Bioequivalence Study of Two Treatments in the Treatment of Inflammatory Lesions of Rosacea on the Face: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Bioequivalence Study of Two Treatments in the Treatment of Inflammatory Lesions of Rosacea on the Face (NCT02800148), a randomized phase 3 study. The primary outcome is Percent Change (Reduction) of Lesion Count From Day 1.

2. Clinical Question

The clinical question is whether the lesion-count response reported for the test azelaic acid foam is sufficiently similar to the response for Finacea Foam under the study’s bioequivalence approach, while the placebo arm provides additional context for the endpoint. The registry record does not state the formal equivalence margin, the detailed eligibility criteria, or the original rationale for selecting the endpoint. It also does not report secondary outcomes. Interpretation therefore rests on the posted Day 84 summaries and the sponsor’s posted equivalence analysis, with the limits of those records kept in view.

3. Trial Design

The registry record describes a completed, randomized, double-masked, parallel-group Phase 3 study sponsored by Padagis LLC. The listed enrollment is 667. The trial concerned rosacea and compared three arms: Azelaic Acid Foam, Finacea Foam, and Placebo Foam. The summary states that the purpose was to compare the bioequivalence of Perrigo’s azelaic acid foam product with Finacea Foam for treatment of inflammatory lesions of rosacea.

Randomization indicates that assignment to study arms was described as random, while double masking indicates that the record identifies the study as double-masked. The registry record does not specify who was masked, how the random sequence was generated, whether allocation was concealed, or how masking was maintained. The parallel design indicates that the listed treatment groups were compared as separate arms rather than as a crossover sequence; details of the treatment period and visit schedule beyond the primary endpoint timeframe are not reported in the registry record.

The primary outcome was a continuous measure: percent change (reduction) of lesion count from Day 1, with the reported timeframe at Day 84. Posted endpoint summaries give the number analyzed, mean, and standard deviation for each arm. These endpoint counts are 178 for Azelaic Acid Foam, 181 for Finacea Foam, and 178 for Placebo Foam. The record separately reports safety groups at risk, and does not explain how those counts relate to the endpoint analysis counts.

The study started in 2016-11, reached primary completion in 2017-10, and is marked completed. The original sample-size justification, detailed protocol, treatment duration beyond the stated assessment timing, planned analysis populations, and original statistical analysis plan 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 Percent Change (Reduction) of Lesion Count From Day 1, measured over Day 84.

The primary endpoint is percent change (reduction) in lesion count from Day 1, assessed at Day 84. It is a continuous outcome: each participant’s response is represented on a percentage scale, and the registry posts an arm-level mean and standard deviation. A lesion count focuses on the number of inflammatory lesions rather than, for example, a symptom rating or a global assessment. Expressing change as a percentage relates the Day 84 result to the Day 1 count, although the registry record does not give the calculation formula or details of how baseline values were handled.

This type of measure is used to quantify change in the feature the study is intended to compare: inflammatory lesions of rosacea on the face. The arm means describe the average reported reduction, while the standard deviations describe variation among observations within each arm. They answer different questions: the mean locates the group’s average result, and the standard deviation indicates how dispersed the individual results were around that average.

The posted endpoint is specifically tied to Day 84. It does not by itself describe the course of response at other times, durability after that visit, or outcomes not measured by lesion count. The registry record does not provide secondary endpoint results, baseline lesion-count summaries, or details about missing Day 84 observations. These omissions limit how fully the endpoint can be reconstructed or interpreted beyond the posted summaries.

7. Results Posted in the Registry

• Azelaic Acid Foam: mean 61.14 versus 49.43 on control; difference 11.71 (95% CI 3.52 to 19.90), standardized effect d = 0.30; z-test p = 0.005.
• Finacea Foam: mean 57.27 versus 49.43 on control; difference 7.84 (95% CI -0.40 to 16.08), standardized effect d = 0.20; z-test p = 0.062.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary measure is continuous, so the registry reports a mean and standard deviation for each treatment arm. The mean describes the average percent reduction in lesion count at Day 84. The standard deviation describes the spread of participant results within an arm; it is not the uncertainty in the mean difference between arms. Larger within-arm variation can make a treatment contrast less precise when sample sizes are otherwise similar.

The simple pairwise contrasts are unadjusted recalculations from the posted arm summaries. Each mean difference compares an active arm with the placebo arm. The reported differences are 11.71 for Azelaic Acid Foam versus Placebo Foam and 7.84 for Finacea Foam versus Placebo Foam. Their confidence intervals and p-values describe these recalculated contrasts, not the sponsor’s ratio-based equivalence analysis. The recalculations use the posted means and dispersion summaries and are not a substitute for a more detailed analysis using participant-level data or a full trial analysis plan.

The recalculated pooled standard deviations are 39.4 for the Azelaic Acid Foam comparison and 39.74 for the Finacea Foam comparison. A pooled standard deviation combines information about variability in the two groups being compared. The posted standardized effect estimates are 0.297 and 0.197, respectively. In general, a standardized effect expresses a mean contrast relative to a measure of variability, which can help describe the size of a contrast on a scale that is less dependent on the endpoint’s original units. These values do not replace the original-scale mean differences and do not establish clinical importance.

The recalculated standard errors for the placebo and azelaic acid arm means are 3.331 and 2.52; for the placebo and Finacea means they are 3.331 and 2.565. In general, a standard error represents uncertainty in an estimate, rather than the spread of individual observations. Confidence intervals use uncertainty information to indicate a range of estimates compatible with the data and the calculation method. Wider intervals indicate less precision. The recalculated intervals are 3.524 to 19.9 for Azelaic Acid Foam versus placebo, and -0.400 to 16.08 for Finacea Foam versus placebo.

The p-values for those recalculations are unadjusted: 0.005 and 0.062, respectively. A p-value summarizes how unusual the observed data, or more extreme data, would be under a specified null model. It is not the probability that a treatment effect is true, and it does not convey the magnitude or practical importance of an effect. Because the values are unadjusted, they do not account for a family of multiple comparisons. The registry record does not report a multiplicity procedure for the trial’s analyses.

The sponsor’s posted comparison answers a different question. It uses Fieller’s method and reports an equivalence ratio of 107 with a 90% confidence interval from 96.1 to 115.5. In general, equivalence analysis asks whether the uncertainty around a comparison is contained within prespecified bounds that represent acceptable similarity. Fieller’s method is one approach for constructing uncertainty intervals for a ratio. The ratio interval alone cannot establish whether the formal equivalence requirement was met, because the equivalence bounds and decision rule are not reported in the registry record. The sponsor’s analysis is the relevant posted analysis for the sponsor’s equivalence question; the unadjusted mean-difference calculations are descriptive additional comparisons against placebo.

Over-dispersion is a general concern when data vary more than a model assumes: standard errors and intervals can then be too narrow if the extra variation is not accounted for. The posted summaries show substantial variability in each arm, but the registry record does not identify a model that assumes a particular dispersion structure for the primary analysis. The endpoint is continuous, and it would not be appropriate to infer a count-data model merely because the underlying feature is a lesion count.

The sample-size planning illustrations use the observed recalculated effect and the stated planning assumptions: two-sided significance level 0.05, equal allocation between the two arms, normal approximation, and an effect set to the stated fraction of the observed effect. These are planning calculations rather than the trial’s original design justification. The original sample-size assumptions and any original interim-analysis plan are not reported in the registry record. The planning values therefore explain how hypothetical sample sizes change under the stated assumptions; they do not tell us what methods were prespecified or used in the trial.

One posted primary outcome measure and one posted analysis are identified, and no secondary outcome results are listed. The registry record does not report detailed analysis populations, an imputation method, covariate adjustment, baseline adjustment, handling of protocol deviations, or the analysis plan’s treatment of missing endpoint data. Those items cannot be reconstructed from the group summaries.

10. Confidence Intervals and Precision

The recalculated Azelaic Acid Foam versus placebo mean difference is 11.71, with a confidence interval from 3.524 to 19.9. The interval does not include zero and indicates that the data are compatible with a range of positive mean differences under the recalculation. Its width also matters: the point estimate is not known with the exactness implied by a single number.

For Finacea Foam versus placebo, the recalculated mean difference is 7.84, with a confidence interval from -0.400 to 16.08. This interval includes zero and also includes positive values. It therefore expresses uncertainty about the direction and size of the mean contrast. The corresponding unadjusted p-value is 0.062, but the interval is more informative about the range of estimates compatible with the calculation than a binary reading of the p-value alone.

In general, a confidence interval is a range produced by a statistical procedure that reflects sampling uncertainty under its assumptions. It is not a range containing a fixed proportion of individual participants’ responses, nor does it account automatically for unreported sources of uncertainty such as missing data or analysis choices. The posted endpoint standard deviations describe participant-level spread, while the recalculated confidence intervals concern uncertainty in group contrasts.

The sponsor’s ratio estimate is 107, with a 90% confidence interval from 96.1 to 115.5. This interval gives the uncertainty for the sponsor’s reported ratio analysis. It cannot be judged against an equivalence requirement without the prespecified equivalence bounds, which are not reported in the registry record. The confidence level differs from the confidence intervals for the unadjusted mean differences, so these results should not be treated as interchangeable presentations of the same calculation.

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 values are participants per arm, not total events. They apply to the two-arm recalculated comparisons and use two-sided significance level 0.05, equal allocation between arms, and a normal approximation. The target effect is set to 100%, 75%, or 50% of the observed effect, depending on the planning scenario. These assumptions describe planning illustrations and are not reported as the trial’s original design assumptions.

The 80% power column gives the estimated participants per arm under those assumptions for a hypothetical design with an 80% chance of detecting the specified effect if that effect is the true one and the model assumptions hold. The 90% power column gives the corresponding per-arm planning figure for a higher target probability of detection. Neither column reports what power the completed trial actually had. This is not observed power.

The figures increase as the assumed effect becomes smaller: planning for 75% or 50% of the observed effect requires more participants per arm than planning for 100% of that effect. In general, smaller differences are harder to distinguish from sampling variation, so more participants are needed to achieve the same target power under otherwise unchanged assumptions. The illustrations are based on observed recalculated effects, which are uncertain estimates themselves; planning around a fraction of an observed effect does not make that effect known or guaranteed.

The values are not a reconstruction of the trial’s enrollment target or its original sample-size calculation. The registry record does not report the original design assumptions or sample-size justification. The planning numbers are best read as conditional examples: they answer how large a two-arm study might be under the stated assumptions, not how the completed study was designed.

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 = 11.710; pooled standard deviation σ = 39.403.
2. n = 2 × (1.96 + 0.842)² × 39.403² / 11.710² = 177.7, rounded up to 178 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 <- 11.71                      # observed difference in means
sigma <- 39.4027479879259                     # 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(2800148)
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 = 178 (80% power), 238 (90% power)
 75% of observed effect: n per arm = 316 (80% power), 424 (90% power)
 50% of observed effect: n per arm = 711 (80% power), 952 (90% power)
power.t.test: 178.7 
Simulated power at n = 178 per arm: 0.798 (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. Analyses Reported by the Sponsor

The sponsor’s posted analysis compares Azelaic Acid Foam with Finacea Foam using Fieller’s method for an equivalence ratio. It reports a ratio of 107 and a 90% confidence interval from 96.1 to 115.5. This is the sponsor’s own analysis and is the relevant posted result for the study’s stated bioequivalence question.

The separate recalculations compare each active arm’s mean percent reduction with Placebo Foam. They report unadjusted mean differences of 11.71 for Azelaic Acid Foam and 7.84 for Finacea Foam, with their own confidence intervals and p-values. These calculations are not a reproduction of the sponsor’s ratio method, do not directly test equivalence between the two active treatments, and should not be used in place of the sponsor’s analysis for that question.

The registry record does not report the equivalence margin or decision rule needed to assess the ratio interval against the formal equivalence criterion. Thus the ratio and interval can be stated, but the formal basis for an equivalence conclusion cannot be independently evaluated from the registry record alone. There is no reported discrepancy between the posted results and the simple recalculations.

14. Multiplicity, Missing Data and Analysis Populations

The registry record lists one primary outcome measure and one posted analysis, with no secondary outcome measures posted. It does not report a multiplicity adjustment or a plan for controlling error across multiple comparisons. The recalculated p-values are explicitly unadjusted. Because comparisons involving multiple arms can raise multiplicity questions, their interpretation should remain tied to the particular contrast and calculation reported rather than being treated as a fully adjusted trial-wide conclusion.

Details of missing endpoint data are not reported in the registry record. The posted outcome summaries give analysis counts of 178 for Azelaic Acid Foam, 181 for Finacea Foam, and 178 for Placebo Foam, but do not state why any enrolled participants are absent from those summaries, whether data were missing, or how missing observations were handled. No imputation procedure, sensitivity analysis, or missing-data assumption is reported.

The analysis population is also not identified. The record does not state whether the primary analysis used an intention-to-treat, modified intention-to-treat, per-protocol, or other defined population. It does not report the population used in the sponsor’s equivalence analysis, or how protocol deviations and treatment discontinuations were treated. The arm summaries therefore cannot establish which participants were included under the analysis rules.

These are reporting limits, not evidence that a particular method was or was not used. The original statistical analysis plan and further details are not reported in the registry record. Without them, the posted results do not allow an assessment of prespecification, multiplicity handling, missing-data assumptions, or consistency between analysis populations.

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.

Most frequent serious adverse event terms

Serious events with the highest arm-level rate: aseptic meningitis (0.5%), major depression (0.5%), suicidal ideation (0.5%), esophageal cancer (0.4%).

The registry reports serious adverse event counts among the safety groups at risk. For Azelaic Acid Foam, 224 were at risk and 1 had a serious adverse event. For Finacea Foam, 224 were at risk and 0 had a serious adverse event. For Placebo Foam, 219 were at risk and 2 had serious adverse events. The record lists 0 deaths in each group and 0 other adverse events in each group as reported in the posted safety fields.

These are counts, not comparisons adjusted for exposure time or differences in follow-up. The registry record does not provide event timing, participant-level detail, seriousness criteria, or a causal assessment. The safety groups at risk are reported separately from the endpoint analysis counts, and the record does not explain the relationship between these sets of counts.

The listed serious-event terms are Aseptic Meningitis at 0.5%, Major Depression at 0.5%, Suicidal ideation at 0.5%, and Esophageal Cancer at 0.4%. The registry record does not link these listed terms to a specific treatment arm in the posted summary. They should therefore be read as reported serious-event terms and percentages, not assigned to a particular arm from these data alone.

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

The posted Day 84 results describe average percent reduction in lesion count in three randomized arms. The mean values were 61.14 for Azelaic Acid Foam, 57.27 for Finacea Foam, and 49.43 for Placebo Foam. The arm-level standard deviations indicate that individual results varied around those means. The unadjusted comparisons with placebo provide estimates of mean differences and their uncertainty, while the sponsor’s ratio analysis addresses the distinct comparison of the two active treatments.

The sponsor reports an equivalence ratio of 107, with a 90% confidence interval from 96.1 to 115.5. A formal interpretation of equivalence depends on comparing that interval with prespecified bounds. Those bounds and the associated decision rule are not reported in the registry record, so the ratio interval alone does not permit an independent determination of whether the formal equivalence criterion was met. The registry summary does not state the sponsor’s conclusion in the posted analysis field.

The recalculated comparisons against placebo are also not evidence of equivalence between the active treatments. They are unadjusted analyses of mean differences, not the sponsor’s Fieller ratio analysis. Their p-values do not measure clinical importance, and their intervals do not account for analysis features that are not described in the registry record.

These results do not establish effects at other assessment times, outcomes beyond lesion count, or responses in participant subgroups. The registry record does not report secondary outcome results, detailed eligibility criteria, analysis populations, missing-data methods, or the original statistical plan. Nor do the posted summaries establish causation beyond the trial’s design and analyses as described. The most defensible reading stays close to the Day 84 estimates and their uncertainty, while recognizing that essential details for a complete equivalence assessment are not reported in the registry record.

17. Why This Trial Matters Statistically

This study illustrates why a clinical trial can have more than one relevant statistical comparison. The sponsor’s central question concerns equivalence between Azelaic Acid Foam and Finacea Foam, and the posted analysis uses a ratio with Fieller’s method. The additional recalculations compare each active arm with placebo on the mean percentage reduction. Those contrasts provide different information and cannot be substituted for the sponsor’s equivalence analysis.

It also illustrates why effect estimates should be read alongside uncertainty. The two recalculated mean differences are 11.71 and 7.84, but their confidence intervals differ in whether they include zero and in the range of values they allow. The interval for Finacea Foam versus placebo includes both negative and positive values, while the interval for Azelaic Acid Foam versus placebo lies above zero. The point estimates alone do not convey this distinction in precision.

The record further highlights the importance of reporting equivalence margins, analysis populations, missing-data methods, and multiplicity handling. Without the equivalence bounds, the sponsor’s ratio interval cannot be evaluated against the formal criterion. Without the analysis and missing-data details, readers cannot fully assess how the posted endpoint summaries were produced.

Finally, the study includes a placebo arm and a sponsor-focused active-treatment comparison, while reporting only one primary endpoint analysis and no secondary results. Careful separation of these questions helps prevent an unadjusted comparison from being mistaken for the trial’s stated equivalence analysis, or an endpoint mean from being mistaken for a complete account of the 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.

The registry record gives a limited description of the trial methods. It identifies randomization, double masking, and a parallel design, but does not report sequence generation, allocation concealment, masking roles, or other implementation details. Arm descriptions are not populated with further information. The record also does not provide detailed eligibility criteria, baseline participant characteristics, or baseline lesion-count summaries.

The primary endpoint is reported at Day 84, and no other endpoint results are posted. The outcome summary provides arm-level means, standard deviations, and analysis counts, but not individual data, distributions, or results at other visits. This limits independent evaluation of the endpoint’s behavior and prevents assessment of response patterns over time. The calculation details for percent change are not reported in the registry record.

The sponsor’s equivalence analysis gives a ratio and a 90% confidence interval but does not report the equivalence bounds or decision rule. This prevents an independent assessment against the formal equivalence criterion. The recalculated mean differences are unadjusted and do not replace that analysis. The record does not explain whether covariates, baseline values, or other design features were included in the sponsor’s analysis.

Important analysis details are also absent: the analysis population, missing-data approach, handling of protocol deviations, and multiplicity plan are not reported in the registry record. Safety counts are presented separately from endpoint analysis counts, without an explanation of their relationship. The serious-event term list is not mapped to specific arms in the posted summary. These limitations constrain interpretation of both efficacy summaries and safety counts, without establishing that any particular method was absent from the full study record.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Bioequivalence Study of Two Treatments in the Treatment of Inflammatory Lesions of Rosacea on the Face — NCT02800148.
• Registry record last updated 2021-11-08; status last verified 2021-11.
• Results first posted 2020-12-09.
• 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

NCT02800148 is a completed, randomized, double-masked, parallel-group Phase 3 study sponsored by Padagis LLC. The registry record lists enrollment of 667 and describes a comparison of azelaic acid foam, Finacea Foam, and Placebo Foam for inflammatory lesions of rosacea on the face. The primary endpoint is percent reduction in lesion count from Day 1 at Day 84.

The posted sponsor analysis reports an equivalence ratio of 107, with a 90% confidence interval from 96.1 to 115.5. Unadjusted recalculations compare each active arm with placebo. The formal equivalence bounds, original design assumptions, analysis populations, missing-data methods, and multiplicity plan are not reported in the registry record. Interpretation should distinguish the sponsor’s ratio analysis from the separate mean-difference recalculations.