Smell Changes & Efficacy of Nasal Theophylline: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Smell Changes & Efficacy of Nasal Theophylline (NCT03990766), a randomized phase 2 study. The primary outcome is Number of Patients With Improvement in Global Rating of Smell Change.

2. Clinical Question

3. Trial Design

The SCENT trial, formally titled Nasal Theophylline Irrigation for Treatment of Post-Viral Olfactory Dysfunction, was a Phase 2 randomized, quadruple-masked, parallel-group study. Washington University School of Medicine was the sponsor. The registry lists an enrollment of 27 and a completed status. The recorded study start was 2019-05-15, and the primary completion date was 2021-01-15.

The comparison was between theophylline irrigation and placebo saline irrigation. In the active-treatment arm, theophylline 12 mg capsule contents were dissolved in a sinus rinse bottle with distilled or boiled tap water and a commercially prepared sodium chloride and sodium bicarbonate mixture. The placebo used identical-appearing lactose monohydrate capsule contents in the corresponding rinse. Both were described as delivered to both nasal cavities twice daily. The registry describes allocation as randomized and masking as quadruple, but the operational details of allocation concealment and masking are not reported in the registry record.

The study summary says participants had smell tested before and after 6 weeks of treatment and were regularly asked about potential side effects. It also states that the first 10 participants were to have blood drawn after 1 week of treatment to measure theophylline levels. The primary outcome was the count of participants with improvement in a self-reported global rating of smell change at 6 weeks. Three secondary outcomes are listed: change in the University of Pennsylvania Smell Identification Test total score, the Questionnaire of Olfactory Disorders-Negative Statements score and the Olfactory Dysfunction Outcomes Ratings score.

The registry record does not report the trial's original sample-size justification, its prespecified statistical analysis plan, or detailed analysis-population definitions. The posted outcome denominators differ from the enrollment figure, but the reasons for the denominators and any relationship to treatment discontinuation or missing outcome data are not reported in the registry record.

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 Number of Patients With Improvement in Global Rating of Smell Change, measured over 6 weeks.

The primary endpoint counts participants who reported an improvement in smell at 6 weeks. Each participant rated change on a 7-point Likert scale, from 1, much worse, to 7, much better. A rating of 4 meant neither better nor worse, and ratings of 5 or higher were classified as clinical improvement. The endpoint therefore turns an individual self-reported rating into a binary outcome: improvement or no improvement.

A binary count can make a group comparison direct to interpret: it asks how often a specified improvement threshold was reached in each arm. It also focuses on a threshold regarded by the registry as improvement, rather than the size of each person's change across the full scale. That choice discards distinctions among ratings within each category, including differences between slight, somewhat and much better. The endpoint is patient-reported, so it captures perceived change but is not the same measure as a smell-identification test.

The posted results record 4 participants meeting the improvement definition in the Theophylline arm and 3 in the Placebo arm. The outcome is relevant to the stated treatment question because it assesses reported change after the treatment period, but the registry record does not report a justification for selecting this threshold as the primary endpoint. Results for the listed smell-test and questionnaire outcomes are not included in the registry record for this analysis, so their findings cannot be characterized.

7. Results Posted in the Registry

• Theophylline: 33.3% (4/12) versus 30.0% (3/10) on control; risk difference 3.3 percentage points (95% CI -35.6 to 42.3), risk ratio 1.11 (0.32–3.84); unadjusted two-proportion z-test p = 0.867.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is binary because each participant is classified as either having met the improvement threshold or not. The underlying response was a 7-point self-reported global rating, with 4 neutral and scores of 5 or higher counted as improvement. For each arm, the event count is interpreted alongside the number of participants contributing to that outcome. Here, the posted counts are 4 of 12 in the Theophylline arm and 3 of 10 in the Placebo arm. The registry record does not report whether participants without a recorded outcome were included in any separate analysis.

What does a risk difference express?

A risk difference compares the event proportion in one group with the event proportion in the comparison group by subtraction. It is an absolute measure: it describes how far apart the groups are on the event-probability scale. A value at zero corresponds to equal event proportions. Positive or negative values indicate direction according to the order of the comparison. The recalculated risk difference for this outcome is 0.033. This is an unadjusted calculation from the posted event counts and denominators, not an adjusted model estimate.

The sponsor's reported result is expressed as a risk difference of 3.3, with limits of -35.6 and 42.3 for its 95% confidence interval. The recalculated result is expressed in the proportion scale, while the sponsor's reported estimate is expressed on a percentage scale. The registry record does not give a method for the sponsor's analysis, and its reported p-value is not listed. Since the record does not indicate a discrepancy between the recalculation and the sponsor's result, the two presentations can be read as corresponding descriptions of the same comparison on different scales.

What does the confidence interval add?

A confidence interval describes the statistical uncertainty around an estimate under the assumptions of the analysis. It is not a range in which every value is equally plausible, and it is not a guarantee that the true effect lies inside the particular interval. For the recalculated risk difference, the 95% interval is -0.356 to 0.423. Its width indicates that the observed counts do not estimate the between-group difference precisely. Because the interval spans zero, the data do not identify a direction with confidence. Interpretation should account for both the point estimate and this broad range, rather than treating the point estimate as the whole result.

What does the p-value tell us?

The unadjusted p-value is 0.867. In general, a p-value measures how unusual data at least as discrepant as those observed would be under a specified null hypothesis and analysis procedure. It is not the chance that the null hypothesis is true, nor the chance that the findings are due to chance. A large p-value does not prove equivalence or absence of an effect. Here, it accompanies an estimate with a wide confidence interval, so the central issue is that the comparison is imprecise as well as not statistically distinguishable from zero by this unadjusted test.

The registry lists a sponsor-reported superiority analysis and gives its risk difference and 95% confidence interval, but does not report the method used for that analysis or a sponsor-reported p-value. The registry record does not report whether the analysis adjusted for baseline factors or used any model beyond a group comparison. The recalculation is explicitly unadjusted and should not be treated as a replacement for a fully described prespecified analysis if one exists outside the registry record.

Why can binary outcomes be sensitive to small counts?

With a limited number of observed events, moving a small number of classifications can noticeably change the event proportions and the estimated difference. The interval reflects the resulting uncertainty. The binary threshold also makes results depend on where the cutoff is placed: a rating just below the improvement threshold is categorized differently from one just above it, even though the ratings are close. The full score distribution would preserve more information about degrees of reported change, but that distribution is not reported for the primary outcome.

General statistical note: binary outcomes can be analyzed with methods that model event probabilities, but a method's suitability depends on the design, data and analysis plan. The registry record does not identify the sponsor's statistical method, handling of any missing values, or planned covariate adjustment. No assumption about those choices should be made from the summary result alone.

What about other endpoints and multiplicity?

The registry lists three secondary measures: the University of Pennsylvania Smell Identification Test total score change, the Questionnaire of Olfactory Disorders-Negative Statements score change and the Olfactory Dysfunction Outcomes Ratings score change. A trial examining several outcomes can generate several statistical comparisons. In general, the more comparisons considered, the greater the chance that at least one appears unusual by chance if results are interpreted without accounting for multiplicity. Whether a multiplicity procedure was planned or used is not reported in the registry record, and numerical secondary results are not available in the registry record. The primary outcome should therefore be interpreted on its own terms, without implying that it summarizes all measured outcomes.

10. Confidence Intervals and Precision

The recalculated 95% confidence interval for the risk difference extends from -0.356 to 0.423, around a point estimate of 0.033. This is a wide interval relative to the point estimate and includes zero. It also extends to values on both sides of zero, so the estimate does not establish whether the event proportion was higher in the Theophylline arm or the Placebo arm in the underlying population. The posted counts, 4 of 12 and 3 of 10, provide the observed comparison; the interval conveys how uncertain that comparison is.

The sponsor's result is reported as a risk difference of 3.3 with a 95% confidence interval from -35.6 to 42.3. The sponsor's interval likewise spans zero and extends in both directions. The registry record gives no sponsor-reported p-value and does not identify the sponsor's analysis method. The recalculated unadjusted p-value is 0.867. These statistics should be read together: the point estimate is not a precise estimate of the difference, and the data do not clearly distinguish a difference from zero under the unadjusted comparison.

A confidence interval is not a statement that the effect has a 95% chance of being within its limits. In general, the stated confidence level describes the long-run performance of the interval procedure under its assumptions. The interval does not account for concerns that are not represented in the calculation, such as missing-data choices or selective reporting. The registry record does not report enough analysis detail to assess all such concerns.

The outcome counts are limited, and the interval indicates that the estimate has substantial uncertainty. The result should not be reduced to the point estimate alone, nor should the interval be read as proof that all values within it are equally likely. More precise estimation would require evidence that narrows the range while preserving an appropriate design and analysis; the current registry result does not provide that precision.

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 are illustrations based on the observed effect, rather than the trial's own original design assumptions. The registry record does not report the original sample-size justification or the assumptions used when the study was designed. For the displayed planning exercise, the stated assumptions are a two-sided significance level of 0.05, equal allocation between the arms, a normal approximation and an effect to detect set at the stated fraction of the observed effect.

For planning for 100% of the observed effect, the figures are 3,056 participants per arm for 80% power and 4,091 participants per arm for 90% power. For planning for 75% of the observed effect, they are 5,395 participants per arm for 80% power and 7,222 participants per arm for 90% power. For planning for 50% of the observed effect, they are 12,051 participants per arm for 80% power and 16,133 participants per arm for 90% power.

The 80% power column represents the planning number of participants per arm under which the assumed effect would be detected at the stated significance level in 80% of repeated studies, if the model assumptions held. The 90% column uses a higher target probability of detecting that assumed effect and consequently gives a larger planning figure. These are planning illustrations, not observed power.

The rows make the effect assumption explicit: planning to detect a smaller fraction of the observed effect requires more participants per arm. The curve illustrates the same relationship across effect assumptions. Because the calculation is anchored to the observed effect from a small posted comparison, it should be treated as an illustration, not as a reliable design recommendation. A study's actual planning also depends on design choices and assumptions that 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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.300; treatment proportion p₁ = 0.333; average p̄ = 0.317.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6579 = 1.2894.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6574 = 0.5533.
4. n = (1.2894 + 0.5533)² / (0.0333)² = 3,056.0, rounded up to 3,056 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
p0 <- 0.3                          # control proportion
p1 <- 0.333333333333333                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(3990766)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 3,056 (80% power), 4,091 (90% power)
 75% of observed effect: n per arm = 5,395 (80% power), 7,222 (90% power)
 50% of observed effect: n per arm = 12,051 (80% power), 16,133 (90% power)
power.prop.test: 3056 
Simulated power at n = 3,056 per arm: 0.804 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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. Analyses Reported by the Sponsor

The sponsor-reported analysis gives a risk difference of 3.3 and a 95% confidence interval from -35.6 to 42.3. The registry record labels this as a superiority analysis but does not report the analysis method or a sponsor-reported p-value. The recalculated unadjusted comparison from the posted event counts and denominators gives a risk difference of 0.033, with a 95% confidence interval from -0.356 to 0.423, and an unadjusted p-value of 0.867.

The sponsor's estimate and interval are on a percentage scale, while the recalculation uses a proportion scale. Their values express the same direction and broadly the same interval when read on their respective scales. The registry record indicates no discrepancy between the posted sponsor result and the recalculation. The sponsor's own analysis therefore remains the primary reported analysis; the recalculation is a simple unadjusted check based on the posted summary statistics, not an independent replacement or a reconstruction of an undocumented model.

Both presentations show a point estimate near zero relative to the uncertainty and confidence limits spanning zero. The sponsor's analysis does not report a p-value in the registry record, so the recalculated p-value should not be attributed to the sponsor. Further interpretation of the sponsor analysis is limited because its method, missing-data handling, analysis population and any adjustment are not reported in the registry record.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists the primary outcome and three secondary outcomes. The primary endpoint is the number of participants with improvement in global rating of smell change at 6 weeks. The secondary outcomes are change in the University of Pennsylvania Smell Identification Test total score, change in the Questionnaire of Olfactory Disorders-Negative Statements score and change in the Olfactory Dysfunction Outcomes Ratings score. Numerical results for the secondary outcomes are not included in the registry record for this analysis.

When a study evaluates several outcomes or performs several comparisons, multiplicity can affect the interpretation of statistical evidence. General statistical note: testing multiple hypotheses without an adjustment or prespecified hierarchy can increase the chance of at least one apparently positive result arising by chance. This does not mean an adjustment was necessarily needed or absent in this trial; whether multiplicity was addressed, and how, is not reported in the registry record. The record also does not report whether the primary outcome was formally protected from other analyses through a prespecified testing sequence.

Missing-data information is limited. The posted primary result has outcome denominators of 12 for Theophylline and 10 for Placebo, while the registry lists enrollment of 27. The registry record does not explain why these denominators differ from the enrollment figure, how many participants lacked an outcome, whether any participants discontinued treatment, or how missing outcome values were handled. It does not report a sensitivity analysis for missing data. These omissions make it difficult to assess whether the posted comparison represents all randomized participants or a subset with available outcome data.

The analysis population is also not identified. The registry record does not state whether the analysis followed intention-to-treat, per-protocol or another population definition. It does not report the method used for the sponsor analysis, any covariate adjustment, or whether an analysis plan was prespecified. These details matter because choices about which participants and observations enter an analysis can affect the estimate and its uncertainty. No specific approach should be inferred from the summary results alone.

15. Safety Results

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

Deaths

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 serious adverse event record lists 0 serious adverse events among 14 participants at risk in the Theophylline group and 0 among 13 participants at risk in the Placebo group. Deaths are recorded as 0 in both groups. Other adverse events are also recorded as 0 among 14 participants at risk in the Theophylline group and 0 among 13 participants at risk in the Placebo group. These are the figures recorded for the relevant safety categories.

Counts of zero in the registry record mean that no events are recorded in those categories for the stated at-risk groups; they do not establish that an event is impossible or that the treatment has no safety risks. The group sizes contributing to the safety record differ from the denominators in the posted primary outcome. The registry record does not explain the relationship between these safety denominators, the enrollment figure and the primary outcome denominators.

The study summary says participants were regularly asked about potential side effects and describes blood testing for the first 10 participants after 1 week to assess theophylline levels. Results of those blood measurements are not reported in the registry record. The available adverse-event counts do not provide event descriptions, timing, severity beyond the serious-event category, or a detailed account of collection and coding. They should be interpreted as the recorded safety counts, not as a comprehensive characterization of all possible harms.

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

The primary result describes a small observed difference in the number of participants meeting the registry's improvement threshold: 4 of 12 in the Theophylline arm and 3 of 10 in the Placebo arm. The sponsor reports a risk difference of 3.3 with a 95% confidence interval from -35.6 to 42.3. The unadjusted recalculation gives a risk difference of 0.033, with a 95% confidence interval from -0.356 to 0.423 and an unadjusted p-value of 0.867. The interval is broad and includes zero, so the result does not precisely establish the direction or size of a difference.

This finding does not show that the groups were equivalent. A result that is not statistically distinguishable from zero is not, by itself, evidence that any difference is absent or sufficiently small to be unimportant. Establishing equivalence or non-inferiority would require a relevant prespecified margin and an analysis designed for that question; such details are not reported in the registry record.

The endpoint is a self-reported rating classified using a threshold of 5 or higher. It measures whether participants crossed the improvement threshold, not the full range or degree of change in smell. The registry also lists smell-test and questionnaire outcomes, but their numerical results are not reported in the registry record. The primary result therefore cannot stand in for the unreported findings on those measures.

The record's enrollment figure is 27, whereas the posted primary outcome denominators are 12 and 10. The relationship between these figures, the analysis population and missing outcome handling is not reported in the registry record. That limits assessment of how complete the primary comparison is. The result is best understood as an uncertain comparison of the posted outcome data, not as a definitive conclusion about treatment effect, all outcomes or safety.

The serious adverse-event and death counts are recorded as zero in both groups, but those counts do not establish the absence of risk. They describe what was recorded among the listed safety groups. Neither the efficacy estimate nor the safety counts support a universal conclusion beyond the trial record.

17. Why This Trial Matters Statistically

This trial illustrates how a clinically direct endpoint can still produce an uncertain statistical estimate. Counting participants who report improvement is easy to communicate, and the registry defines improvement in advance through a threshold on a global smell-change rating. Yet the observed counts are 4 of 12 in the Theophylline arm and 3 of 10 in the Placebo arm, and the confidence interval around the estimated difference is wide. The point estimate alone would conceal how much uncertainty remains.

It also demonstrates the importance of distinguishing a failure to identify a clear difference from evidence of equivalence. The unadjusted p-value is 0.867, and the confidence interval includes zero while extending to values on either side. Those statistics do not prove that the treatments have the same effect; they indicate that this comparison does not estimate the difference precisely enough to establish its direction or magnitude.

Another statistical lesson is that outcome definitions shape what a result means. A threshold of 5 or higher turns a 7-point response into a binary count, which is straightforward to interpret but does not preserve all information in the rating scale. A participant just below the cutoff is categorized differently from a participant just above it, even though the responses are close. The registry record does not report the full distribution of primary ratings.

The registry also lists three secondary outcomes, but their numerical results, multiplicity approach, missing-data handling and analysis-population definition are not reported in the record. Those gaps matter when considering whether the primary result is a complete representation of the trial. Finally, the sample-size planning illustration shows how estimates based on an observed effect can imply very large future planning figures, especially when planning for smaller effects. Such figures depend on assumptions and should not be confused with information about the trial's original design or its observed evidential strength.

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.

The posted primary result is based on outcome denominators of 12 in the Theophylline arm and 10 in the Placebo arm, while the registry lists enrollment of 27. The registry record does not explain this difference, report participant flow, or state how missing primary outcome data were handled. Without those details, it is not possible to determine from the record whether the posted comparison includes all randomized participants or how missing results may have affected it.

The analysis method is not reported for the sponsor's result, and the analysis population, any covariate adjustment and any prespecified statistical plan are also not reported in the registry record. The recalculation is unadjusted and based on the posted summary counts. It cannot address choices or procedures that are not described in the record.

The primary endpoint is a binary classification of a self-reported smell-change rating. The threshold of 5 or higher is specified, but the record does not report the distribution of all ratings or a rationale for selecting the cutoff. The binary result therefore does not show the full range of participant-reported change. Although smell testing and questionnaires are listed as secondary outcomes, their numerical findings are not included in the registry record.

The record does not report whether multiplicity was considered, whether an outcome hierarchy was used, or whether sensitivity analyses were conducted. Its safety counts are recorded for groups of 14 and 13 participants at risk, and the relationship between those groups and the primary outcome denominators is not explained. Results of the planned blood-level measurements are not reported in the registry record. These record-level omissions limit interpretation; they do not establish that the corresponding procedures or analyses were not performed.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Smell Changes & Efficacy of Nasal Theophylline — NCT03990766.
• Registry record last updated 2022-03-31; status last verified 2022-03.
• Results first posted 2022-03-31.
• 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

The SCENT trial was a completed Phase 2 randomized, quadruple-masked, parallel-group comparison of nasal theophylline irrigation with placebo saline irrigation for post-viral olfactory dysfunction. Washington University School of Medicine was the sponsor. The registry lists enrollment of 27, a study start date of 2019-05-15 and a primary completion date of 2021-01-15.

The primary outcome counted participants reporting improvement in smell at 6 weeks, defined as a global rating of 5 or higher on a 7-point scale. The posted results record 4 of 12 participants improved in the Theophylline arm and 3 of 10 in the Placebo arm. The sponsor reported a risk difference of 3.3 with a 95% confidence interval from -35.6 to 42.3. The recalculated unadjusted estimate is 0.033, with a 95% confidence interval from -0.356 to 0.423 and p = 0.867.

The interval is broad and includes zero, so the posted primary result is imprecise. Three secondary outcomes are listed, but their numerical results are not reported in the registry record. Missing-data handling, analysis-population definitions and the sponsor's statistical method are also not reported.