This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for Clinical End Point Study of Generic Adapalene and Benzoyl Peroxide Gel Versus Epiduo® Forte Gel in Treatment of Acne Vulgaris (NCT02651220), a randomized phase 3 study. The primary outcome is Percent Change From Baseline to Week 12 in the Number of Inflamed Lesions..
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02651220 |
| Phase | Phase 3 |
| Condition | Acne |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Quadruple |
| Enrollment | 1001 |
| Arms in the primary outcome | 3 |
| Lead sponsor | Actavis Inc. |
| Results posted | Yes |
2. Clinical Question
Population
People with acne vulgaris were enrolled. The registry record does not report further eligibility details, such as age range or baseline disease severity. The primary endpoint was assessed in the per-protocol population; the criteria for that population are not reported in the registry record.
Intervention
Adapalene and benzoyl peroxide gel, 0.3%/2.5% w/w, was compared with the branded active gel and with vehicle. The study description identifies the adapalene and benzoyl peroxide product as a generic formulation. The registry record lists topical gel interventions.
Comparator
The active comparator was Epiduo® Forte Gel, 0.3%/2.5% w/w. Vehicle topical gel served as the control for the comparisons used in the posted primary endpoint summaries. The study also included a reported comparison between the active formulations.
Primary question
At week 12, what was the percent change from baseline in the number of inflamed lesions in each group, and how did the mean change with each active gel compare with vehicle? The registry record identifies this as a continuous endpoint analyzed in the per-protocol population.
The registered study was designed to evaluate therapeutic equivalence and safety of the generic adapalene and benzoyl peroxide gel relative to Epiduo® Forte. The posted primary outcome is a lesion-count change measure, while the registry also reports an active-to-active equivalence analysis for bioavailability. These are different outcomes: the lesion endpoint describes change in inflamed lesions, whereas the bioavailability analysis concerns the active formulations. The record does not provide enough detail to treat the bioavailability result as a direct statistical test of equivalence on the primary lesion endpoint.
The question is also framed by a vehicle group. That comparison helps distinguish change observed with an active gel from change observed with the topical vehicle over the study period. The registry record does not report participant demographic characteristics, the study sites, or further eligibility criteria, so the population represented by the results cannot be described more specifically from this record.
3. Trial Design
This was a randomized, quadruple-masked, parallel-group phase 3 study. The registry record lists acne as the condition and Actavis Inc. as the sponsor. The study description calls it a double-blind, placebo-controlled, multiple-site clinical study; the registry design fields separately identify quadruple masking. The record does not explain how masking was implemented or who was included in the masking description.
The registered enrollment was 1001. The study status is completed, with a start date of 2015-11 and primary completion in 2016-04. These are registry dates and do not by themselves describe the timing of individual participants’ treatment or follow-up. The primary outcome timeframe is 12 weeks.
Three groups are listed: adapalene and benzoyl peroxide gel, Epiduo® Forte Gel, and vehicle topical gel. The primary result is reported for the per-protocol population. The available record does not describe the allocation ratio, the randomization procedure, the concealment process, treatment adherence, or the criteria used to define the per-protocol population. Nor does it report whether participants were analyzed according to assigned group for the primary endpoint.
The trial’s stated purpose was to evaluate therapeutic equivalence and safety of the generic active gel relative to Epiduo® Forte. The primary endpoint, however, is percent change from baseline to week 12 in inflamed lesion count. A secondary outcome records clinical success based on the investigator’s global assessment at week 12. There are three posted outcome measures and three analyses in the record, but detailed methods for every analysis are not given. The original sample-size justification and the study’s prespecified statistical plan are not reported in the registry record.
Randomization and masking are design features intended, in general, to reduce bias in group comparisons. Their presence in a registry description does not establish how well they were implemented. The results should therefore be interpreted as posted, with the distinction between the registered design and the statistical details actually reported kept in view.
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.
Before assignment: 1001 patients were randomized, 24 did not receive any study medication.
Overall Study
| Stage | Adapalene and Benzoyl Peroxide Gel, 0.3%/2.5% w/w | Epiduo® Forte Gel 0.3%/2.5% w/w | Vehicle Topical Gel |
|---|---|---|---|
| STARTED | 337 | 335 | 329 |
| COMPLETED | 314 | 308 | 300 |
| NOT COMPLETED | 23 | 27 | 29 |
Reasons for not completing this period:
| Reason | Adapalene and Benzoyl Peroxide Gel, 0.3%/2.5% w/w | Epiduo® Forte Gel 0.3%/2.5% w/w | Vehicle Topical Gel |
|---|---|---|---|
| Adverse Event | 1 | 5 | 1 |
| Lost to Follow-up | 8 | 14 | 14 |
| Non-Compliance with Study Drug | 4 | 0 | 1 |
| Pregnancy | 1 | 0 | 1 |
| Protocol Violation | 0 | 0 | 1 |
| Withdrawal by Subject | 5 | 6 | 8 |
| Miscellaneous | 4 | 1 | 2 |
| Withdrawal by Parent/Guardian | 0 | 1 | 1 |
Analysis population for the primary outcome, as defined in the registry: Using the Per Protocol Population
5. Baseline Characteristics
The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.
Population: Data is presented here for the Safety Population
| Characteristic | Unit | Adapalene and Benzoyl Peroxide Gel, 0.3%/2.5% w/w | Epiduo® Forte Gel 0.3%/2.5% w/w | Vehicle Topical Gel | Total |
|---|---|---|---|---|---|
| Participants analysed | 332 | 323 | 322 | 977 | |
| Age, Continuous | years | 22.5 (SD 7.1) | 22.5 (SD 7.1) | 22.5 (SD 7.0) | 22.5 (SD 7.1) |
| Sex: Female, Male: Female | Participants | 197 | 202 | 215 | 614 |
| Sex: Female, Male: Male | Participants | 135 | 121 | 107 | 363 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 139 | 148 | 134 | 421 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 193 | 175 | 188 | 556 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 3 | 0 | 0 | 3 |
| Race (NIH/OMB): Asian | Participants | 25 | 18 | 16 | 59 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 1 | 1 | 2 |
| Race (NIH/OMB): Black or African American | Participants | 111 | 114 | 123 | 348 |
| Race (NIH/OMB): White | Participants | 186 | 187 | 175 | 548 |
| Race (NIH/OMB): More than one race | Participants | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 7 | 3 | 7 | 17 |
6. Primary Endpoint
The registry lists the primary outcome as Percent Change From Baseline to Week 12 in the Number of Inflamed Lesions., measured over 12 weeks.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | percentage of change from baseline |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is the percent change from baseline to week 12 in the number of inflamed lesions. It is a continuous measure, reported as a group mean with a standard deviation, and the stated analysis population is the per-protocol population. A negative percent change represents a decrease from baseline; more negative group means indicate larger average decreases in the measured lesion count.
Lesion counts provide a direct measure of one aspect of acne severity and can be used to compare average changes between randomized groups. A continuous endpoint retains information about the magnitude of change across participants rather than reducing every participant to a yes-or-no response. That can be useful when the research question concerns the average degree of change. This is a general explanation of the endpoint type, not a claim about how the study team chose or validated the measure.
The posted group means are -74.2 for adapalene and benzoyl peroxide gel, -73.0 for Epiduo® Forte Gel, and -30.6 for vehicle. The standard deviations are 25.0, 27.8, and 32.7, respectively. These values describe the observed group summaries; they do not reveal the distribution of individual participant outcomes. The registry record does not give baseline lesion-count summaries, endpoint-assessment procedures, or details about how percent change was calculated for participants with missing measurements.
The primary endpoint should also be distinguished from the secondary clinical-success outcome, which is based on the investigator’s global assessment. One is a continuous lesion-change measure and the other is a categorical response measure. They answer related but non-identical questions.
7. Results Posted in the Registry
- Adapalene and Benzoyl Peroxide Gel, 0.3%/2.5% w/w: mean -74.20 versus -30.60 on control; difference -43.60 (95% CI -48.42 to -38.78), standardized effect d = -1.50; z-test p = <0.001.
- Epiduo® Forte Gel 0.3%/2.5% w/w: mean -73.00 versus -30.60 on control; difference -42.40 (95% CI -47.44 to -37.36), standardized effect d = -1.40; z-test p = <0.001.
Mean difference: Adapalene and Benzoyl Peroxide Gel, 0.3%/2.5% w/w
95% CI: -48.42 to -38.78
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Percentage of Patients With a Clinical Response of "Clinical Success" Using the Investigator's Global Assessment (IGA) at Week 12 | Binary Endpoint | Risk difference | +29.2 pts (23.6 to 34.8) | 28 per arm |
Percentage of Patients With a Clinical Response of "Clinical Success" Using the Investigator's Global Assessment (IGA) at Week 12
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Adapalene and Benzoyl Peroxide Gel, 0.3%/2.5% w/w: 33.8% (112/331) versus 4.7% (15/321) on control; risk difference 29.2 percentage points (95% CI 23.6 to 34.8), risk ratio 7.24 (4.32–12.14); unadjusted two-proportion z-test p = <0.001.
- Epiduo® Forte Gel 0.3%/2.5% w/w: 33.0% (106/321) versus 4.7% (15/321) on control; risk difference 28.3 percentage points (95% CI 22.7 to 34.0), risk ratio 7.07 (4.21–11.86); unadjusted two-proportion z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Adapalene and Benzoyl Peroxide Gel, 0.3%/2.5% w/w than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Epiduo® Forte Gel 0.3%/2.5% w/w than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary outcome is clinical success according to the investigator’s global assessment at week 12. Across the posted group summaries, the active-treatment groups have more participants classified as clinical successes than the vehicle group. The registry also reports an ANOVA superiority analysis for the generic active gel versus vehicle. This broad direction is consistent with the primary endpoint pattern, in which the active groups’ mean percent changes in inflamed lesions were more negative than the vehicle mean.
The two outcomes are related in that both concern acne status at week 12, but they measure different things. The primary endpoint is a continuous change in inflamed lesion count, whereas clinical success is a categorical investigator assessment. Agreement in the overall direction can provide context, but it does not make the endpoints interchangeable or ensure that they capture the same participant experience.
Secondary findings generally carry less confirmatory weight than a prespecified primary result, particularly when several outcomes or comparisons are examined. Each additional test creates another opportunity for a chance finding. The registry record does not report a multiplicity adjustment, a hierarchy of secondary hypotheses, or a plan that would control the overall error rate across outcomes. The unadjusted secondary p-values therefore should be interpreted as evidence for the particular comparisons reported, not as proof that all secondary conclusions are protected from multiple testing.
The record lists one secondary outcome and gives an ANOVA result for the generic active gel versus vehicle. It does not describe the model details or how missing assessments were handled. The recalculated binary comparisons are likewise unadjusted. The secondary outcome supports the descriptive pattern across the groups but should not be used to infer unreported analyses or to substitute for a direct active-to-active test on the primary endpoint.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Percentage of Patients With a Clinical Response of "Clinical Success" Using the Investigator's Global Assessment (IGA) at Week 12
9. Statistical Interpretation
For the primary outcome, the mean percent changes were -74.2 with adapalene and benzoyl peroxide gel, -73.0 with Epiduo® Forte Gel, and -30.6 with vehicle. In each active-versus-vehicle comparison, the recalculated unadjusted mean difference is negative because the active group’s mean change was more negative than the vehicle group’s mean change. The estimated difference was -43.6 for the generic gel versus vehicle, with a 95% confidence interval from -48.42 to -38.78, and -42.4 for Epiduo® Forte versus vehicle, with a 95% confidence interval from -47.44 to -37.36. Both posted unadjusted p-values are <0.001.
These comparisons describe the observed data and their uncertainty under the simple unadjusted calculations. The intervals lie below zero, indicating that the estimated average changes in the active groups were more negative than the vehicle mean in these comparisons. Statistical evidence against a zero mean difference does not, on its own, establish the clinical importance of a difference. The registry record does not report a threshold for a clinically meaningful difference or a primary endpoint equivalence margin.
The active groups’ mean changes are close in the posted summaries, but a direct inferential conclusion about equivalence on the primary lesion endpoint cannot be drawn from their separate comparisons with vehicle. The registry reports an equivalence analysis for bioavailability between the active formulations, with a 90% confidence interval of 96.78 to 103.91 around the value 100.28. That is a different measure from the primary lesion outcome. The equivalence margins and the method used for that reported analysis are not reported in the registry record.
The secondary clinical-success outcome follows a broadly consistent direction: the posted group summaries show more participants meeting the investigator’s global-assessment definition in each active group than in vehicle. The registry reports an ANOVA superiority analysis comparing the generic active gel with vehicle, with p < 0.001. Recalculated unadjusted comparisons also have p-values <0.001. These findings are supportive context, not a replacement for the primary endpoint, and the record does not report adjustment for testing multiple outcomes or comparisons.
Interpretation is limited by the analysis population and reporting detail. The primary endpoint is labeled per protocol, but the record does not explain who qualified for that population or how missing outcome data were handled. The posted analyses therefore should not be read as a complete account of every planned analysis or as proof that all potential biases were controlled. The registry record reports no discrepancy between the posted primary summaries and the simple recalculations, but the recalculated comparisons remain unadjusted analyses based on summary statistics.
10. Statistical Methods Explained
The primary endpoint is continuous: it is a percent change, summarized by a mean and standard deviation. A mean describes the arithmetic average within a group. A standard deviation describes the spread of individual observations around that group’s mean; it is not the uncertainty of the mean itself. The primary group summaries are -74.2 with a standard deviation of 25.0 for adapalene and benzoyl peroxide gel, -73.0 with a standard deviation of 27.8 for Epiduo® Forte Gel, and -30.6 with a standard deviation of 32.7 for vehicle.
What does a mean difference represent?
A mean difference subtracts one group mean from another. The recalculated comparisons use vehicle as the reference and report -43.6 for adapalene and benzoyl peroxide gel versus vehicle, and -42.4 for Epiduo® Forte versus vehicle. Because the outcome is percent change, the negative estimates indicate that the active-group mean changes were more negative than the vehicle mean. The sign depends on the subtraction order, so the comparison should be read together with the named groups rather than by sign alone.
These mean differences are simple unadjusted recalculations from the posted summary statistics. They do not incorporate covariate adjustment, a model fitted to participant-level data, or any unreported features of the sponsor’s analysis. The registry’s discrepancy flag is false. The recalculations therefore do not identify a reported-versus-recalculated discrepancy that would require prioritizing the sponsor’s analysis on that basis.
How should the confidence intervals be read?
A confidence interval gives a range of values compatible with the observed estimate under the assumptions of the method used. In repeated use, a confidence-interval procedure is designed to cover the underlying quantity at its stated confidence level. It is not a range containing a specified proportion of individual participant outcomes, and it is not a probability statement that the fixed true effect lies inside this particular interval.
The recalculated 95% intervals for the mean differences are -48.42 to -38.78 for the generic active gel versus vehicle and -47.44 to -37.36 for Epiduo® Forte versus vehicle. Both intervals are entirely negative. That supports a difference in the direction of more negative mean change in the active group under these unadjusted calculations. The width reflects uncertainty in the estimated group contrast; it does not address unmeasured bias, adherence, missingness, or clinical importance.
What does an unadjusted p-value tell us?
A p-value is a measure of how incompatible the observed data are with a specified null hypothesis, assuming the statistical model and other relevant assumptions hold. It is not the probability that the null hypothesis is true, nor does it measure the size or importance of an effect. The primary comparisons have unadjusted p-values <0.001. “Unadjusted” means these values are not reported as corrected for the number of outcomes or comparisons being examined.
General statistical interpretation requires caution when many hypotheses are tested: the chance of at least one small p-value can increase as the number of tests grows. The registry record does not report a multiplicity adjustment or a prespecified hierarchy for interpreting outcomes. The p-values therefore describe the individual reported comparisons and should not be treated as a family-wide error-controlled conclusion.
Why does variation matter?
Participants’ outcomes vary, and the standard deviation describes this observed dispersion. In general, greater variability makes a mean less precisely estimated when other design features are held constant. The standard deviation is not the same as a standard error: a standard error describes uncertainty in an estimate, whereas a standard deviation describes variation among observations. The recalculated comparison summaries include standard errors of 1.965 and 1.481 for vehicle and generic active gel, and 1.965 and 1.658 for vehicle and Epiduo® Forte, respectively.
Over-dispersion is a general concern when outcome variability exceeds what a statistical model assumes. It can make standard errors and p-values unreliable if the model does not account for the extra variability. The posted primary endpoint uses a continuous mean and standard deviation, but the registry record does not identify the sponsor’s primary statistical model. It is therefore not possible to assess from this record whether a particular over-dispersion correction was considered or needed.
How is the secondary response analyzed?
The secondary clinical-success outcome is binary: each participant either met the investigator’s global-assessment definition of clinical success or did not. The posted counts are 112 of 331 in the generic active group, 106 of 321 with Epiduo® Forte, and 15 of 321 with vehicle. A risk difference expresses the difference between the proportions in two groups. The recalculated risk differences versus vehicle are 0.292 and 0.283, with 95% intervals of 0.236 to 0.348 and 0.227 to 0.340, respectively.
The record also lists relative risks and odds ratios for these secondary comparisons, but those are alternative ways to express associations between group assignment and a binary outcome. Different measures have different interpretations and should not be conflated. The registry reports an ANOVA superiority analysis for the generic active gel versus vehicle, with p < 0.001; its detailed specification is not reported. The secondary recalculations are unadjusted and should be read as descriptive comparisons rather than a substitute for the original analysis plan.
In general, random allocation supports comparisons between groups by reducing systematic differences at assignment, while masking may limit some expectation-related influences. Neither design feature removes uncertainty or resolves incomplete reporting. The registry record does not provide enough methodological detail to assess randomization implementation, adherence, missing-data methods, or the full statistical analysis plan.
11. Confidence Intervals and Precision
Precision concerns how narrowly an estimate is bounded by its uncertainty interval. For the primary endpoint, the recalculated mean difference for adapalene and benzoyl peroxide gel versus vehicle is -43.6, with a 95% confidence interval from -48.42 to -38.78. For Epiduo® Forte versus vehicle, the estimate is -42.4, with a 95% confidence interval from -47.44 to -37.36. The intervals are finite and lie below zero, so the posted summaries estimate the direction of the average contrast with more precision than a wide interval spanning both negative and positive values would.
Precision is not the same as validity. A narrow interval can reflect limited sampling uncertainty under the calculation while leaving open concerns about missing data, analysis-population selection, measurement, or model assumptions. The registry record does not give the primary analysis method or missing-data procedure, so the intervals should be understood as recalculated estimates rather than a full reconstruction of the sponsor’s analysis.
The active-versus-vehicle intervals do not directly quantify the uncertainty in the difference between the two active formulations. The group means are -74.2 and -73.0, but a direct confidence interval and test for the primary lesion endpoint between those active groups are not reported in the record. The separate comparisons with vehicle cannot be used as a replacement for that direct contrast.
For the reported bioavailability equivalence analysis, the registry gives a value of 100.28 and a 90% confidence interval from 96.78 to 103.91. A confidence interval can only support an equivalence interpretation relative to prespecified margins. Those margins and the analysis method are not reported in the registry record, so the interval should not be independently labeled as establishing equivalence on the primary lesion endpoint. It pertains to bioavailability, not the continuous lesion-change outcome.
Confidence intervals quantify statistical uncertainty under an analysis; they do not show the range of responses likely for an individual participant, guarantee replication, or establish clinical relevance. Clinical interpretation would also require an appropriate meaningful-difference threshold, which is not reported in the registry record.
12. Planning a Similar Trial: Sample Size
This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 7 | 10 |
| 75% of the observed effect | 13 | 17 |
| 50% of the observed effect | 28 | 38 |
The planning illustrations express sample size as participants per arm for 80% power and participants per arm for 90% power. They are not total event counts. The calculation assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set as the stated fraction of the observed effect. The trial’s own original design assumptions and sample-size justification are not reported in the registry record.
The 80% power column gives the per-arm sample size estimated to detect the specified effect with 80% power under those planning assumptions. The 90% power column gives the corresponding per-arm size for 90% power. In plain terms, power describes the chance that a study using the assumed effect and method would meet the chosen statistical criterion if that effect were the true one. These figures are planning illustrations based on observed results, not observed power.
Rows using 100% of the observed effect use the full observed difference as the planning target. Rows using 75% or 50% use smaller target effects. Smaller effects generally require more participants to distinguish them from random variation with the same power and significance level. The displayed per-arm estimates illustrate that relationship for the specified comparisons and assumptions.
These calculations should not be read as a recommendation for a future study or as evidence that the original trial was adequately sized. The calculations use the observed effect, which is uncertain and may be larger or smaller than the effect a new study would encounter. They also rely on the stated equal-allocation and normal-approximation assumptions. Different outcome definitions, analysis methods, allocation plans, missingness, or target effects could produce different planning needs. The record does not report the original design assumptions, so the illustrations cannot establish whether they match the decisions made when the trial was designed.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−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
- Observed difference Δ = -43.600; pooled standard deviation σ = 29.051.
- n = 2 × (1.96 + 0.842)2 × 29.0512 / -43.6002 = 7.0, rounded up to 7 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 <- -43.6 # observed difference in means
sigma <- 29.0511875832986 # 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(2651220)
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 = 7 (80% power), 10 (90% power)
75% of observed effect: n per arm = 13 (80% power), 17 (90% power)
50% of observed effect: n per arm = 28 (80% power), 38 (90% power)
power.t.test: 8.1
Simulated power at n = 7 per arm: 0.732 (20000 replicates)
The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| not stated | Bioavailability 100.28 | 96.78 to 103.91 | not reported |
The primary endpoint’s group summaries permit simple unadjusted recalculation of the mean differences versus vehicle. The recalculated estimates are -43.6 for adapalene and benzoyl peroxide gel and -42.4 for Epiduo® Forte, with both unadjusted p-values <0.001. The registry’s discrepancy indicator is false, so no discrepancy between the posted primary summaries and these simple recalculations is flagged.
The registry also reports a sponsor analysis labeled as an equivalence analysis between the active formulations for bioavailability. Its value is 100.28, with a 90% confidence interval from 96.78 to 103.91. This is not the same outcome as percent change in inflamed lesion count. The registry record does not report the equivalence margins or method for that analysis, and does not provide a sponsor-reported primary lesion-endpoint contrast between the active formulations.
The secondary outcome record lists an ANOVA superiority analysis comparing the generic active gel with vehicle, with p < 0.001. That reported analysis is distinct from the unadjusted recalculated risk differences and p-values. No discrepancy is flagged, but the detailed ANOVA specification is not reported in the registry record. Recalculated results are not a replacement for the sponsor’s analysis when the questions or methods differ; they are useful as transparent, simple comparisons of the posted summaries.
15. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when a study evaluates several outcomes, groups, time points, or contrasts. If each test is judged separately at a conventional significance threshold, the overall chance of at least one false-positive result can increase. This is a general statistical concern, not a statement that any particular finding in this trial is false. The registry lists three outcome measures and three analyses, but the full prespecified testing plan is not reported.
The primary endpoint includes comparisons of each active group with vehicle in the recalculated summaries. The record does not report whether these comparisons were prespecified as co-primary tests, whether an adjustment was used, or whether a testing hierarchy controlled the overall error rate. The reported p-values are unadjusted. The secondary outcome also has recalculated unadjusted comparisons, while the registry reports an ANOVA superiority analysis for the generic active gel versus vehicle. The precise relationship among these analyses is not described.
Missing-data handling is also not reported in the registry record. It does not state how participants without a week 12 assessment were handled, whether values were imputed, or whether sensitivity analyses examined alternative assumptions. Because the primary endpoint is described as using the per-protocol population, the criteria for that population and the number excluded from it are not reported. The record also does not provide enough detail to determine how the per-protocol analysis relates to randomized assignment.
The registry names randomization and masking, but does not provide the allocation procedure, concealment details, or an account of implementation. These omissions do not negate the design features; they limit independent assessment of how they were carried out. The original statistical analysis plan, interim-analysis information, and sample-size justification are not reported in the registry record. No assumptions about those matters should be inferred from the posted results.
These limitations affect how definitive the posted p-values and intervals can be considered. They do not change the numerical summaries themselves, but they leave uncertainty about analysis choices and the scope of inference. A complete interpretation would require prespecified methods, analysis-population definitions, and missing-data procedures that are not available in the registry record.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Adapalene and Benzoyl Peroxide Gel, 0.3%/2.5% w/w | 0 | 332 | 0.0% |
| Epiduo® Forte Gel 0.3%/2.5% w/w | 0 | 323 | 0.0% |
| Vehicle Topical Gel | 2 | 322 | 0.6% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Adapalene and Benzoyl Peroxide Gel, 0.3%/2.5% w/w | 0 of 332 |
| Epiduo® Forte Gel 0.3%/2.5% w/w | 0 of 323 |
| Vehicle Topical Gel | 0 of 322 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Adapalene and Benzoyl Peroxide Gel, 0.3%/2.5% w/w | 27 of 332 |
| Epiduo® Forte Gel 0.3%/2.5% w/w | 41 of 323 |
| Vehicle Topical Gel | 26 of 322 |
Most frequent serious adverse event terms
| Event term | Organ system | Adapalene and Benzoyl Peroxide Gel, 0.3%/2.5% w/w | Epiduo® Forte Gel 0.3%/2.5% w/w | Vehicle Topical Gel |
|---|---|---|---|---|
| Limb injury | Injury, poisoning and procedural complications | 0 of 332 | 0 of 323 | 1 of 322 |
| Pneumothorax | Respiratory, thoracic and mediastinal disorders | 0 of 332 | 0 of 323 | 1 of 322 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Adapalene and Benzoyl Peroxide Gel, 0.3%/2.5% w/w | Epiduo® Forte Gel 0.3%/2.5% w/w | Vehicle Topical Gel |
|---|---|---|---|---|
| Influenza | Infections and infestations | 4 of 332 | 10 of 323 | 6 of 322 |
| Nasopharyngitis | Infections and infestations | 7 of 332 | 8 of 323 | 5 of 322 |
| Heachache | Nervous system disorders | 4 of 332 | 2 of 323 | 3 of 322 |
| Oropharyngeal pain | Respiratory, thoracic and mediastinal disorders | 2 of 332 | 4 of 323 | 1 of 322 |
| Application site dryness | General disorders | 0 of 332 | 5 of 323 | 1 of 322 |
| Application site pain | General disorders | 1 of 332 | 5 of 323 | 0 of 322 |
| Application site pruritus | General disorders | 0 of 332 | 2 of 323 | 1 of 322 |
| Pyrexia | General disorders | 2 of 332 | 1 of 323 | 0 of 322 |
| Pregnancy | Pregnancy, puerperium and perinatal conditions | 2 of 332 | 0 of 323 | 1 of 322 |
| Rhinorrhoea | Respiratory, thoracic and mediastinal disorders | 1 of 332 | 2 of 323 | 0 of 322 |
Serious events with the highest arm-level rate: limb injury (0.3%), pneumothorax (0.3%).
The posted serious adverse event counts are 0 among 332 participants at risk in the adapalene and benzoyl peroxide gel group, 0 among 323 at risk with Epiduo® Forte Gel, and 2 among 322 at risk in the vehicle group. No deaths are listed in any group. The record identifies limb injury and pneumothorax among the top serious-event terms, each listed as 0.3%.
Other adverse events are reported for 27 of 332 participants in the generic active group, 41 of 323 in the Epiduo® Forte group, and 26 of 322 in the vehicle group. These are registry counts and should be read alongside the corresponding numbers at risk; they do not describe severity, duration, relatedness to treatment, or whether an event led to discontinuation.
Serious-event counts are sparse, so the absence of recorded serious events in an active group does not establish that serious risks are absent. Nor do these summaries alone permit a reliable comparative safety conclusion. The registry record does not provide event narratives, definitions, causal assessments, or detailed follow-up information. Safety interpretation should remain limited to the recorded counts and terms.
17. What the Result Does, and Does Not, Mean
The posted primary results show that the mean percent change in inflamed lesion count was more negative in each active-treatment group than in vehicle at week 12. The recalculated unadjusted mean differences versus vehicle have confidence intervals entirely below zero and p-values <0.001. This describes a clear statistical separation in the posted group summaries under the simple comparison method.
That statistical pattern is not, by itself, a complete clinical judgment. The registry record does not report a threshold for clinical importance, detailed participant-level outcome distributions, or the methods used in the sponsor’s primary analysis. A group average also does not imply that every participant had the same response. The record does not provide the information needed to characterize the range of individual responses.
The primary active-versus-vehicle results do not establish equivalence between the active formulations on the lesion endpoint. Their group means are close, but the record does not report a direct primary-endpoint active-to-active comparison with a confidence interval and equivalence margin. The separately reported bioavailability equivalence analysis concerns a different outcome and cannot answer that lesion-endpoint question.
The secondary clinical-success summaries show a similar overall direction, but they are a different measure and the record does not report multiplicity control. The safety counts are also limited registry summaries and do not establish the absence of risk. Missing-data methods, the per-protocol criteria, and the original statistical plan are not reported. These results therefore describe the evidence posted in the registry, rather than resolving every question about effectiveness, equivalence, safety, or generalizability.
No treatment decision follows from these statistics alone. The findings should be interpreted within the recorded study population and outcomes, with the stated methodological and reporting limitations in mind.
18. Why This Trial Matters Statistically
This trial illustrates why the estimand and comparator matter when reading clinical results. The primary endpoint concerns average percent change in inflamed lesion count, and the posted recalculations compare each active group with vehicle. Those contrasts answer whether the observed average changes differ from vehicle under the simple unadjusted calculations; they do not directly test equivalence between the active formulations.
It also shows why an outcome label should not be mistaken for a complete analysis description. The registry reports an active-to-active equivalence analysis for bioavailability, while the primary lesion endpoint is continuous and analyzed in the per-protocol population. Without the equivalence margins and the details of the primary analysis, those results cannot be merged into one broad conclusion about therapeutic equivalence.
The distinction between a mean difference, a confidence interval, and a p-value is important. The point estimate describes the observed contrast, the interval conveys uncertainty under its method, and the p-value measures compatibility with a null hypothesis under assumptions. None of these alone establishes clinical importance or addresses missing data and bias.
Finally, the record demonstrates the value of separating primary from secondary findings and of reading safety summaries in context. The secondary response outcome follows a similar broad direction, but multiplicity methods are not reported. Serious adverse event counts are small and do not establish comparative safety. Together, the results offer useful statistical evidence while making clear how much interpretation depends on transparent methods and prespecified analysis choices.
19. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
Several trial-specific reporting gaps limit interpretation. The primary endpoint is specified for the per-protocol population, but the criteria defining that population are not reported. The record does not state how participants with missing week 12 measurements were handled, whether an intention-to-treat analysis was conducted, or whether sensitivity analyses were performed. The relationship between the primary analysis population and randomized assignment therefore cannot be assessed.
The registered enrollment is 1001, while the posted endpoint summaries use group-specific analysis counts. The registry record does not explain the difference between enrollment and the populations represented in each outcome summary. The original sample-size justification and design assumptions are also not reported; the planning illustrations are based on observed effects rather than the trial’s original design calculation.
Although the study is identified as randomized and quadruple-masked, the record does not describe the randomization sequence, allocation concealment, masking implementation, adherence, or treatment discontinuation. The study description calls it double-blind, while the design field identifies quadruple masking; the record does not explain this difference in terminology.
The primary statistical method is not reported, and the method for the bioavailability equivalence analysis and its equivalence margins are not given. Multiplicity adjustment, interim-analysis plans, and a full prespecified analysis plan are also not reported. The posted unadjusted recalculations cannot resolve those missing details.
Finally, the record provides limited detail about population characteristics, baseline lesion counts, outcome assessment procedures, adverse-event relatedness, and duration. The registry dates and multiple-site description do not substitute for those details. These limitations restrict assessment of generalizability, robustness, and the clinical meaning of the estimates.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Clinical End Point Study of Generic Adapalene and Benzoyl Peroxide Gel Versus Epiduo® Forte Gel in Treatment of Acne Vulgaris — NCT02651220.
- Registry record last updated 2020-06-23; status last verified 2020-06.
- Results first posted 2020-06-23.
- 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.
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23. Record Summary
NCT02651220 is a completed randomized, quadruple-masked, parallel phase 3 study of adapalene and benzoyl peroxide gel, Epiduo® Forte Gel, and vehicle topical gel for acne vulgaris. The registered enrollment was 1001. The study began in 2015-11, and primary completion was in 2016-04. Actavis Inc. is listed as sponsor.
The primary endpoint was percent change from baseline to week 12 in inflamed lesion count, assessed in the per-protocol population. Posted means were -74.2 for the generic active gel, -73.0 for Epiduo® Forte, and -30.6 for vehicle. Recalculated unadjusted comparisons versus vehicle yielded mean differences of -43.6 and -42.4, both with p <0.001.
The record also reports a secondary investigator-assessed clinical-success outcome, an ANOVA superiority analysis with p < 0.001 for the generic active gel versus vehicle, and an active-to-active bioavailability equivalence analysis. Statistical-plan details, missing-data methods, and the original sample-size justification are not reported in the registry record.