Safety and Efficacy of ARQ-154 Foam in Subjects With Seborrheic Dermatitis: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Safety and Efficacy of ARQ-154 Foam in Subjects With Seborrheic Dermatitis (NCT04091646), a randomized phase 2 study. The primary outcome is Achievement of Investigator Global Assessment (IGA) Success at Week 8.

2. Clinical Question

3. Trial Design

The registry describes NCT04091646 as a Phase 2 study, while the official title calls it a Phase 2b study. It was randomized, quadruple masked, parallel group, and vehicle controlled. The sponsor was Arcutis Biotherapeutics, Inc. The record lists an enrollment of 226 and a status of completed. The study start date was 2019-12-04, and the primary completion date was 2020-08-18.

The two interventions were roflumilast foam 0.3% and vehicle foam. Participants assigned to roflumilast applied it once daily to all areas affected by seborrheic dermatitis for 8 weeks. Participants in the comparison arm applied matched inactive vehicle foam once daily for 8 weeks. The brief summary describes the study as evaluating safety and efficacy against placebo foam.

The primary outcome was IGA success at Week 8. The outcome data list 141 participants in the roflumilast arm and 66 in the vehicle arm, with 104 and 27 successes, respectively. These outcome counts should not be conflated with the separate safety populations, which list 154 and 72 participants at risk. The registry’s primary-outcome population excludes participants who missed the Week 8 assessment because of COVID-19 disruption.

The record lists seven secondary outcomes, covering IGA success at earlier visits, erythema, scaling, and itch. The registry record does not report the trial’s original sample-size justification or its original design assumptions. It also does not report an interim-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.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: All randomized participants are included, with the exception of those who missed the Week 8 assessment due to COVID-19 disruption.

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 Achievement of Investigator Global Assessment (IGA) Success at Week 8, measured over Week 8.

The primary endpoint counts participants who achieved Investigator Global Assessment success at Week 8. IGA is a 5-point assessment of seborrheic dermatitis severity, with scores from 0, completely clear, to 4, severe; higher scores indicate greater severity. For this trial, success required a Week 8 score of 0 or 1 and an improvement of at least 2 grades from baseline.

This endpoint combines a disease-severity status at the assessment visit with improvement from the participant’s baseline. Requiring both conditions means that a low Week 8 score alone is not sufficient for success. The endpoint is binary for each participant: the success criterion is either met or not met. The arm-level outcome is therefore reported as a count of participants with the event, alongside the number in the outcome population.

Binary endpoints allow a direct comparison of the proportions meeting a defined criterion, and can be expressed using measures such as a risk difference or odds ratio. These measures answer different statistical questions: the risk difference describes an absolute contrast on the probability scale, while the odds ratio compares odds. The endpoint description states that IGA scores are based on observed data, whereas the odds ratio and p-values were calculated using multiple imputation for missing values.

7. Results Posted in the Registry

• Roflumilast Foam 0.3%: 73.8% (104/141) versus 40.9% (27/66) on control; risk difference 32.8 percentage points (95% CI 18.9 to 46.8), risk ratio 1.80 (1.33–2.45); unadjusted two-proportion z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary: each participant either met the IGA success definition at Week 8 or did not. The registry reports the number meeting the definition by arm. For binary outcomes, the count is interpreted in relation to the number assessed in that arm; the count alone does not convey the event frequency. The posted arm-level estimates are 0.738 for roflumilast foam and 0.409 for vehicle foam.

What does a risk difference describe?

The recalculated risk difference is 0.329, with a 95% confidence interval from 0.189 to 0.468. A risk difference subtracts the event probability in one arm from the event probability in the other, so it expresses an absolute contrast on the probability scale. General explanation: an interval around an estimate describes the range of values compatible with the observed data under the method’s assumptions; it is not a guarantee that the true value falls inside that range. The interval stays above zero, which is consistent with a positive absolute difference under this unadjusted calculation.

What does an odds ratio describe?

An odds ratio compares the odds of the event between arms. The recalculated unadjusted odds ratio is 4.06, with a 95% confidence interval from 2.189 to 7.53. The sponsor-reported Cochran-Mantel-Haenszel odds ratio is 4.95, with a 95% confidence interval from 2.51 to 9.76. An odds ratio is not a risk difference and should not be read as an absolute increase in the probability of success. General explanation: odds and probabilities are related but are distinct scales, so the numerical size of an odds ratio does not directly state how many additional participants meet an outcome.

Why are there two odds ratios?

The recalculation uses posted arm-level summary statistics and is unadjusted. The sponsor’s analysis is identified as Cochran-Mantel-Haenszel, a method that can combine comparisons across strata. General explanation: a stratified method can account for specified groupings when estimating an association, while an unadjusted comparison uses the overall arm summaries without such adjustment. The registry record does not identify the strata or give enough detail to reconstruct the sponsor’s analysis from the posted counts. The methods therefore answer related, but not identical, analytic questions.

How should the p-values be read?

The recalculated unadjusted p-value is <0.001; the sponsor-reported p-value is < 0.001. A p-value describes how unusual data at least as incompatible with a specified null hypothesis would be if that hypothesis and the analysis assumptions held. It is not the probability that the null hypothesis is true, and it does not measure the size or practical importance of an effect. General explanation: a small p-value is evidence against the null model, but interpretation also depends on the study design, endpoint, analysis choices, and precision of the estimate.

The endpoint description notes a distinction between observed IGA scores and inferential results: the odds ratio and p-values were calculated using multiple imputation for missing values. Multiple imputation uses a model to represent uncertainty about missing observations rather than treating a single filled-in value as known. General explanation: results can depend on the assumptions used to model missingness and on the variables included in the imputation procedure. The registry record does not report those details, so the imputation cannot be independently evaluated from this record.

The registry describes the study as randomized and quadruple masked. Randomization supports an arm comparison by assigning participants through a random process, while masking is intended to limit the influence of treatment knowledge on study conduct or assessment. These design features do not eliminate all potential bias, and the record does not provide enough detail to assess every aspect of implementation.

10. Confidence Intervals and Precision

The recalculated risk difference is 0.329, and its 95% confidence interval extends from 0.189 to 0.468. This interval provides information about the precision of the absolute contrast: values across that range are compatible with the data under the unadjusted method and its assumptions. The interval does not include zero, the value representing no difference in the risk-difference scale. The width of the interval also matters: the point estimate alone would not convey the uncertainty around the comparison.

For the unadjusted odds ratio, the estimate is 4.06 and the 95% confidence interval ranges from 2.189 to 7.53. The sponsor’s Cochran-Mantel-Haenszel estimate is 4.95, with its 95% confidence interval from 2.51 to 9.76. Both intervals are on the odds-ratio scale, where 1 represents equal odds. Their lower limits exceed 1, but the intervals cover a range of possible association magnitudes rather than fixing the effect at the point estimate.

The sponsor and recalculated intervals should be interpreted alongside their methods. The first is the sponsor’s reported stratified analysis; the second is an unadjusted calculation from posted summary statistics. Differences between the estimates and intervals do not by themselves demonstrate an error. The registry record does not report the sponsor analysis strata, and the unadjusted calculation does not reproduce the sponsor’s method.

Confidence intervals describe statistical uncertainty under the assumptions of the analysis. They do not account automatically for all possible sources of bias, missing-data uncertainty, or limitations in generalizing beyond the study population and setting. The outcome description states that the odds ratio and p-values used multiple imputation, but the record does not report the imputation model or sensitivity analyses. Precision should therefore be understood in relation to the reported methods, not as a complete measure of certainty about every aspect of the result.

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 for 80% power and participants per arm for 90% power. They are not total events. The planning illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses the observed effect as its reference and considers effects equal to 100%, 75%, or 50% of that observed effect. The trial’s own original design assumptions and sample-size justification are not reported in the registry record.

For planning at 100% of the observed effect, the figures are 35 participants per arm for 80% power and 46 participants per arm for 90% power. For planning at 75% of the observed effect, they are 64 participants per arm for 80% power and 85 participants per arm for 90% power. For planning at 50% of the observed effect, they are 145 participants per arm for 80% power and 193 participants per arm for 90% power. The 80% column means the planning calculation targets an 80% chance of detecting the stated effect under its assumptions; the 90% column uses a higher target chance. Smaller effects need more participants to reach the same power target.

The sample-size curve expresses the same planning relationship visually: as the effect to be detected becomes smaller, the required participant count increases. These figures are planning illustrations based on the observed trial effect, not observed power. They do not establish that the trial was designed using these assumptions, and they should not be treated as a substitute for the trial’s unreported original design rationale.

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 = 0.409; treatment proportion p₁ = 0.738; average p̄ = 0.573.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6995 = 1.3709.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6598 = 0.5553.
4. n = (1.3709 + 0.5553)² / (0.3285)² = 34.4, rounded up to 35 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 <- 0.409090909090909                          # control proportion
p1 <- 0.737588652482269                          # 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(4091646)
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 = 35 (80% power), 46 (90% power)
 75% of observed effect: n per arm = 64 (80% power), 85 (90% power)
 50% of observed effect: n per arm = 145 (80% power), 193 (90% power)
power.prop.test: 34.4 
Simulated power at n = 35 per arm: 0.802 (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’s reported primary comparison used the Cochran-Mantel-Haenszel method and gave an odds ratio of 4.95, with a 95% confidence interval from 2.51 to 9.76 and p < 0.001. The registry record identifies that as the reported superiority analysis. It also states that odds ratios and p-values were calculated using multiple imputation of missing values.

The unadjusted recalculation from the posted arm summaries gives an odds ratio of 4.06, with a 95% confidence interval from 2.189 to 7.53 and p < 0.001. It is a simple comparison without the sponsor’s Cochran-Mantel-Haenszel method. The two estimates are related but should not be presented as if they were the same analysis; the registry record does not report the sponsor’s strata or full analytic details needed to reproduce its result.

The posted record indicates no discrepancy flag. The sponsor’s reported analysis is therefore the primary account of the trial’s inferential result, while the recalculation serves as a transparent, unadjusted comparison based on posted summaries. Differences in the estimates do not, by themselves, imply inconsistency or error.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists seven secondary outcomes in addition to the primary endpoint and reports eight outcome measures and 18 analyses. The secondary outcomes concern IGA success at Weeks 2 and 4, changes and success in erythema and scaling assessments, and change and success in the Worst Itch Numeric Rating Scale. Considering several outcomes and analyses can increase the chance that at least one result appears statistically notable by chance when each is tested separately.

The registry record does not report whether the primary and secondary analyses used a multiplicity adjustment, a prespecified testing hierarchy, or another procedure to control the overall false-positive risk. It also does not report which secondary analyses were designated confirmatory or exploratory. Consequently, the primary endpoint’s reported p-value should not be assumed to account for testing across the other outcomes, and secondary findings would need to be interpreted with their testing context in mind.

The primary-outcome population is described as all randomized participants except those who missed Week 8 assessment because of COVID-19 disruption. The IGA scores are based on observed data, while the odds ratio and p-values were calculated using multiple imputation for missing values. The record does not report the number or pattern of missing values beyond the stated COVID-19 exception, the imputation model, the assumptions about missingness, or sensitivity analyses. These details matter because inferences can change when missing observations are handled under different assumptions.

The record does not fully define an analysis population beyond the stated primary-outcome description, nor does it report other analysis-population conventions. It does not report an interim-analysis plan or the trial’s original sample-size justification. Absence of those details from the registry record does not establish that such procedures were or were not used; it means they cannot be assessed from the record.

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 5% reporting threshold.

The serious adverse event figures report zero serious adverse events among 154 participants at risk in the roflumilast foam 0.3% group and zero among 72 participants at risk in the vehicle foam group. The record also reports zero other adverse events and zero deaths in both groups. No top serious-event terms are listed.

These are counts for the safety populations recorded in the registry, which differ from the outcome counts used for the Week 8 IGA analysis. The figures describe the events reported during the study and within the listed at-risk groups. Zero reported events does not establish that an event is impossible, or that the treatments have identical safety profiles; rare events and events outside the study’s observation period cannot be ruled out by these counts alone.

The registry record does not provide further detail in these figures about event definitions, severity grading, timing, or the duration of safety follow-up beyond the study description. The counts should therefore be read as a concise summary of reported adverse events, not as a complete assessment of all potential safety outcomes.

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

The primary outcome shows that more participants in the roflumilast arm met the defined IGA success criterion than in the vehicle arm, based on the posted counts: 104 of 141 and 27 of 66, respectively. The unadjusted risk difference is 0.329, and the reported confidence interval from 0.189 to 0.468 indicates the statistical uncertainty around that absolute comparison under the recalculation’s assumptions. The sponsor’s Cochran-Mantel-Haenszel analysis reports an odds ratio of 4.95, with a 95% confidence interval from 2.51 to 9.76 and p < 0.001.

These results describe the study’s comparison at Week 8 for its defined IGA endpoint. They do not quantify every aspect of disease severity, nor do they establish what would happen at other follow-up times or in populations not represented in the trial. The endpoint combines a specified IGA status with improvement from baseline; it is not a measure of every symptom or clinical outcome.

The results also do not prove that the observed difference is free of bias or that the same estimates would arise under every analytic approach. The sponsor’s reported method and the unadjusted recalculation differ, and details of the sponsor’s strata and missing-data model are not reported in the registry record. The primary-outcome population also excludes participants who missed Week 8 assessment because of COVID-19 disruption.

The safety summary records no serious adverse events, other adverse events, or deaths in the listed at-risk groups. Such counts are bounded by the study population and its observation period and cannot establish the absence of all possible harms. The outcome and safety results are statistical descriptions of this completed study, not medical advice or a guarantee of a particular individual outcome.

17. Why This Trial Matters Statistically

This trial offers a clear example of why the choice of effect measure matters. The same binary Week 8 endpoint can be expressed as a risk difference or an odds ratio, and those statistics describe different contrasts. The risk difference of 0.329 communicates an absolute probability-scale separation, while the sponsor’s odds ratio of 4.95 compares odds using a Cochran-Mantel-Haenszel analysis. Neither measure should be substituted for the other without explaining its scale and method.

The comparison also illustrates the distinction between a trial’s reported analysis and an unadjusted recalculation. The sponsor’s reported odds ratio is 4.95, whereas the unadjusted recalculation is 4.06. Both are accompanied by confidence intervals, but they arise from different methods. Reporting each with its method helps readers understand why results need not match exactly and why summary data may not reproduce a stratified analysis.

Missing-data handling is another important part of interpretation. The record states that IGA scores were observed, while odds ratios and p-values used multiple imputation. It also identifies an exception for participants who missed the Week 8 assessment because of COVID-19 disruption. Without the imputation details and sensitivity analyses, readers cannot assess how robust the inferential results are to alternative assumptions.

Finally, the secondary outcomes and 18 analyses raise a multiplicity question. The registry record does not report whether an adjustment or testing hierarchy was used. That absence matters when interpreting findings across multiple endpoints, even though the primary comparison can still be described on its own terms. Statistical interpretation depends not only on the numerical estimate but also on the endpoint definition, analysis method, missingness, and broader testing context.

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 registry record does not report the strata used in the sponsor’s Cochran-Mantel-Haenszel analysis, so that analysis cannot be independently reconstructed from the posted arm summaries. The unadjusted recalculation provides a separate reference but does not replace or reproduce the sponsor’s method. The record also does not report the multiple-imputation model, the amount and pattern of missing data beyond the stated COVID-19 exception, or sensitivity analyses.

The primary-outcome population excludes participants who missed the Week 8 assessment because of COVID-19 disruption. This exception is important to the interpretation of the endpoint counts and raises questions that cannot be resolved from the registry record, including how those missing outcomes were represented in each part of the analysis. The endpoint description distinguishes observed IGA scores from inferential estimates using imputation, but provides no further technical detail.

The record lists seven secondary outcomes and 18 analyses, but does not report whether multiplicity was controlled or how confirmatory analyses were prioritized. The trial’s original sample-size justification and design assumptions are also not reported; the available sample-size figures are illustrations calculated from the observed effect, rather than the original design rationale.

The safety figures report zero events for the listed categories, but do not provide further detail about event definitions, timing, or follow-up in those counts. The results are limited to the study’s population, 8-week treatment period, and reported assessment. The registry record does not support conclusions about longer-term outcomes or populations beyond those studied.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Safety and Efficacy of ARQ-154 Foam in Subjects With Seborrheic Dermatitis — NCT04091646.
• Registry record last updated 2023-07-03; status last verified 2023-06.
• Results first posted 2023-07-03.
• 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

NCT04091646 is a completed randomized, quadruple-masked, parallel-group, vehicle-controlled Phase 2 study; its official title describes it as Phase 2b. It compared roflumilast foam 0.3% applied once daily for 8 weeks with matched inactive vehicle foam applied once daily for 8 weeks in participants with seborrheic dermatitis.

The primary endpoint was IGA success at Week 8, defined as a score of 0 or 1 with at least a 2-grade improvement from baseline. The posted counts were 104 of 141 in the roflumilast arm and 27 of 66 in the vehicle arm. The sponsor-reported Cochran-Mantel-Haenszel odds ratio was 4.95, with a 95% confidence interval from 2.51 to 9.76 and p < 0.001. An unadjusted recalculation gave an odds ratio of 4.06 and a risk difference of 0.329.

The registry record lists zero serious adverse events, other adverse events, and deaths in both safety groups. Details on the original sample-size rationale, multiplicity procedures, and imputation methods are not reported in the registry record.