Nasal Physiologic Reactivity of Nonallergic Rhinitics to Cold Air Provocation: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Nasal Physiologic Reactivity of Nonallergic Rhinitics to Cold Air Provocation (NCT00415493), a randomized na study. The primary outcome is Net Proportional Change in Nasal Airway Resistance.

2. Clinical Question

3. Trial Design

This completed study enrolled 24 participants and used randomized order in a crossover design. The two orders were cold-dry air followed on a separate day by warm-moist air, or warm-moist air followed on a separate day by cold-dry air. Thus, the exposures were compared within participants across separate testing days, while the clinical comparison was between people with vasomotor rhinitis and nonallergic, non-rhinitic controls. The registry record does not describe random assignment to the case or control groups; these groups are defined by participant status.

The registry lists 14 cases and 10 controls. Its study summary further describes 10 cases with symptoms triggered predominantly by cold air and four with symptoms triggered predominantly by chemicals. The primary outcome results combine the cases into one group, and separate outcome estimates for these two symptom-trigger groups are not reported in the registry record.

Masking is recorded as single, but who was masked and how masking was implemented are not reported in the registry record. The randomization sequence method, allocation concealment, and procedures for ensuring that the two testing days were comparable are also not reported in the registry record. The record gives an overall study status of completed, with start and primary-completion dates recorded as 2006-12 and 2007-10. It does not state how many enrolled participants completed both exposure days or contributed to the primary analysis.

The trial lists cold-dry and warm-moist air provocation as interventions. The comparison of interest is not simply a post-exposure resistance value: it is the difference between each person's pre-to-post response on the cold-air day and that person's pre-to-post response on the warm-air day, followed by a comparison of those net responses between cases and controls.

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.

Overall Study

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.

6. Primary Endpoint

The registry lists the primary outcome as Net Proportional Change in Nasal Airway Resistance, measured over One hour.

The primary endpoint is the net proportional change in nasal airway resistance, expressed as a unit-less measure. Nasal airway resistance was measured in triplicate at baseline, immediately after exposure, and at 15-, 30-, 45- and 60 minutes after exposure. Measurements at each time point were averaged. The post-exposure averages were combined using a time-weighted average over one hour, then compared with that testing day's baseline average to obtain a proportional change.

The endpoint then subtracts the warm-air day's pre-to-post change from the cold-air day's pre-to-post change for each person. A positive net value therefore represents a larger proportional change on the cold-air day than on the warm-air day under this definition; a value near zero indicates similar changes on the two days. The group means of these individual net responses are 0.11 for cases and 0.04 for controls.

Using a within-person contrast is intended to account for variation between people and variation within a person across testing days. The registry description notes that nasal airway resistance varies considerably both between and within individuals. The endpoint therefore focuses on the difference between the exposure-day responses rather than on a single raw resistance reading. The registry record does not report a separate outcome for each post-exposure time point.

7. Results Posted in the Registry

• Cases: mean 0.11 versus 0.04 on control; difference 0.07 (95% CI -0.55 to 0.69), standardized effect d = 0.08; z-test p = 0.824.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary measure is continuous: each participant has a unit-less net proportional change, and the reported group summaries are means. For cases, the mean is 0.11 and the standard error is 0.27. For controls, the mean is 0.04 and the standard error is 0.16. A mean gives the average value in a group, while the standard error describes uncertainty in estimating that group mean. It is not the same as the spread of individual participant values. The registry record does not provide standard deviations of the individual net changes.

What does the mean difference describe?

The posted mean difference is 0.07, calculated as the case mean minus the control mean. It compares the average net cold-versus-warm response between the two groups. The sign indicates that the case mean is higher than the control mean in this comparison. It does not indicate that every case had a larger response, nor does it describe the difference between cold air and warm air for a typical individual without considering the group summaries.

The within-person construction of the endpoint and the between-group comparison are distinct steps. First, each participant's response on the warm-air day is contrasted with that same participant's response on the cold-air day. Then the resulting net values are summarized for cases and controls and compared. The registry describes the exposure order as randomized, but the analysis method for accounting for the paired measurements and the crossover structure is not reported in the registry record.

How should the p-value be read?

The unadjusted p-value is 0.824. In general, a p-value measures how unusual data at least as inconsistent with a specified null model would be if that model and the test assumptions were correct. It does not measure the size or clinical importance of an effect, and it does not give the probability that the null hypothesis is true. The registry record does not report a full statistical analysis plan, so the exact test procedure and its assumptions are not reported in the registry record.

The term unadjusted indicates that the reported p-value is not presented as adjusted for multiple comparisons. No secondary outcome results are posted, but the registry record does not state whether any other outcomes or analyses were examined. The record also does not describe covariate adjustment, a model for repeated observations, or a plan for handling the randomized order of exposure days. Those details should not be inferred from the p-value alone.

Why does a confidence interval add information?

A confidence interval gives a range of estimates compatible with the data and the interval procedure. It communicates uncertainty in the mean difference rather than focusing only on whether a p-value crosses a threshold. For this comparison, the interval extends to both sides of zero. That means the posted summary does not precisely determine whether the underlying difference is positive, negative, or close to no difference. The interval is broad relative to the point estimate, so the point estimate should not be read as a precise value.

In general, confidence intervals depend on the method used, the variability in the data, and the amount of information available. In a crossover study, the relationship between each participant's measurements across testing days can contribute to precision. The registry record does not report the paired variability or the statistical procedure used to incorporate that relationship. As a result, the posted interval can be described, but the analysis details behind it cannot be reconstructed from the registry record.

What does over-dispersion mean in general?

In general, over-dispersion means that observed variability is greater than a statistical model expects. It can make standard errors too small and confidence intervals too narrow if the model does not allow for that extra variation. This concept is most often discussed for count outcomes and is not itself a description of the posted continuous endpoint. For this study, the registry record highlights considerable variation in nasal airway resistance between and within individuals, which is one reason the endpoint uses a net proportional contrast. It does not report a formal assessment of over-dispersion.

The primary comparison is based on 14 cases and 10 controls. Those group sizes are modest, and the reported standard errors are large in relation to the group means. The posted analysis does not include a separate estimate for the 10 cold-triggered cases and the four chemical-triggered cases, nor does it report individual-level data. No conclusion about the similarity of these subgroups can be drawn from the combined case result.

Recalculated summaries are not identified as a replacement for a sponsor analysis in this record: the discrepancy indicator is false. The comparison can therefore be described using the posted mean difference and its reported uncertainty. The registry record does not report an inferential analysis plan, prespecified covariates, missing-data procedures, or the analysis population definition. These omissions limit the ability to evaluate whether the displayed comparison matches a planned model or how sensitive it is to alternative methods.

10. Confidence Intervals and Precision

The estimated mean difference between cases and controls is 0.07. Its confidence interval extends below and above zero, so it includes no difference as well as differences in either direction. This is an important feature of the result: the estimate is not precise enough to establish the direction of the underlying group contrast. The interval is also broad compared with the point estimate, indicating substantial uncertainty about the size of any difference.

A confidence interval is not a list of all possible true values and does not assign equal probability to every value within its limits. In general, it is produced by a method that, under repeated use and its assumptions, captures the target parameter at the stated confidence level. The confidence level for this particular interval is not reported in the registry record. The exact interval endpoints are therefore not repeated; the relevant interpretation is that the reported range crosses zero.

The group standard errors are 0.27 for cases and 0.16 for controls. A standard error describes uncertainty about a group mean, whereas a standard deviation would describe how individual values vary within a group. The registry reports standard errors, not standard deviations, for these group summaries. The standard errors and the broad interval are consistent with caution about treating the point estimate as stable or precise.

Precision is affected by the number of participants, variability, and the analysis method. The study includes 14 cases and 10 controls, but the registry record does not report the number with complete paired measurements or the paired variability that would clarify the contribution of the crossover measurements to precision. It also does not report whether missing observations or other analysis choices altered the effective information. The interval should therefore be interpreted as uncertainty around the posted comparison, not as evidence of a narrowly determined group difference.

11. 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 figures are participants per arm, not total events. They illustrate the sample size that a hypothetical two-arm study would require under the stated assumptions, using the observed mean difference as a starting point. The entries consider detecting 100%, 75% or 50% of the observed effect. For the full observed effect, the illustration gives 2,268 participants per arm for 80% power and 3,036 participants per arm for 90% power. For 75% of the observed effect, it gives 4,032 participants per arm for 80% power and 5,397 participants per arm for 90% power. For 50% of the observed effect, it gives 9,071 participants per arm for 80% power and 12,143 participants per arm for 90% power.

The planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. These are planning illustrations based on the observed comparison, not the trial's original design assumptions; those original assumptions are not reported in the registry record. The registry record describes a randomized-order crossover study, so the illustration's two-arm assumptions should not be mistaken for a reconstruction of the study's actual design or analysis.

In general, 80% power means that a study designed under the stated assumptions would have an 80% chance of detecting the specified effect at the stated significance level if that effect were the true one. The 90% column expresses the corresponding chance at 90% power. Higher target power requires more participants under otherwise unchanged assumptions. Smaller effects require more participants because they are harder to distinguish from random variation. These planning figures are not observed power.

The curve represents the general relationship between effect size and planned sample size under the assumptions used for the illustration. It should be read as a planning aid, not as evidence about what the completed study was capable of detecting under its actual crossover analysis. The original sample-size justification and power target are not reported in the registry record.

12. 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 = 0.070; pooled standard deviation σ = 0.841.
2. n = 2 × (1.96 + 0.842)² × 0.841² / 0.070² = 2,267.6, rounded up to 2,268 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 <- 0.07                      # observed difference in means
sigma <- 0.841313907473953                     # 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(415493)
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 = 2,268 (80% power), 3,036 (90% power)
 75% of observed effect: n per arm = 4,032 (80% power), 5,397 (90% power)
 50% of observed effect: n per arm = 9,071 (80% power), 12,143 (90% power)
power.t.test: 2268.5 
Simulated power at n = 2,268 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.

13. Multiplicity, Missing Data and Analysis Populations

The registry record lists one primary outcome measure and no posted secondary outcome results. It does not report a multiplicity adjustment, a hierarchy of outcomes, or a plan for controlling the chance of false-positive findings across multiple analyses. Although the posted primary comparison is described as unadjusted, the record does not establish whether other outcomes, subgroup comparisons, time points, or analytic choices were considered. No claim about multiplicity control can therefore be made.

Missing-data methods are not reported in the registry record. The record gives enrollment of 24 and group counts of 14 cases and 10 controls, but it does not state how many participants completed both testing days, whether measurements were missing at any time point, or how missing values were handled. It also does not say whether participants with incomplete exposure-day data were excluded, whether any values were imputed, or whether sensitivity analyses were conducted.

The analysis population is not defined in the registry record. There is no reported distinction among an intention-to-treat population, a per-protocol population, or a population with complete crossover measurements. The posted results should therefore be understood as the reported summaries for the listed groups, without assuming which participants were included beyond the group counts shown.

The record does not describe the statistical handling of crossover features. In general, crossover analyses may need to account for repeated observations within people, exposure period, sequence, and possible carryover from one testing day to another. Whether such factors were evaluated or modeled is not reported in the registry record. The analysis plan, including any prespecified method for handling these issues, is also not reported in the registry record.

Other potentially relevant procedures are not documented, including protocol deviations, exclusions after enrollment, and whether analyses were prespecified before results were examined. These gaps do not alter the numerical result that is posted, but they limit assessment of how the result was produced and whether analytic decisions could affect its interpretation.

14. 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 3% reporting threshold.

The registry reports zero participants affected by serious adverse events among the 14 cases and zero among the 10 controls. It also reports zero participants affected by other adverse events in each of those groups. These figures describe what was recorded for the listed groups; they do not establish that no symptoms or events occurred outside the registry's reporting definitions or observation period.

The death counts are not reported in the registry record. No serious adverse event terms are listed. The record does not provide event descriptions, severity grading, timing, relatedness to either air exposure, or the method used to collect safety information. It also does not describe whether adverse events were assessed over the full study or only during particular visits.

Because the groups are small, zero recorded affected participants should be read as a count in this study, not as evidence that an event cannot occur. The safety entries do not support broader conclusions about the frequency of events in other populations or settings. They are a report of the registry entries for this completed study, with the limitations of the information recorded there.

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

The result describes a comparison of average net proportional nasal airway resistance changes between cases and controls under the study's cold-dry and warm-moist air challenges. Cases had a reported mean of 0.11 and controls had a mean of 0.04. The unadjusted difference was 0.07. The confidence interval spans zero and the unadjusted p-value is 0.824, so the posted result is uncertain about the direction and size of the underlying group contrast.

This finding does not establish that the groups are equivalent. Demonstrating equivalence requires a prespecified margin and an analysis designed to assess whether the difference falls within that margin; no such margin or equivalence analysis is reported in the registry record. Nor does the result establish that there is a meaningful difference. The estimate is compatible with more than one interpretation because its uncertainty is substantial.

The comparison is based on a particular endpoint: the net proportional change from baseline on the cold-air day minus the corresponding change on the warm-air day, using a time-weighted post-exposure average over one hour. It is not a comparison of absolute resistance values at a single time point, and it does not report results for each measurement time separately. The group summary also does not show each participant's response.

The posted cases result combines participants with predominantly cold-triggered symptoms and those with predominantly chemical-triggered symptoms. It therefore cannot describe whether these groups respond differently. The results apply to the participants and measures recorded in this study; the registry record does not support extending them to other patient groups, exposures, outcomes, or clinical circumstances.

Finally, the trial randomized exposure order, not rhinitis status. The numerical case-control contrast is not a randomized estimate of the effect of having vasomotor rhinitis. It is a comparison between the groups as enrolled. The study's completed status and reported outcome do not remove the uncertainty created by the limited group sizes, broad confidence interval, and unreported analysis details.

16. Why This Trial Matters Statistically

This study illustrates how an endpoint can be shaped to address substantial biological and measurement variability. Instead of relying on one nasal airway resistance reading, the endpoint averages repeated measurements at each time point, summarizes the post-exposure period using a time-weighted average, compares that with baseline, and then contrasts cold-air and warm-air days within each participant. That construction aims to focus the analysis on the exposure contrast while reducing the influence of stable differences between people and variation within a person.

It also demonstrates that a carefully constructed measure does not guarantee a precise group comparison. The case and control means differ by 0.07, but the confidence interval crosses zero and is broad. A point estimate alone can look definite even when the data allow a wide range of plausible values. Reading the estimate together with its uncertainty is essential, especially with 14 cases and 10 controls.

The design raises statistical questions particular to crossover studies. Randomizing the order can help balance order effects, but analysis may need to reflect paired measurements and testing periods. The registry record does not report whether period, sequence, or carryover were addressed. The example therefore underscores the value of reporting both the design and the analysis model in enough detail to assess how repeated measurements informed the result.

The combined case group also highlights the difference between a study's enrolled subgroups and the subgroup results it reports. The study summary distinguishes cold-triggered from chemical-triggered symptoms, but no separate endpoint estimates are posted. Without those estimates, the aggregate mean cannot answer whether the two groups have different response patterns.

Finally, the sample-size illustrations show how strongly planned sample size can depend on the effect a future study aims to detect. The figures grow as the assumed effect becomes smaller and as the desired power rises. They are planning scenarios based on the observed estimate, not a retrospective measure of the completed study's power and not a substitute for a design justified by the intended research question.

17. 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.

The registry record leaves several design and analysis details unspecified. Although masking is recorded as single, it does not identify who was masked or how masking was maintained. The method used to generate the randomized exposure order and the approach to allocation concealment are not reported in the registry record. The record also does not describe the interval between testing days beyond stating that each exposure followed on a separate day.

The comparison includes 14 cases and 10 controls, with no separate outcome estimates for the 10 participants whose symptoms were predominantly triggered by cold air and the four whose symptoms were predominantly triggered by chemicals. As a result, the reported case mean does not show whether responses differ by symptom-trigger group. The registry record does not report baseline characteristics that would help describe other differences between cases and controls.

Although the endpoint uses measurements from multiple time points and both exposure days, the number of participants with complete measurements is not reported. Missing-data handling, exclusions, protocol deviations, and the analysis population are also not reported in the registry record. The statistical method for accounting for paired observations, order, period, or possible carryover is not described.

The posted comparison is imprecise, and the record does not provide individual-level values or standard deviations for the group outcomes. It reports standard errors, which do not describe the full distribution of participant responses. No secondary outcome results or analysis records are posted, limiting assessment of whether the primary comparison was considered alongside other analyses.

These limitations restrict what can be inferred from the group means. They do not invalidate the values recorded, but they make it difficult to assess the robustness of the estimate, how representative the analyzed participants were of those enrolled, or whether the statistical procedure fully reflected the crossover design.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Nasal Physiologic Reactivity of Nonallergic Rhinitics to Cold Air Provocation — NCT00415493.
• Registry record last updated 2017-03-06; status last verified 2017-01.
• Results first posted 2012-10-26.
• 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.

21. Record Summary

NCT00415493 is a completed randomized, single-masked crossover study titled “Nasal Physiologic Reactivity of Nonallergic Rhinitics to Cold Air Provocation.” It enrolled 24 participants: 14 cases with vasomotor rhinitis and 10 nonallergic, non-rhinitic controls. Participants were assigned to one of two orders of cold-dry and warm-moist air provocation on separate days.

The primary outcome was the net proportional change in nasal airway resistance: the pre-to-post change on the cold-air day minus the pre-to-post change on the warm-air day, using a time-weighted post-exposure average over one hour. The reported means were 0.11 for cases and 0.04 for controls. The unadjusted mean difference was 0.07, with a confidence interval spanning zero and an unadjusted p-value of 0.824.

The registry record does not report secondary outcome results, analysis records, the original sample-size justification, or several details of the statistical plan. It records zero participants affected by serious and other adverse events in both groups; deaths are not reported in the registry record.