 2018-04-12; status last verified 2018-03.
• Results first posted 2018-04-12.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

NCT01581710 is a completed randomized, quadruple-masked crossover study sponsored by CHA University, enrolling 32 children with mild persistent asthma. The recorded treatment sequences were montelukast followed by placebo and placebo followed by montelukast, with 14-day treatment periods and a listed 14-day washout.

The primary endpoint was pre-bronchodilator Rrs 5 measured by impulse oscillometry. The posted means were 0.74 kPa/L/s after placebo and 0.73 kPa/L/s after montelukast. The unadjusted mean difference was -0.01, with a 95% confidence interval spanning zero and an unadjusted p-value of 0.825. The registry also posts a secondary FEV1 outcome and adverse-event counts.

The record does not report a detailed analysis plan, analysis population, missing-data method, or multiplicity procedure. The displayed comparison should therefore be interpreted as an uncertain summary of the named measure, not as a fully documented analysis of all aspects of the crossover trial.