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Chronic Plaque Psoriasis Phase 3 Binary Endpoint NCT02581345

Phase 3 Study of M923 and Humira® in Subjects With Chronic Plaque-type Psoriasis: Complete Statistical Analysis

This analysis examines the Week 16 PASI 75 response comparing M923 with the EU reference product in a randomized Phase 3 psoriasis trial. It also considers the registry-reported equivalence analyses, secondary outcomes, precision, and safety summaries.

Trial start: 2015-09  ·  Enrollment: 572  ·  Sponsor: Momenta Pharmaceuticals, Inc.
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 Phase 3 Study of M923 and Humira® in Subjects With Chronic Plaque-type Psoriasis (NCT02581345), a randomized phase 3 study. The primary outcome is Percentage of Participants Who Achieved a 75% Reduction in Psoriasis Area and Severity Index (PASI) (PASI 75) Scores at Week 16.

572
Enrollment
Phase 3
2
Arms
In the primary outcome
-1.2 pts
Risk difference
Part 1: EU RPP
-8.0 to 5.6 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT02581345
PhasePhase 3
ConditionChronic Plaque Psoriasis, Psoriasis
AllocationRandomized
Design modelFactorial
MaskingTriple
Enrollment572
Arms in the primary outcome2
Lead sponsorMomenta Pharmaceuticals, Inc.
Results postedYes

2. Clinical Question

Population

Participants with moderate to severe chronic plaque-type psoriasis were enrolled. The primary analysis used the Per Protocol (PP) Analysis Set, described in the registry as a subgroup of the Intent-To-Treat (ITT) Analysis Set. It included participants who received at least 1 dose and had no protocol deviations considered significant enough to exclude them from the efficacy analysis.

Intervention

The intervention of interest was M923, an adalimumab biosimilar. The study also included M923 and Humira interventions in its broader design, but the posted primary comparison is between M923 and the EU RPP group.

Comparator

The primary comparison is M923 versus Part 1: EU RPP. The primary outcome reports 267 participants in the M923 group and 271 in the EU RPP group. The registry record does not define the EU RPP abbreviation.

Primary question

At Week 16, what proportion of participants achieved PASI 75, defined as at least a 75% reduction in PASI score from baseline? The registry reports group percentages with 95% confidence intervals and also records analyses labelled as equivalence analyses for the difference in proportions.

This is a question about comparative response proportions at a specified assessment time, not about the full course of disease or every outcome included in the trial. The primary endpoint uses a threshold on the change in PASI score: a participant either meets the criterion or does not. The reported group percentages therefore describe the fraction meeting that criterion in each analysis group. The comparison asks how far apart those fractions are, while the confidence intervals communicate the uncertainty around the estimates.

The trial’s brief summary says it was intended to evaluate efficacy, safety, and immunogenicity of M923 and Humira in participants with moderate to severe chronic plaque-type psoriasis. The posted primary outcome addresses efficacy through Week 16 PASI 75. The registry record does not report a primary immunogenicity result in the registry record for this analysis, and the primary question should not be read as covering every aspect of the broader study purpose.

3. Trial Design

This was a randomized Phase 3 study with triple masking and a factorial model, with 572 participants enrolled. The registry record describes a multicenter study and lists M923 and Humira as biological interventions. The study status is completed. Its start is recorded as 2015-09, and primary completion is recorded as 2017-04-04.

The posted primary outcome compares Part 1: M923 with Part 1: EU RPP. The primary endpoint is the percentage of participants achieving PASI 75 at Week 16. The registry identifies the analysis population as the Per Protocol (PP) Analysis Set: participants from the ITT Analysis Set who received at least 1 dose and did not have protocol deviations judged significant enough to exclude them from the efficacy analysis. The primary outcome groups include 267 participants assigned to M923 and 271 assigned to EU RPP.

The trial record also describes Part 2 groups, including M923, Transition EU RPP, and Continuous EU RPP, and posts Week 52 outcomes. These later groups belong to a distinct part of the record and should not be combined with the Part 1 Week 16 primary comparison. Although the model is listed as factorial and the study includes several groups, the registry entries do not explain the factorial structure, allocation ratios, treatment sequence, or detailed operational procedures. Those aspects are not reported in the registry record.

The record lists 36 outcome measures and 7 analyses. It gives a broad study purpose covering efficacy, safety, and immunogenicity, while the available primary result is a binary Week 16 response outcome. The total enrollment and the analysis-group counts describe different aspects of the study: the primary outcome is reported for its stated PP analysis population, rather than as a direct tally of all enrolled participants. The registry record does not provide a detailed account of participant flow or reasons for any differences between enrollment and outcome denominators.

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.

Part 1: up to Week 16

StagePart 1 and Part 2: M923Part 1: EU RPPPart 1: EU RPP; Part 2: TransitionPart 1: EU RPP; Part 2: Continous
STARTED28628600
COMPLETED27126300
NOT COMPLETED152300

Reasons for not completing this period:

ReasonPart 1 and Part 2: M923Part 1: EU RPPPart 1: EU RPP; Part 2: TransitionPart 1: EU RPP; Part 2: Continous
Adverse Event3800
Physician Decision2400
Withdrawal by Subject4700
Lost to Follow-up2000
Unspecified Reason3300
Did Not Receive Treatment1100

Part 2: Week 17 to Week 47

StagePart 1 and Part 2: M923Part 1: EU RPPPart 1: EU RPP; Part 2: TransitionPart 1: EU RPP; Part 2: Continous
STARTED2710132131
COMPLETED2420117119
NOT COMPLETED2901512

Reasons for not completing this period:

ReasonPart 1 and Part 2: M923Part 1: EU RPPPart 1: EU RPP; Part 2: TransitionPart 1: EU RPP; Part 2: Continous
Adverse Event5022
Physician Decision3021
Withdrawal by Subject9075
Failure to Achieve at Least a PASI 508032
Lost to Follow-up2001
Unspecified Reason2011

Analysis population for the primary outcome, as defined in the registry: Per Protocol (PP) Analysis Set: subgroup of the Intent-To-Treat (ITT) Analysis Set that included all participants who did not have any deviations from the protocol deemed significant enough for exclusion from the efficacy analysis and received at least 1 dose of study drug

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: Intent-to-Treat (ITT) Analysis Set: all consenting participants randomized to study treatment

CharacteristicUnitPart 1 and Part 2: M923Part 1 and Part 2: EU RPPTotal
Participants analysed286286572
Age, Continuousyears44.6 (SD 12.4)45.5 (SD 12.9)45.0 (SD 12.6)
Sex: Female, Male: FemaleParticipants95100195
Sex: Female, Male: MaleParticipants191186377
Race (NIH/OMB): American Indian or Alaska NativeParticipants011
Race (NIH/OMB): AsianParticipants213
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants000
Race (NIH/OMB): Black or African AmericanParticipants314
Race (NIH/OMB): WhiteParticipants281282563
Race (NIH/OMB): More than one raceParticipants000
Race (NIH/OMB): Unknown or Not ReportedParticipants011
Psoriasis Area and Severity Index (PASI) Scoreunits on a scale21.24 (SD 9.27)20.16 (SD 8.16)20.70 (SD 8.74)
Number of Participants with the Indicated Static Physician's Global Assessment (sPGA) Score: ModerateParticipants170182352
Number of Participants with the Indicated Static Physician's Global Assessment (sPGA) Score: SevereParticipants10391194
Number of Participants with the Indicated Static Physician's Global Assessment (sPGA) Score: Very SevereParticipants121224
Number of Participants with the Indicated Static Physician's Global Assessment (sPGA) Score: ClearParticipants000
Number of Participants with the Indicated Static Physician's Global Assessment (sPGA) Score: Almost ClearParticipants000
Number of Participants with the Indicated Static Physician's Global Assessment (sPGA) Score: MildParticipants000

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants Who Achieved a 75% Reduction in Psoriasis Area and Severity Index (PASI) (PASI 75) Scores at Week 16, measured over Baseline; Week 16.

ElementRegistry entry
Result typeNumber
Measure of spread95% Confidence Interval
Unitpercentage of participants
Endpoint classificationBinary Endpoint

The primary endpoint is the percentage of participants achieving PASI 75 at Week 16. PASI combines the extent of psoriasis involvement across the head, arms, trunk, and legs with assessments of scaling, redness, and thickness in each region. The overall score ranges from 0 for no disease to 72 for the most severe disease. A PASI 75 response means that the Week 16 score is at least 75% lower than the participant’s baseline score.

This endpoint turns a change in a continuous clinical score into a binary outcome: each participant either meets the response threshold or does not. The group percentage then expresses how often that threshold was reached in the analysis population. Such a responder definition can make a result easier to interpret as the proportion of participants attaining a prespecified degree of improvement, while losing information about differences among people who fall on the same side of the threshold.

The Week 16 timing gives the outcome a defined assessment point. It does not, on its own, describe response at other times or establish whether a response persists. The registry also lists other PASI and sPGA outcomes, including follow-up outcomes, but those address different thresholds, measures, or time points. The primary endpoint is therefore a specific summary of response at Week 16, rather than a complete description of all clinical outcomes in the study.

7. Results Posted in the Registry

Risk difference: Part 1: EU RPP

-1.2

95% CI: -8.0 to 5.6 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals72.775.277.880.483.085.6Part 1: M923 (n=267)Part 1: EU RPP (n=271)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Part 1: EU RPP-9.09-5.93-2.760.403.566.72risk 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 With a Response of Clear or Almost Clear on the Static Physician Global Assessment (sPGA) at Week 16Binary EndpointRisk difference-2.9 pts (-10.8 to 5.1)4,204 per arm
Number of Participants Achieving PASI 50 Response at Week 16Binary EndpointRisk difference+2.3 pts (-2.2 to 6.9)2,053 per arm
Number of Participants Achieving PASI 50 Response at Week 52 (Follow-Up Visit)Binary EndpointRisk difference-3.0 pts (-10.2 to 4.2)2,004 per arm

Percentage of Participants With a Response of Clear or Almost Clear on the Static Physician Global Assessment (sPGA) at Week 16

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Part 1: EU RPP-12-8.37-4.70-1.032.646.32risk difference (percentage points) vs control (95% CI)

Number of Participants Achieving PASI 50 Response at Week 16

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Part 1: EU RPP-2.91-0.811.293.405.507.61risk difference (percentage points) vs control (95% CI)

Number of Participants Achieving PASI 50 Response at Week 52 (Follow-Up Visit)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Part 2: Transition EU RPPPart 2: Continuous EU RPP-12-7.73-3.94-0.153.647.44risk difference (percentage points) vs control (95% CI)

The posted secondary results cover several types of response and assessment. They include sPGA clear or almost clear status at Week 16, PASI 50 at Week 16 and Week 52, and PASI 90 at Week 16 and Week 52, as well as absolute PASI score outcomes. The registry lists 35 secondary outcomes. The results available in the registry entries span Part 1 Week 16 and Part 2 follow-up comparisons, so they do not all address the same population, time point, or comparison as the primary endpoint.

Across the reported binary outcomes, the observed response proportions are generally high in the posted Part 1 and Part 2 groups, and the recalculated comparisons have confidence intervals that include zero. This broad pattern is compatible with the primary result’s close group estimates, but secondary outcomes do not independently establish the primary finding or formal equivalence. They use different thresholds and time points, and some involve different treatment groups. Their estimates should be interpreted within their own comparisons rather than combined into a single overall treatment effect.

Unadjusted secondary analyses carry less weight when many outcomes and comparisons are examined. With multiple opportunities to observe differences, some results may appear notable by chance even when no consistent underlying difference exists. The registry does not report a multiplicity adjustment or a prespecified hierarchy for the secondary analyses. Consequently, these outcomes are best read as supporting descriptive context, not as a collection of independent confirmatory tests.

The secondary results can help show whether the primary endpoint’s general pattern is echoed across other response definitions and assessment times. They cannot resolve limitations in the primary analysis population, missing-data reporting, or the absent details of the sponsor’s methods. Nor do the secondary outcomes permit a broader conclusion about outcomes that are not posted with the same level of detail in the record.

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

9. Statistical Interpretation

Clinical Biostats interpretation

In the PP analysis, 80.1% of the M923 group achieved PASI 75 at Week 16, with a 95% confidence interval from 74.9% to 84.8%. In the EU RPP group, the response was 79.0%, with a 95% confidence interval from 73.6% to 83.7%. The estimates are close, and the intervals overlap substantially. These summaries describe the observed response proportions and their precision; they do not establish that the treatments are identical.

The registry reports two analyses labelled as equivalence analyses for the difference in proportions (M923 - EU RPP). The reported estimate is 0.014, with a 90% confidence interval from -0.043 to 0.072, and a 95% confidence interval from -0.054 to 0.082. Both intervals include zero, so the posted data are compatible with differences in either direction under these intervals. A formal equivalence conclusion also depends on a prespecified equivalence margin. That margin and the method used for the sponsor’s analysis are not reported in the registry record, so the equivalence label alone does not allow the reader to assess whether the reported interval lies within an appropriate margin.

A simple unadjusted recalculation from the posted summary statistics gives a risk difference of -0.012, with a 95% confidence interval from -0.08 to 0.056 and an unadjusted p-value of 0.734. This recalculation uses the posted group counts and denominators and is not the sponsor’s reported estimate. The sponsor-reported estimate and the recalculated estimate differ in value and direction as expressed for the comparison; the registry record does not explain the reason. The sponsor’s reported analyses should be read as their own analysis, while the recalculation is a separate, unadjusted summary.

For this recalculation, the interval includes zero and is compatible with a range of possible differences. The unadjusted p-value does not quantify the probability that the treatments are equivalent, nor does it measure the probability that the observed result arose by chance. It is a measure tied to a particular null hypothesis and analysis. The result should be read alongside the effect estimate, confidence interval, analysis population, and limitations in the registry reporting.

These findings apply to the posted Week 16 PP comparison. They should not be generalized automatically to all enrolled participants, other time points, or the separate Part 2 comparisons. Nor does a close point estimate by itself establish clinical interchangeability, which is not determined by this outcome alone. The result describes the observed PASI 75 response and the uncertainty captured by the reported intervals.

10. Statistical Methods Explained

The primary outcome is binary at the participant level. A participant either achieved the PASI 75 threshold at Week 16 or did not. The percentage in each group is a proportion expressed as a percent, and its confidence interval reflects uncertainty in estimating the underlying response proportion from the participants in that analysis group.

What does a confidence interval communicate?

A confidence interval is a range of values generated by a statistical procedure that, under its assumptions, is designed to capture the quantity being estimated at the stated confidence level over repeated samples. It is not a range containing a fixed proportion of individual participant outcomes, and it is not a probability statement about the particular treatment difference after the data have been observed. Wider intervals indicate less precision; narrower intervals indicate greater precision, given the same kind of estimate and method.

The registry gives 95% confidence intervals for each primary-group percentage and posts equivalence analyses with both 90% and 95% confidence intervals for the difference in proportions. A confidence interval for a difference is useful because it keeps the estimated direction and plausible magnitude in view. If it includes zero, the data are compatible with no difference under that interval, but also with nonzero differences within its limits. Whether an interval supports equivalence requires comparison with a prespecified equivalence margin; the margin is not reported in the registry record.

What is the role of the risk difference?

The risk difference is a subtraction-based comparison of two response proportions. It expresses the absolute separation between groups on the proportion scale, rather than a relative comparison. Its sign depends on the order in which groups are subtracted. In the registry’s reported analysis, the comparison is explicitly labelled M923 - EU RPP. The unadjusted recalculation is derived from the posted summary statistics and has its own direction and estimate; it should not be conflated with the sponsor’s reported analysis.

Relative measures such as a risk ratio or odds ratio can express the same binary outcome on different scales, but the registry’s sponsor-reported analyses for the primary outcome are differences in proportion. The recalculated record includes relative estimates as well, but a measure’s numerical value is meaningful only with its scale and comparison direction understood. Different scales do not answer precisely the same interpretive question.

What does the p-value add?

The unadjusted recalculation reports p = 0.734. A p-value measures how unusual data at least as extreme as the observed data would be under a specified null model and its assumptions. It is not the probability that the null hypothesis is true, a measure of clinical importance, or proof of equality when it is not small. The registry does not post a p-value for the sponsor’s equivalence analyses. A p-value also does not replace an effect estimate and confidence interval, which show the scale and precision of the estimated difference.

Why distinguish reported and recalculated results?

The sponsor’s analysis is the analysis recorded in the registry, with its stated comparison and confidence intervals. A recalculated result is a simple unadjusted calculation from the posted summary counts and denominators. It does not reproduce adjustments, modeling choices, or other details that may have been used in the sponsor’s analysis. The method for the sponsor’s reported primary analysis is not reported in the registry record. The recalculation is therefore a transparent descriptive check, not a substitute for the sponsor’s analysis.

For binary outcomes, the observed proportion depends on both the event count and the denominator. A difference in denominators, the population included, handling of missing outcomes, or analysis method can affect a comparison. The primary population is PP, and the registry defines it by receipt of study drug and absence of protocol deviations deemed important for efficacy exclusion. Details of missing-data handling and the exact statistical procedures are not reported in the registry record.

General statistical context: over-dispersion is a concern when observed variability exceeds what a chosen probability model expects. It can make standard errors too small if ignored. It is more commonly discussed for count or clustered data than for a simple two-group binary summary. The registry entries do not identify an over-dispersion issue or a model-based adjustment for this primary comparison, so it should not be assumed to have influenced these results.

11. Confidence Intervals and Precision

The primary-group confidence intervals show that the response proportions are estimated with uncertainty. For M923, the registry reports 80.1% with a 95% confidence interval from 74.9% to 84.8%. For EU RPP, it reports 79.0% with a 95% confidence interval from 73.6% to 83.7%. The intervals overlap substantially, and each covers a range of response proportions rather than a single known value.

The sponsor-reported difference in proportions is 0.014. Its 90% confidence interval runs from -0.043 to 0.072, and its 95% confidence interval runs from -0.054 to 0.082. The interval includes zero and permits differences on either side of zero. The width indicates that the result does not pin down the difference to a very narrow range. Whether the range is sufficiently narrow for an equivalence conclusion depends on a margin defined before analysis; that margin is not reported in the registry record.

The unadjusted recalculation gives a risk difference of -0.012, with a 95% confidence interval from -0.08 to 0.056. It also spans zero and allows a range of possible differences. Because the recalculation and sponsor analysis are not the same analysis, their intervals should not be treated as interchangeable. The registry does not identify the sponsor’s method, which limits a direct explanation of why their estimates differ.

Confidence intervals describe statistical precision, not every source of uncertainty. They do not address possible selection effects from the PP population, missing outcomes, protocol deviations, or the applicability of the findings beyond the analyzed groups. The registry record also does not report a detailed missing-data analysis. Precision should therefore be considered together with the analysis population and the limits of the posted methods information.

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 effect18,24124,418
75% of the observed effect32,25343,177
50% of the observed effect72,17696,622
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect20,00050,000100,000200,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
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: Part 1: EU RPP.

The planning figures are participants per arm for 80% power and participants per arm for 90% power. They are planning illustrations based on the observed effect, not a report of the trial’s original design calculation. The stated 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 the stated fraction of the observed effect.

The 80% power column gives the number of participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting the specified effect under those assumptions, if that effect and the calculation’s model were applicable. The 90% power column uses a higher target chance of detecting the same specified effect and therefore generally requires more participants per arm. These are hypothetical design quantities, not outcomes from the completed trial.

Rows based on 100%, 75%, and 50% of the observed effect illustrate how planning changes when the effect of interest is smaller than the observed estimate. Smaller effects are harder to distinguish from random variation, so more participants are needed for the same power target. These rows do not establish that the effect will recur in another study or that any particular effect is clinically important.

For binary outcomes such as the primary response, the figures refer to participants per arm; they are not total event counts. The registry’s stated convention is that time-to-event calculations use total events, but the primary outcome is not time-to-event. This is not observed power: it is a planning illustration under stated assumptions, not a retrospective probability that the completed trial detected its true effect. The original trial’s sample-size assumptions and justification are not reported in the registry record.

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 = 0.801; treatment proportion p1 = 0.790; average p̄ = 0.796.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5703 = 1.1178.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5703 = 0.4799.
  4. n = (1.1178 + 0.4799)2 / (-0.0118)2 = 18,240.0, rounded up to 18,241 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 <- 0.801498127340824                          # control proportion
p1 <- 0.789667896678967                          # 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(2581345)
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 = 18,241 (80% power), 24,418 (90% power)
 75% of observed effect: n per arm = 32,253 (80% power), 43,177 (90% power)
 50% of observed effect: n per arm = 72,176 (80% power), 96,622 (90% power)
power.prop.test: 18240 
Simulated power at n = 18,241 per arm: 0.802 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
not statedDifference in proportion (M923 - EU RPP) 0.014-0.043 to 0.072not reported
not statedDifference in proportion (M923 - EU RPP) 0.014-0.054 to 0.082not reported

The sponsor-reported primary analysis is labelled as an equivalence analysis of the difference in proportion (M923 - EU RPP). It reports an estimate of 0.014, with a 90% confidence interval from -0.043 to 0.072 and a 95% confidence interval from -0.054 to 0.082. The registry does not post a p-value for these analyses, and the method and equivalence margin are not reported in the registry record.

The recalculated unadjusted risk difference from the posted summary statistics is -0.012, with a 95% confidence interval from -0.08 to 0.056 and an unadjusted p-value of 0.734. It is a simple calculation from the posted counts and denominators, rather than a reconstruction of the sponsor’s method. The sponsor’s estimate and the recalculation differ in value and direction as expressed for the comparison. The registry record does not explain that difference, and the method details needed to reconcile the analyses are not reported.

Neither estimate should be silently substituted for the other. The sponsor analysis is the registry-reported analysis; the recalculation is a separate unadjusted summary. The registry does not flag a discrepancy for this result, but that does not supply the missing method details or establish why the estimates differ. Interpretation of the sponsor’s equivalence label also requires the prespecified margin, which is not reported in the registry record.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary outcome and 35 secondary outcomes, along with 7 analyses. When multiple outcomes and comparisons are tested, the chance of obtaining at least one apparently unusual result can increase. Statistical procedures for controlling multiplicity, or a prespecified hierarchy that identifies which results are confirmatory, can help manage that issue. Such procedures and a hierarchy are not reported in the registry record.

The primary endpoint is identified as PASI 75 at Week 16, which gives a clear focal outcome. However, the registry entries do not describe how the analyses were prioritized, whether secondary outcomes were exploratory or confirmatory, or how multiplicity was addressed. The unadjusted secondary p-values and intervals, where available, should therefore not be interpreted as though every analysis were an isolated confirmatory test.

The primary analysis population is the PP Analysis Set. The record defines this group as a subgroup of the ITT Analysis Set who received at least 1 dose and did not have protocol deviations considered significant enough for exclusion from efficacy analysis. This clarifies the broad eligibility rule for that analysis but does not give participant-level reasons for exclusion, the number excluded from the ITT set, or the implications of exclusions for the comparison.

Missing-data handling for the primary and secondary outcomes is not reported in the registry record. The record does not explain how participants without an observed Week 16 assessment were handled, whether imputation was used, or whether sensitivity analyses were performed. Those details matter because a response proportion can depend on the denominator and on how unavailable outcomes are treated.

The record also does not report the sponsor’s primary statistical method, the equivalence margin, or the original sample-size justification. These omissions limit assessment of the formal equivalence claim and of how the analysis was designed. No interim analyses or detailed statistical analysis plan are reported in the registry record; their absence from the record should not be taken as evidence about what was or was not done.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Part 1: M92342851.4%
Part 1: EU RPP72852.5%
Part 2: M923102713.7%
Part 2: Transition EU RPP101327.6%
Part 2: Continuous EU RPP81316.1%
Participants with at least one serious adverse event
Serious adverse events by armPart 1: M9231.4%Part 1: EU RPP2.5%Part 2: M9233.7%Part 2: Transition EU RPP7.6%Part 2: Continuous EU RPP6.1%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Part 1: M9230 of 285
Part 1: EU RPP0 of 285
Part 2: M9230 of 271
Part 2: Transition EU RPP0 of 132
Part 2: Continuous EU RPP0 of 131

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
Part 1: M92392 of 285
Part 1: EU RPP104 of 285
Part 2: M92396 of 271
Part 2: Transition EU RPP47 of 132
Part 2: Continuous EU RPP63 of 131

Most frequent serious adverse event terms

Event termOrgan systemPart 1: M923Part 1: EU RPPPart 2: M923Part 2: Transition EU RPPPart 2: Continuous EU RPP
CardiomyopathyCardiac disorders0 of 2850 of 2851 of 2710 of 1321 of 131
Meniscus injuryInjury, poisoning and procedural complications0 of 2850 of 2850 of 2711 of 1321 of 131
AppendicitisInfections and infestations0 of 2850 of 2851 of 2710 of 1321 of 131
Acute Myocardial InfarctionCardiac disorders0 of 2851 of 2850 of 2710 of 1320 of 131
Myocardial ischaemiaCardiac disorders0 of 2851 of 2850 of 2710 of 1320 of 131
Angina pectorisCardiac disorders0 of 2850 of 2851 of 2710 of 1320 of 131
Cardiac failureCardiac disorders0 of 2850 of 2851 of 2710 of 1320 of 131
Hypertensive cardiomyopathyCardiac disorders0 of 2850 of 2851 of 2710 of 1320 of 131
Left ventricular failureCardiac disorders0 of 2850 of 2850 of 2710 of 1321 of 131
Supraventricular tachycardiaCardiac disorders0 of 2850 of 2851 of 2710 of 1320 of 131

Most frequent non-serious adverse event terms

Event termOrgan systemPart 1: M923Part 1: EU RPPPart 2: M923Part 2: Transition EU RPPPart 2: Continuous EU RPP
Injection site reactionGeneral disorders68 of 28579 of 28527 of 27115 of 13219 of 131
NasopharyngitisInfections and infestations19 of 28517 of 28540 of 27116 of 13220 of 131
PsoriasisSkin and subcutaneous tissue disorders8 of 2858 of 28528 of 27114 of 13221 of 131
Upper respiratory tract infectionInfections and infestations9 of 2856 of 28515 of 2716 of 13211 of 131
HeadacheNervous system disorders9 of 28510 of 2852 of 2717 of 1325 of 131

Serious events with the highest arm-level rate: cardiomyopathy (0.8%), left ventricular failure (0.8%), drug-induced liver injury (0.8%), hypersensitivity (0.8%), hip fracture (0.8%).

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 serious adverse event summaries are listed separately for Part 1 and Part 2 groups. In Part 1, the record reports 4 serious adverse events among 285 at risk in M923 and 7 among 285 at risk in EU RPP. In Part 2, it reports 10 among 271 at risk in M923, 10 among 132 at risk in Transition EU RPP, and 8 among 131 at risk in Continuous EU RPP. The record lists 0 deaths in each of these groups.

These figures are descriptive counts in the registry’s stated at-risk groups. They should not be treated as a direct comparison of safety without considering the different groups, follow-up, exposure, and analysis definitions. The registry record does not provide the statistical method for comparing serious adverse events or a detailed account of event timing and exposure duration.

The listed serious terms include Cardiomyopathy, Left ventricular failure, Drug-induced liver injury, Hypersensitivity, Hip fracture, and Meniscus injury, each reported as 0.8%. These term summaries add detail to the safety record but do not by themselves establish causation or permit a full assessment of risk. No medical advice or treatment conclusion follows from these descriptive summaries.

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

The primary result describes the proportion of participants in the PP analysis who reached a defined PASI improvement threshold by Week 16. The recorded group estimates are close, and the confidence intervals for the group proportions overlap. The sponsor-reported difference interval and the unadjusted recalculated interval both include zero. These features mean the posted summaries do not establish a clear separation between the groups on this endpoint, while also leaving uncertainty about the size and direction of any underlying difference.

The registry labels its sponsor analyses as equivalence analyses, but a formal equivalence interpretation depends on an equivalence margin and a suitable analysis. The margin and method are not reported in the registry record. An interval that includes zero is not sufficient by itself to demonstrate equivalence: it can also include differences that may matter under a prespecified margin. The reported label should therefore be distinguished from an independently assessable equivalence conclusion.

The result does not prove that the groups are identical, nor does it show that all participants responded similarly. A group percentage compresses variation among individuals into a single summary, and PASI 75 classifies participants according to a threshold. It does not describe the full distribution of score changes, other aspects of disease, or persistence of response beyond the stated assessment.

The result also does not address every question raised by the trial’s broader purpose. The primary endpoint is efficacy at Week 16 in the PP population; it is not a complete assessment of safety, immunogenicity, long-term outcomes, or every Part 2 comparison. The registry record’s missing details about statistical methods, missing data, and multiplicity further limit how broadly the result can be interpreted.

Accordingly, the most defensible reading is descriptive and bounded: the posted Week 16 PP response estimates are similar in magnitude, but their precision and the incompletely reported equivalence framework do not justify a claim of identity or a wider clinical conclusion. The data should be considered alongside the analysis population, the separate sponsor and recalculated analyses, and the other limitations of the registry record.

18. Why This Trial Matters Statistically

This trial is statistically interesting because the primary question is framed around equivalence rather than only whether a conventional difference test detects a difference. Equivalence asks whether the data are precise enough to exclude differences beyond a prespecified margin. That makes the margin and interval central to interpretation. The registry reports equivalence-labelled analyses and confidence intervals, but does not report the margin or method, leaving an important part of the inferential framework unavailable to readers.

The contrast between sponsor-reported and unadjusted recalculated summaries is another useful statistical lesson. A recalculation from counts and denominators is transparent and can provide a check on the posted group summaries, but it does not reproduce an analysis that may use other methods or populations. Here the reported estimates differ, and the registry record does not explain why. Keeping these analyses distinct prevents an unadjusted calculation from being mistaken for the sponsor’s result.

The endpoint illustrates how a continuous clinical score can be summarized using a responder threshold. This may be easier to communicate, but thresholding discards some information about the magnitude of changes within each response category. Confidence intervals and the population definition help readers see that the observed proportions are estimates, not exact descriptions of all eligible participants.

Finally, the record includes multiple outcomes, comparisons, and treatment groups. Recognizing their different time points and populations, and the absence of reported multiplicity and missing-data procedures, is essential to avoid treating every estimate as equally confirmatory. The central statistical lesson is that a close point estimate is only one component of interpretation; design, estimand, precision, and reporting detail all matter.

19. Limitations

The registry record leaves several trial-specific interpretive details unavailable. It lists a factorial model and several treatment groups, but does not explain the factorial structure, allocation ratios, or treatment sequence. The acronym EU RPP is not defined in the registry record for this analysis. These omissions make it difficult to reconstruct the full design and the exact meaning of each comparison from the record alone.

The primary analysis uses the PP population, which excludes participants with protocol deviations deemed important for efficacy analysis. The record gives the general definition but not the number or characteristics of participants excluded from that set, participant flow, or reasons for exclusions. The effect of this population choice on the comparison cannot be assessed from the registry entries.

The sponsor’s primary method and equivalence margin are not reported. That limits independent evaluation of the equivalence-labelled analyses, particularly because the sponsor estimate differs from the unadjusted recalculation. The registry does not explain the source of that difference. The original sample-size justification and statistical analysis plan are also not reported, so the planning illustrations should not be mistaken for the study’s original design rationale.

Missing-data procedures, sensitivity analyses, multiplicity control, and a secondary-outcome hierarchy are not reported in the registry record. These omissions matter for interpreting a collection of outcomes and for evaluating how unavailable assessments may affect response proportions. Safety summaries are descriptive, and the record does not provide details of comparative safety methods or exposure duration. These limitations constrain interpretation of the posted results but do not, by themselves, establish that the trial was improperly conducted.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

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23. Record Summary

NCT02581345 is a completed randomized Phase 3 study with triple masking and a factorial model, enrolling 572 participants with moderate to severe chronic plaque-type psoriasis. The registry describes a multicenter evaluation of M923 and Humira and lists efficacy, safety, and immunogenicity among the study aims.

The primary outcome is PASI 75 response at Week 16 in the PP Analysis Set. The registry reports 80.1% for M923 and 79.0% for EU RPP, with 95% confidence intervals for each group. It also posts equivalence-labelled analyses of the difference in proportions. A separate unadjusted recalculation gives a different estimate; the registry record does not explain the difference.

Interpretation is limited by unreported details including the equivalence margin, statistical method, missing-data handling, multiplicity approach, and original sample-size justification. The posted findings are best read as estimates for the stated analysis population and time point, with the uncertainty and reporting limitations kept in view.

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