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Plaque Psoriasis Phase 3 Binary Endpoint NCT01194219

Study to Evaluate Safety and Effectiveness of Oral Apremilast (CC-10004) in Patients With Moderate to Severe Plaque Psoriasis: Complete Statistical Analysis

This analysis examines the registry’s Week 16 PASI-75 comparison of apremilast and placebo in participants with moderate to severe plaque psoriasis. It explains the reported and recalculated estimates, their precision, the secondary outcomes, and the safety information recorded.

Trial start: 2010-09-09  ·  Enrollment: 844  ·  Sponsor: Amgen
Scope of this record

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 Study to Evaluate Safety and Effectiveness of Oral Apremilast (CC-10004) in Patients With Moderate to Severe Plaque Psoriasis (NCT01194219), a randomized phase 3 study. The primary outcome is Percentage of Participants Who Achieved a 75% Improvement (Response) in the Psoriasis Area Severity Index (PASI-75) at Week 16 From Baseline.

844
Enrollment
Phase 3
2
Arms
In the primary outcome
-27.8 pts
Risk difference
Placebo (PBO)
-32.5 to -23.1 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01194219
PhasePhase 3
ConditionPlaque Psoriasis
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment844
Arms in the primary outcome2
Lead sponsorAmgen
Results postedYes

2. Clinical Question

Population

Participants with moderate to severe plaque psoriasis. The primary analysis describes a Full Analysis Set consisting of participants randomized per protocol, analyzed in the group to which they were assigned.

Intervention

Oral apremilast, including an arm described as apremilast 30 mg twice a day. The registry describes a treatment period in which participants initially assigned to placebo were assigned apremilast beginning at Week 16; the primary outcome timeframe is baseline to Week 16.

Comparator

Placebo during the placebo-controlled phase. The primary outcome lists the comparison groups as Placebo/Apremilast and Placebo (PBO), so the registry’s arm labels should be retained when interpreting the reported results.

Primary question

What percentage of participants achieved PASI-75 at Week 16? PASI-75 means at least a 75% reduction from baseline in the Psoriasis Area Severity Index score. The registry uses this threshold response as a measure of improvement in psoriasis signs and symptoms.

The trial was designed to evaluate efficacy and safety, with a placebo comparison during the initial treatment period. The primary endpoint is a binary response: each participant either met the PASI-75 threshold or did not. The registry records a higher response percentage for the Placebo/Apremilast group than for the placebo group. This comparison describes the observed trial results; it does not by itself establish how the treatment would perform in other populations or settings.

3. Trial Design

The registry identifies this as a Phase 3, randomized, quadruple-masked, parallel-group study. Its official title describes a multicenter, double-blind, placebo-controlled evaluation of apremilast efficacy and safety in subjects with moderate to severe plaque psoriasis. The recorded enrollment is 844. The study status is completed; its recorded start date is 2010-09-09 and its primary completion date is 2012-02-23.

The intervention list includes apremilast, placebo, and topical treatments or phototherapy. The arm descriptions give more detail about the treatment sequence. Participants initially randomized to placebo were assigned apremilast 30 mg twice a day beginning at Week 16. Participants initially assigned apremilast who demonstrated a PASI 75 response at Week 32 were to be randomized to continue apremilast or receive oral placebo until effect was lost. The available arm description is truncated after that point, so further details of the subsequent treatment are not reported in the registry record.

The primary comparison concerns baseline to Week 16, before the described Week 16 assignment of the initial placebo group to apremilast. The registry’s primary outcome lists the active-treatment arm as Placebo/Apremilast and the comparator as Placebo (PBO). Those labels reflect the registry record and should not be treated as a complete account of every participant’s treatment history.

The registry gives the randomization and masking features, but the original allocation ratio, concealment procedures, and detailed protocol procedures are not reported in the registry record. The trial’s original sample-size justification and planned statistical assumptions are also 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.

Only the first 6 of 10 groups are shown.

Placebo-Controlled Phase Weeks 0-16

StageApremilastPlaceboApremilast-ApremilastPlacebo-ApremilastAPR-APR-Re-randomized to PBOAPR-APR-Re-randomized to APR
STARTED5622820000
Received Apremilast5602820000
COMPLETED5032490000
NOT COMPLETED59330000

Reasons for not completing this period:

ReasonApremilastPlaceboApremilast-ApremilastPlacebo-ApremilastAPR-APR-Re-randomized to PBOAPR-APR-Re-randomized to APR
Adverse Event2350000
Lack of Efficacy270000
Noncompliance with study drug700000
Withdrawal by Subject1290000
Death010000
Lost to Follow-up790000
Protocol Violation710000
Miscellaneous110000

Maintenance Phase Weeks16-32

StageApremilastPlaceboApremilast-ApremilastPlacebo-ApremilastAPR-APR-Re-randomized to PBOAPR-APR-Re-randomized to APR
STARTED0049424500
Received Apremilast0049324400
COMPLETED0042421500
NOT COMPLETED00703000

Reasons for not completing this period:

ReasonApremilastPlaceboApremilast-ApremilastPlacebo-ApremilastAPR-APR-Re-randomized to PBOAPR-APR-Re-randomized to APR
Adverse Event008900
Lack of Efficacy00371500
Non-compliance with Study Drug002100
Withdrawal by Subject0012300
Lost to Follow-up009000
Protocol Violation000100
Other002100

Randomized Withdrawal Phase-Weeks 32-52

StageApremilastPlaceboApremilast-ApremilastPlacebo-ApremilastAPR-APR-Re-randomized to PBOAPR-APR-Re-randomized to APR
STARTED00007777
Received Topical + Light Therapy000000
COMPLETED00007373
NOT COMPLETED000044

Reasons for not completing this period:

ReasonApremilastPlaceboApremilast-ApremilastPlacebo-ApremilastAPR-APR-Re-randomized to PBOAPR-APR-Re-randomized to APR
Adverse Event000001
Lack of Efficacy000011
Non-compliance with Study Drug000010
Withdrawal by Subject000010
Lost to Follow-up000012
Protocol Violation000000
Other000000

Long-Term Extension Weeks 52 to 260

StageApremilastPlaceboApremilast-ApremilastPlacebo-ApremilastAPR-APR-Re-randomized to PBOAPR-APR-Re-randomized to APR
STARTED000000
Received at Least 1 Dose of IP000000
COMPLETED000000
NOT COMPLETED000000

Reasons for not completing this period:

ReasonApremilastPlaceboApremilast-ApremilastPlacebo-ApremilastAPR-APR-Re-randomized to PBOAPR-APR-Re-randomized to APR
Adverse Event000000
Lack of Efficacy000000
Noncompliance with IP000000
Withdrawal by Subject000000
Death000000
Lost to Follow-up000000
Protocol Violation000000
Miscellaneous000000

Analysis population for the primary outcome, as defined in the registry: The Full Analysis Set (FAS) consisted of all participants who were randomized per protocol. Participants were included in the treatment group to which they were randomized APR 30 BID or placebo for the FAS. Last observation carried forward (LOCF) imputation was used.

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: The full analysis set (FAS) consisted of all participants who were randomized as specified in the protocol. Those who were randomized in error and did not receive any dose of Investigational product were excluded from FAS. Participants were included in the treatment group to which they were randomized APR 30 BID or placebo for the FAS.

CharacteristicUnitApremilastPlaceboTotal
Participants analysed562282844
Age, Continuousyears45.8 (SD 13.07)46.5 (SD 12.72)46.0 (SD 12.95)
Sex: Female, Male: FemaleParticipants18388271
Sex: Female, Male: MaleParticipants379194573
Race/Ethnicity, Customized: American Indian or Alaska Nativeparticipants257
Race/Ethnicity, Customized: Asianparticipants281644
Race/Ethnicity, Customized: Black or African Americanparticipants181028
Race/Ethnicity, Customized: Native Hawaiian or Other Pacific Islanderparticipants516
Race/Ethnicity, Customized: Whiteparticipants507250757
Race/Ethnicity, Customized: Otherparticipants202
Duration of Plaque Psoriasis: <10 yearsyears15085235
Duration of Plaque Psoriasis: 10 to < 20 yearsyears15973232
Duration of Plaque Psoriasis: ≥ 20 yearsyears253122375
Duration of Plaque Psoriasis: Missingyears022

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants Who Achieved a 75% Improvement (Response) in the Psoriasis Area Severity Index (PASI-75) at Week 16 From Baseline, measured over Baseline to Week 16.

ElementRegistry entry
Result typeNumber
Measure of spreadnot applicable
Unitpercentage of participants
Endpoint classificationBinary Endpoint

The primary endpoint is the percentage of participants who achieved PASI-75 at Week 16 from baseline. A participant meets the endpoint by achieving at least a 75% reduction in PASI score. The registry describes PASI as a measure of psoriasis severity that combines lesion characteristics—erythema, thickness, and scaling—with the degree of skin involvement across anatomical regions. Scores range from 0 to 72, with higher scores representing greater disease severity.

Reducing a multi-part severity score to a prespecified responder threshold makes the endpoint interpretable as the proportion of participants reaching a defined level of improvement. That can be useful for communicating how often a clinically meaningful threshold was met, while also discarding information about the size of changes among participants who fall short of the threshold or exceed it. The endpoint therefore represents a particular aspect of treatment response, not the entirety of disease status or the participant’s experience.

The registry says that PASI scores were set to missing if any severity score or degree-of-involvement score was missing. For the primary analysis, the Full Analysis Set included participants randomized per protocol, with participants analyzed in their randomized group. Last observation carried forward was used for imputation. Details beyond this description, including the handling of missing data in other outcomes, are not reported in the registry record.

7. Results Posted in the Registry

Risk difference: Placebo (PBO)

-27.8

95% CI: -32.5 to -23.1 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals0.08.116.224.332.440.5Placebo/Apremilast (n=562)Placebo (PBO) (n=282)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Placebo (PBO)-35-28-20-12-4.932.60risk difference (percentage points) vs control (95% CI)

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 outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Percentage of Participants Who Achieved a Static Physician Global Assessment (sPGA) Score of Clear (0) or Almost Clear (1) With At Least 2 Points Reduction From BaselineBinary EndpointRisk difference+17.8 pts (13.7 to 21.9)55 per arm
Percent Change From Baseline in Percent of Affected Body Surface Area (BSA) at Week 16Continuous EndpointMean difference-40.78 (-46.34 to -35.22)15 per arm
Percent Change From Baseline in the Psoriasis Area Severity Index (PASI) Score at Week 16Continuous EndpointMean difference35.30 (30.65 to 39.95)14 per arm

Percentage of Participants Who Achieved a Static Physician Global Assessment (sPGA) Score of Clear (0) or Almost Clear (1) With At Least 2 Points Reduction From Baseline

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Apremilast-1.753.338.41131924risk difference (percentage points) vs control (95% CI)

Percent Change From Baseline in Percent of Affected Body Surface Area (BSA) at Week 16

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Apremilast-50-39-29-18-7.043.71mean difference vs control (95% CI)

Percent Change From Baseline in the Psoriasis Area Severity Index (PASI) Score at Week 16

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Placebo-3.206.0715253443mean difference vs control (95% CI)

The secondary outcomes cover several related but distinct domains: a static physician global assessment response, body surface area affected, percentage change in PASI, itch, dermatology-related quality of life, and health survey components. The outcomes with detailed estimates in the statistical record show a direction broadly consistent with the primary Week 16 result, with more favorable recorded values for apremilast than placebo. Measures of response status and measures of change on a continuous scale describe different features of the data and should not be treated as duplicate tests of a single endpoint.

The registry lists 13 secondary outcomes, while numerical estimates are available in the statistical record for a subset. The outcomes without detailed estimates in that record cannot be characterized from the entries described. In particular, the existence of an outcome listing does not establish that its result was statistically significant, clinically important, or consistent with the other measures.

Secondary outcomes can help show whether a primary result is accompanied by changes in other relevant measures, but their inferential weight depends on prespecification, analysis methods, and control of multiplicity. When many outcomes are tested, the chance of at least one apparently notable result arising by chance can increase. The registry does not report a multiplicity adjustment for the secondary outcome family. Unadjusted secondary p-values should therefore be read as exploratory evidence, not as independent confirmatory findings.

The secondary results add breadth to the description of the trial but do not change the definition of the primary endpoint or its analysis. Interpretation should prioritize the primary comparison, then consider whether the other recorded measures provide coherent context while accounting for their distinct scales, incomplete result availability, and multiplicity uncertainty.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

9. Statistical Interpretation

Clinical Biostats interpretation

In the primary outcome record, PASI-75 was achieved by 33.1% of the Placebo/Apremilast group and 5.3% of the Placebo (PBO) group. The sponsor-reported risk difference is 27.8 percentage points, with a 95% confidence interval from 23.1 to 32.5 percentage points and p < 0.001. The reported comparison therefore indicates a substantially higher observed response percentage in the Placebo/Apremilast group during the Week 16 assessment.

The unadjusted recalculation expresses the contrast in the opposite direction, as placebo minus Placebo/Apremilast: -0.278, with a 95% confidence interval from -0.325 to -0.231. The negative sign reflects that ordering of the comparison, rather than a conflicting direction of the observed result. The recalculated p-value is <0.001. The sponsor’s own analysis is the primary inferential result; the simple recalculation is a check based on the posted summary statistics and is not an adjusted analysis.

The registry also records secondary outcomes related to physician global assessment, affected body surface area, PASI change, itch, quality of life, and physical and mental health measures. The secondary results with estimates available in the statistical record show a pattern in the same broad direction as the primary response comparison: better reported outcomes in the apremilast group than in placebo at Week 16. These outcomes differ in their scales and meanings, so they should not be read as interchangeable measures. The registry lists 13 secondary outcomes, but numerical results for every listed outcome are not available in the statistical record.

The results are estimates from this trial and its recorded analysis population, not a guarantee of an individual outcome. The primary endpoint captures the proportion crossing one response threshold at one assessment time. It does not alone establish durability, the balance of all benefits and harms, or what would happen under other treatment conditions. The posted results do not provide a basis for inferring those broader conclusions.

10. Statistical Methods Explained

The primary outcome is binary: participants are classified according to whether they achieved PASI-75 by Week 16. A percentage summarizes the share meeting that criterion in each group. The sponsor compared the groups using a chi-squared method and reported the effect as a risk difference. A risk difference expresses the difference between response proportions; its interpretation depends on which group is subtracted from which. The sponsor’s positive value is reported for the order used in its analysis, while the unadjusted recalculation is expressed as placebo minus Placebo/Apremilast and is consequently negative.

What does the confidence interval describe?

A confidence interval describes uncertainty around an estimated group contrast under the assumptions of the analysis. It gives a range of estimates compatible with the observed data and method, rather than a range containing a known true value with certainty. For the sponsor-reported primary risk difference, the 95% interval runs from 23.1 to 32.5 percentage points. The interval does not include zero, consistent with the reported p-value of < 0.001 for the null comparison of no difference under that method. A p-value is not the probability that the null hypothesis is true, and it does not describe the size or practical importance of the effect.

Why are there two reported versions of the comparison?

The registry contains the sponsor’s analysis and a simple unadjusted recalculation from posted summary statistics. The sponsor used a chi-squared analysis for the risk difference. The recalculation uses the recorded group response proportions and denominators to form an unadjusted contrast and its interval. These approaches need not produce identical rounding or exactly identical interval limits. In this record, the estimated contrast has the same direction once the group ordering is taken into account, and the registry marks no discrepancy. The sponsor analysis remains the trial’s reported analysis; the recalculation is supplementary and should not be interpreted as replacing it.

What is the role of the analysis population?

The primary outcome description defines the Full Analysis Set as participants randomized per protocol and says they were included in the group to which they were randomized. It also states that last observation carried forward was used. This method fills a missing assessment using the participant’s last available observation. As a general statistical matter, carrying a prior value forward can affect estimated response rates if outcomes would otherwise change after the last observation; its appropriateness depends on the missingness and outcome process. The registry does not report enough detail to assess those assumptions or the sensitivity of the result to other missing-data methods.

For binary outcomes, the observed response percentage is informative but does not reveal the full participant-level outcome pattern. The risk difference retains an absolute scale, which describes the difference in response proportions, while measures such as a risk ratio or odds ratio express the contrast differently. The posted statistics include recalculated relative measures, but the sponsor’s reported primary effect is the risk difference. No additional adjusted primary estimate is reported in the registry record.

Why does over-dispersion matter in some analyses?

As a general statistical concept, over-dispersion occurs when observed variability exceeds what a model’s assumed distribution allows. It can make standard errors too small and confidence intervals too narrow if ignored. The primary endpoint is analyzed as a binary responder comparison using a chi-squared method; the registry does not report a model-based over-dispersion adjustment for this analysis. The issue should therefore be understood as a general consideration, not a feature established for this trial’s primary result.

The continuous secondary measures are reported as least-squares means with standard errors, and their sponsor analyses use ANCOVA. ANCOVA compares outcomes while accounting for specified covariates, but the covariates and full model specification are not reported in the registry record. Recalculated mean contrasts use summary data and are not equivalent to the sponsor’s covariate-adjusted model. Their role is descriptive and exploratory, not a substitute for the reported ANCOVA result.

The registry does not report whether interim analyses were conducted, whether there was a prespecified statistical analysis plan beyond the brief descriptions, or whether multiplicity adjustments were used for the family of secondary outcomes. These absences limit how confidently the secondary p-values can be interpreted as confirmatory evidence.

11. Confidence Intervals and Precision

The sponsor’s primary estimate is a risk difference of 27.8 percentage points, with a 95% confidence interval from 23.1 to 32.5 percentage points. The interval provides a useful view of precision: estimates across that range are compatible with the observed data and the reported analysis assumptions. It is not a prediction interval for individual participants and does not show the range of outcomes that an individual might experience.

The recalculated contrast is reported as -0.278, with an interval from -0.325 to -0.231, because the recalculation orders the groups as placebo minus Placebo/Apremilast. These values are on the proportion scale and have the same directional interpretation as the sponsor estimate when the group order is accounted for. The recalculated interval is unadjusted and should be distinguished from the sponsor’s chi-squared analysis.

Precision depends on both the amount of information in the data and the variability of the outcome. A confidence interval that is narrower represents less statistical uncertainty about the estimated contrast under the analysis method; it does not remove uncertainty about generalizability, missing-data assumptions, endpoint relevance, or bias. The interval also does not address the multiplicity of evaluating several outcomes.

The sponsor’s reported interval and the recalculated interval are close but not identical. The registry does not mark a discrepancy. Differences in method, computation, and rounding can lead to modest differences in interval endpoints. The sponsor’s own analysis is the result to prioritize when describing the trial’s formal inference, while the recalculation helps readers inspect the contrast using the posted group summaries.

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 detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect3141
75% of the observed effect6383
50% of the observed effect156209
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, pooled-variance normal approximation for two proportions. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: Placebo (PBO).

The sample-size figures are planning illustrations, not the trial’s original design calculations. For the binary primary outcome, the listed figures are participants per arm, not total participants. They are based on the observed effect and the stated assumptions: two-sided significance level 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set at the stated fraction of the observed effect.

The 80% power column gives an illustrative number of participants per arm for a design with an 80% chance of detecting the specified effect under the planning assumptions, if that effect and those assumptions were correct. The 90% power column gives the corresponding illustration for a 90% chance. These are forward-looking design calculations, not probabilities that the completed trial had of finding a result after its data were observed.

For the primary endpoint, the planning rows list 31 participants per arm for 100% of the observed effect, 63 participants per arm for 75% of the observed effect, and 156 participants per arm for 50% of the observed effect at 80% power. At 90% power, the corresponding listed values are 41, 83, and 209 participants per arm. The pattern illustrates a general design principle: smaller effects are harder to distinguish from random variation and therefore require more participants to reach the same target power.

The calculations use assumptions that are not the same as the trial’s reported analysis, including equal allocation and a normal approximation. The original trial’s sample-size justification and design assumptions are not reported in the registry record. These figures are not observed power: observed power is not an informative substitute for the estimated effect and its confidence interval after results are available. They should be used only as illustrations of how planning requirements change with the assumed effect size and target power.

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 = [ z1−α/2 √(2p̄(1−p̄)) + z1−β √(p0(1−p0) + p1(1−p1)) ]2 / (p1 − p0)2

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 = 0.331; treatment proportion p1 = 0.053; average p̄ = 0.192.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5571 = 1.0919.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5213 = 0.4388.
  4. n = (1.0919 + 0.4388)2 / (-0.2778)2 = 30.4, rounded up to 31 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 <- 0.330960854092527                          # control proportion
p1 <- 0.0531914893617021                          # 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(1194219)
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 = 31 (80% power), 41 (90% power)
 75% of observed effect: n per arm = 63 (80% power), 83 (90% power)
 50% of observed effect: n per arm = 156 (80% power), 209 (90% power)
power.prop.test: 30.4 
Simulated power at n = 31 per arm: 0.849 (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.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Chi-squaredRisk Difference (RD) 27.823.1 to 32.5< 0.001

The sponsor reports the primary comparison as a chi-squared analysis of risk difference: 27.8 percentage points, 95% confidence interval 23.1 to 32.5, and p < 0.001. This is the trial’s own reported inferential analysis. It should be used as the primary description of the sponsor’s findings rather than replaced by the simple recalculation.

The recalculated contrast is -0.278, with a 95% confidence interval from -0.325 to -0.231 and p < 0.001. The sign is negative because this version expresses the contrast as placebo minus Placebo/Apremilast; the sponsor’s positive risk difference uses the reverse group order. The estimates therefore point in the same direction once the ordering is made explicit. The different p-value formatting and small differences in interval limits reflect distinct reported and recalculated procedures and rounding, not a registry-identified discrepancy.

The recalculation is simple and unadjusted, using the posted summary statistics. It does not reproduce every element of the sponsor’s analysis or recover any model details not reported in the registry record. For that reason, it is best read as a transparent check on the summarized comparison. The sponsor’s result retains precedence as the analysis reported for the trial, while the recalculation adds context about the magnitude and direction of the observed group contrast.

15. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when several outcomes or comparisons are tested. Even when each test uses a conventional significance threshold, conducting many tests increases the chance of finding one or more small p-values by chance alone. A prespecified strategy can control that issue, for example by defining a hierarchy of tests or adjusting the threshold. The registry lists 13 secondary outcomes and records several analyses, but whether multiplicity was controlled is not reported in the registry record. The secondary p-values should consequently be treated with more caution than the primary analysis, whose role is explicitly identified.

The primary outcome description states that the Full Analysis Set included participants randomized per protocol and that participants were analyzed according to randomized group. It also states that last observation carried forward was used. The registry does not provide the number of participants with missing primary outcome data, the amount or reasons for missingness by group, or sensitivity analyses using alternative missing-data assumptions. It is therefore not possible to assess from the record whether missingness could have influenced the estimated response difference.

Last observation carried forward assigns a participant’s last available outcome to a later missing assessment. As a general statistical matter, this approach assumes that carrying forward the observed value is an acceptable approximation for the missing value. If outcomes would have changed after the last recorded assessment, the imputed value may not represent the unobserved outcome. The registry does not report analyses testing the robustness of the primary result to this assumption.

Other analysis populations, detailed exclusion criteria, and the handling of missing data for each secondary outcome are not reported in the registry record. The original statistical analysis plan, multiplicity procedure, and whether interim analyses took place are likewise not reported in the registry record. These omissions restrict the ability to evaluate the full inferential framework and the degree to which the posted results reflect every planned analysis.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Placebo (Placebo-Controlled Phase) Weeks 0-1682822.8%
Apremilast (Placebo-Controlled Phase) Weeks 0-16125602.1%
APR-APR-PBO Randomized Withdrawal Phase Weeks 32-522772.6%
Apremilast (Apremilast Exposure Period) Weeks 0-260748049.2%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo (Placebo-Controlled P…2.8%Apremilast (Placebo-Controlle…2.1%APR-APR-PBO Randomized Withdr…2.6%Apremilast (Apremilast Exposu…9.2%% of participants with at least one serious adverse event

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

ArmParticipants affected of at risk
Placebo (Placebo-Controlled Phase) Weeks 0-1690 of 282
Apremilast (Placebo-Controlled Phase) Weeks 0-16260 of 560
APR-APR-PBO Randomized Withdrawal Phase Weeks 32-5210 of 77
Apremilast (Apremilast Exposure Period) Weeks 0-260503 of 804

Most frequent serious adverse event terms

Event termOrgan systemPlacebo (Placebo-Controlled Phase) Weeks 0-16Apremilast (Placebo-Controlled Phase) Weeks 0-16APR-APR-PBO Randomized Withdrawal Phase Weeks 32-52Apremilast (Apremilast Exposure Period) Weeks 0-260
Coronary artery diseaseCardiac disorders0 of 2820 of 5600 of 776 of 804
Acute myocardial infarctionCardiac disorders0 of 2821 of 5600 of 774 of 804
Inguinal herniaGastrointestinal disorders1 of 2821 of 5600 of 772 of 804
PneumoniaInfections and infestations1 of 2821 of 5600 of 772 of 804
NephrolithiasisRenal and urinary disorders0 of 2820 of 5600 of 774 of 804
Cardiac failureCardiac disorders0 of 2821 of 5600 of 772 of 804
Myocardial infarctionCardiac disorders1 of 2820 of 5600 of 772 of 804
Non-cardiac chest painGeneral disorders0 of 2820 of 5601 of 772 of 804
OsteoarthritisMusculoskeletal and connective tissue disorders0 of 2820 of 5600 of 773 of 804
Transient ischaemic attackNervous system disorders0 of 2821 of 5600 of 772 of 804

Most frequent non-serious adverse event terms

Event termOrgan systemPlacebo (Placebo-Controlled Phase) Weeks 0-16Apremilast (Placebo-Controlled Phase) Weeks 0-16APR-APR-PBO Randomized Withdrawal Phase Weeks 32-52Apremilast (Apremilast Exposure Period) Weeks 0-260
DiarrhoeaGastrointestinal disorders20 of 282105 of 5600 of 77163 of 804
Upper respiratory tract infectionInfections and infestations21 of 28257 of 5602 of 77183 of 804
NauseaGastrointestinal disorders19 of 28288 of 5600 of 77130 of 804
NasopharyngitisInfections and infestations23 of 28241 of 5603 of 77131 of 804
Tension headacheNervous system disorders12 of 28241 of 5602 of 7784 of 804
HeadacheNervous system disorders13 of 28231 of 5600 of 7762 of 804
HypertensionVascular disorders7 of 28210 of 5600 of 7756 of 804
SinusitisInfections and infestations5 of 28216 of 5601 of 7745 of 804
ArthralgiaMusculoskeletal and connective tissue disorders5 of 2829 of 5602 of 7751 of 804
Back painMusculoskeletal and connective tissue disorders2 of 28214 of 5601 of 7750 of 804

Serious events with the highest arm-level rate: non-cardiac chest pain (1.3%), chemical burns of eye (1.3%), coronary artery disease (0.7%), acute myocardial infarction (0.5%), nephrolithiasis (0.5%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The registry records serious adverse events and other adverse events for several treatment periods. During the placebo-controlled phase from Weeks 0-16, the placebo group has 8 serious adverse events among 282 participants at risk, and the apremilast group has 12 among 560 at risk. For other adverse events in that same phase, the record lists 90 among 282 at risk in the placebo group and 260 among 560 at risk in the apremilast group.

Additional entries cover the APR-APR-PBO randomized withdrawal phase from Weeks 32-52 and an apremilast exposure period from Weeks 0-260. Those entries list 2 serious adverse events and 10 other adverse events among 77 at risk in the withdrawal phase, and 74 serious adverse events and 503 other adverse events among 804 at risk in the exposure period. These are counts for the registry’s specified periods and populations; the longer exposure period should not be compared directly with the placebo-controlled phase as though follow-up were the same.

The record lists serious-event terms with percentages, including non-cardiac chest pain and chemical burns of eye at 1.3% each. It does not report death counts in these entries. Event counts alone do not establish whether an event was caused by treatment, and the registry summary does not provide enough context to evaluate duration, severity beyond the serious-event classification, or exposure-adjusted rates.

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

The primary result describes a higher observed Week 16 PASI-75 response percentage in the Placebo/Apremilast group than in the placebo group. The sponsor’s estimated risk difference is 27.8 percentage points, and its 95% confidence interval is entirely above zero in the sponsor’s stated direction. The result is a group-level comparison in the recorded trial population, analyzed using the registry’s described Full Analysis Set and last-observation-carried-forward procedure.

The result does not establish that every participant receiving apremilast will achieve PASI-75, or that a participant who does not reach this threshold has had no improvement. A binary threshold omits the full range of individual changes in PASI score. Nor does this outcome alone describe durability beyond the Week 16 assessment, quality of life, all symptoms, or the balance of potential benefits and harms.

The trial also includes later treatment periods, but the primary comparison concerns baseline to Week 16. Later observations and the randomized withdrawal phase address different treatment questions and populations. They should not be folded into the primary result without considering the different timing and treatment sequences.

The registry’s statistical result does not by itself resolve limitations arising from missing data, analysis choices, or the multiplicity of secondary outcomes. It also does not establish how the result applies outside the studied population and trial conditions. The record supports a careful description of the observed comparison and its statistical uncertainty, not a universal prediction or individualized treatment conclusion.

18. Why This Trial Matters Statistically

This trial illustrates how a clinical endpoint can convert a complex measure of disease severity into a responder outcome with an interpretable threshold. PASI-75 combines information about lesion characteristics and affected body area, then classifies participants according to whether they achieved a large specified reduction from baseline. Reporting the proportion of responders makes the result accessible, while the accompanying risk difference communicates the absolute contrast between groups.

It also shows why the order of a contrast matters. The sponsor reports a positive difference in its chosen direction, whereas the unadjusted recalculation reports placebo minus Placebo/Apremilast and is negative. Without stating the group order, readers could mistake a sign change for a disagreement. Naming the groups and scale makes the statistical meaning clearer.

The confidence interval adds information that a p-value alone cannot provide. It shows a range of effect estimates compatible with the sponsor’s analysis, helping readers judge precision as well as evidence against a no-difference hypothesis. The distinction between the sponsor’s analysis and a recalculation also demonstrates why summaries derived from posted group statistics should not be treated as equivalent to the trial’s full analysis.

Finally, the record highlights the importance of interpreting secondary outcomes and safety summaries within their limits. Multiple outcomes can broaden the clinical picture, but unadjusted tests carry less confirmatory weight, and event counts do not establish causation. Statistical interpretation is strongest when the endpoint, analysis population, uncertainty, missing-data approach, and limits of the record are considered together.

19. Limitations

The primary analysis uses last observation carried forward, but the registry does not report the extent or pattern of missing primary outcome data or sensitivity analyses under alternative assumptions. The impact of that imputation approach cannot be assessed from the record alone.

The primary arm labels include Placebo/Apremilast and Placebo (PBO), and the arm descriptions indicate changes in assigned treatment at Week 16. Although the primary outcome timeframe is baseline to Week 16, the labels and treatment sequence warrant care when describing who received which treatment throughout the study. The record does not provide a complete participant-level account of exposure in the statistical summary.

The registry does not report the trial’s original sample-size justification, full statistical analysis plan, multiplicity strategy, or whether interim analyses occurred. It also does not give detailed model covariates for the ANCOVA secondary analyses. The sample-size calculations associated with the posted results are planning illustrations based on the observed effects, not the original design basis.

Only a subset of the listed secondary outcomes has numerical estimates in the statistical record described. This restricts assessment of the full range of outcomes and makes it important not to infer results for measures whose numerical estimates are not present. The safety summaries use different periods and populations; the extended apremilast exposure entry should not be treated as a direct concurrent comparison with the placebo-controlled phase. The registry’s serious-event counts also do not establish causation or provide death counts.

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23. Record Summary

The registry describes a completed Phase 3, randomized, quadruple-masked, parallel-group study of apremilast in moderate to severe plaque psoriasis. Recorded enrollment is 844. The primary endpoint is PASI-75 from baseline to Week 16, analyzed in a Full Analysis Set with last observation carried forward.

The sponsor reports a Week 16 risk difference of 27.8 percentage points, with a 95% confidence interval from 23.1 to 32.5 and p < 0.001. The simple unadjusted recalculation is expressed in the opposite group order and has a negative sign. The registry also lists secondary outcomes and adverse-event summaries across several treatment periods. Missing-data sensitivity analyses, the multiplicity approach, and the original sample-size rationale are not reported in the registry record.

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