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Arthritis, Psoriatic Phase 3 Binary Endpoint NCT03162796

A Study Evaluating the Efficacy and Safety of Guselkumab Administered Subcutaneously in Participants With Active Psoriatic Arthritis Including Those Previously Treated With Biologic Anti -Tumor Necrosis Factor (TNF) Alpha Agent(s): Complete Statistical Analysis

This analysis examines the placebo-controlled Week 24 ACR 20 result for guselkumab in active psoriatic arthritis, alongside the trial design, secondary outcomes, and safety counts. It explains the sponsor’s reported comparisons, unadjusted recalculations, and the limits of what can be concluded from the registry record.

Trial start: 2017-08-24  ·  Enrollment: 383  ·  Sponsor: Janssen Research & Development, LLC
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 A Study Evaluating the Efficacy and Safety of Guselkumab Administered Subcutaneously in Participants With Active Psoriatic Arthritis Including Those Previously Treated With Biologic Anti -Tumor Necrosis Factor (TNF) Alpha Agent(s) (NCT03162796), a randomized phase 3 study. The primary outcome is Percentage of Participants Who Achieved an American College of Rheumatology (ACR) 20 Response at Week 24.

383
Enrollment
Phase 3
3
Arms
In the primary outcome
+29.7 pts
Risk difference
Guselkumab 100 mg q8w
18.4 to 41.1 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT03162796
PhasePhase 3
ConditionArthritis, Psoriatic
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment383
Arms in the primary outcome3
Lead sponsorJanssen Research & Development, LLC
Results postedYes

2. Clinical Question

Population

Participants with active psoriatic arthritis, including participants previously treated with biologic anti-TNF alpha agents. The primary endpoint analysis population is described as full analysis set 1 (FAS1); a fuller definition of that population is not reported in the registry record.

Intervention

Subcutaneous guselkumab 100 mg on either a q8w or q4w schedule. The registry describes doses and placebo injections used to maintain blinding through the scheduled visits.

Comparator

Placebo through Week 24 for the primary comparison. Participants assigned to placebo were scheduled to cross over to guselkumab at Week 24, so later follow-up does not preserve the original placebo comparison in the same way.

Primary question

What percentage of participants achieved an ACR 20 response at Week 24, and how did that percentage compare between each guselkumab schedule and placebo? The response definition requires improvement across joint counts and a specified number of additional assessments; missing data or treatment failure criteria counted as non-response.

The trial addresses a treatment-group comparison in a defined clinical-trial population, not a prediction about the outcome for any individual. ACR 20 is a composite response criterion: improvement in swollen and tender joint counts is required, along with improvement in three of five other assessments. Those additional assessments include patient and physician assessments, physical function, and CRP. The measure therefore combines joint findings with patient-reported, clinician-assessed, functional, and laboratory information.

The registry record identifies the study as a Phase 3 randomized, double-blind, placebo-controlled trial. Its primary comparison is at Week 24, before the placebo group’s scheduled crossover to guselkumab. The endpoint population and rules for classifying missing observations and treatment failures are important to interpreting the percentages: participants with missing data or at least one specified treatment-failure criterion were classified as non-responders. The registry record does not report a more detailed definition of FAS1.

3. Trial Design

The registry describes a Phase 3, multicenter, randomized, double-blind, parallel-group, placebo-controlled study sponsored by Janssen Research & Development, LLC. It lists 383 participants enrolled and indicates that the study is completed. The recorded start date is 2017-08-24, and the primary completion date is 2019-03-14. These record details describe the study’s structure and timing; they do not establish how participants were recruited or how allocation was concealed, which are not reported in the registry record.

The study has a placebo group and two guselkumab schedules. One active schedule is 100 mg q8w, with guselkumab at Weeks 0 and 4 and then at Weeks 12, 20, 28, 36, and 44. Placebo injections at other visits were used to maintain the blind. The other active schedule is guselkumab 100 mg q4w from Week 0 through Week 48. Participants assigned to placebo received placebo q4w from Week 0 to Week 20 and were scheduled to cross over at Week 24 to guselkumab 100 mg q4w through Week 48.

The primary endpoint compares ACR 20 response at Week 24. That timing allows comparison with the placebo group before its planned crossover. The record also lists secondary outcomes covering physical function, ACR response levels at other time points, psoriasis response, disease activity, and health-related quality of life. The registry lists 100 outcome measures and 28 analyses, while 99 secondary outcomes are posted in the record.

How randomization was generated, whether it was stratified, the intended sample-size rationale, and the details of the original statistical plan are not reported in the registry record. The sample-size illustrations associated with the posted results are based on observed effects and are not the trial’s original design calculations.

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: One participant was accidentally randomized before completion of screening assessments. Subsequently, this participant screen failed and was later re-screened and randomized using a new participant number.Therefore, this participant was counted twice in the number of participants enrolled, but only once in the number of participants randomized.

Placebo Controlled Period: Week 0 - 24

StagePlaceboGuselkumab 100 mg q8wGuselkumab 100 mg q4w
STARTED126127128
COMPLETED114123125
NOT COMPLETED1243

Reasons for not completing this period:

ReasonPlaceboGuselkumab 100 mg q8wGuselkumab 100 mg q4w
Other011
Initiated prohibited medication100
Death100
Lost to Follow-up100
Withdrawal by Subject301
Lack of Efficacy400
Adverse Event231

Active Treatment Period: Week 24 - 52

StagePlaceboGuselkumab 100 mg q8wGuselkumab 100 mg q4w
STARTED114123125
COMPLETED107116124
NOT COMPLETED771

Reasons for not completing this period:

ReasonPlaceboGuselkumab 100 mg q8wGuselkumab 100 mg q4w
Withdrawal by Subject020
Lack of Efficacy431
Adverse Event320

Safety Follow-up: Week 52 - 60

StagePlaceboGuselkumab 100 mg q8wGuselkumab 100 mg q4w
STARTED107116124
COMPLETED106114123
NOT COMPLETED121

Reasons for not completing this period:

ReasonPlaceboGuselkumab 100 mg q8wGuselkumab 100 mg q4w
Withdrawal by Subject121

Analysis population for the primary outcome, as defined in the registry: Analysis population is full analysis set 1 (FAS1). Participants who achieved ACR 20 response at Week 24 and did not meet any TF criteria before Week 24 were considered as responders. Participants who met 1 or more TF criteria or with missing data were considered as non-responders.

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: Full Analysis Set (FAS) 1 included all participants who received at least 1 dose (complete/partial) of study agent according to randomized treatment group regardless of treatment actually received.

CharacteristicUnitPlaceboGuselkumab 100 mg q8wGuselkumab 100 mg q4wTotal
Participants analysed126127128381
Age, Continuousyears49 (SD 11.1)48.9 (SD 11.52)47.4 (SD 11.59)48.4 (SD 11.39)
Sex: Female, Male: FemaleParticipants655962186
Sex: Female, Male: MaleParticipants616866195
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants2204
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants122124128374
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants2103
Race (NIH/OMB): American Indian or Alaska NativeParticipants0000
Race (NIH/OMB): AsianParticipants1210729
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants0101
Race (NIH/OMB): Black or African AmericanParticipants0000
Race (NIH/OMB): WhiteParticipants112116121349
Race (NIH/OMB): More than one raceParticipants0000
Race (NIH/OMB): Unknown or Not ReportedParticipants2002
Region of Enrollment: AUSTRALIAParticipants58417
Region of Enrollment: CANADAParticipants83415
Region of Enrollment: CZECH REPUBLICParticipants54312
Region of Enrollment: GERMANYParticipants3101023
Region of Enrollment: HUNGARYParticipants34916
Region of Enrollment: MALAYSIAParticipants5128
Region of Enrollment: POLANDParticipants373634107
Region of Enrollment: RUSSIAN FEDERATIONParticipants22192364
Region of Enrollment: SOUTH KOREAParticipants3104
Region of Enrollment: SPAINParticipants56112

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants Who Achieved an American College of Rheumatology (ACR) 20 Response at Week 24, measured over Week 24.

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

The primary endpoint is the percentage of participants who achieved an American College of Rheumatology (ACR) 20 response at Week 24. ACR 20 requires at least 20% improvement from baseline in both swollen joint count, measured across 66 joints, and tender joint count, measured across 68 joints. It also requires at least 20% improvement from baseline in three of five assessments: the patient’s pain assessment, the patient’s global assessment of disease activity, the physician’s global assessment, physical function measured by HAQ-DI, and CRP.

It is a composite endpoint because response depends on a combination of findings rather than a single measure. Requiring improvement in both joint counts and several additional assessments makes the endpoint reflect more than one aspect of psoriatic arthritis. The thresholded response also gives a clear classification—responder or non-responder—for each participant under the stated rules. That can make a group comparison easier to interpret than a collection of separate measures, although it does not show the full degree or pattern of change for each component.

The registry specifies that participants in FAS1 who met one or more treatment-failure criteria before Week 24, or who had missing data, were considered non-responders. Treatment-failure criteria included stopping study drug, starting or increasing specified concomitant treatments, or starting prohibited psoriatic arthritis treatment. The registry does not report the full FAS1 membership definition or further details about handling missing values beyond this non-responder rule.

7. Results Posted in the Registry

Risk difference: Guselkumab 100 mg q8w

+29.7

95% CI: 18.4 to 41.1 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals10.723.135.547.960.372.7Placebo (n=126)Guselkumab 100 mg q8w (n=127)Guselkumab 100 mg q4w (n=128)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Guselkumab 100 mg q8wGuselkumab 100 mg q4w-3.877.3519304152risk 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 an American College of Rheumatology (ACR) 50 Response at Week 24Binary EndpointRisk difference+21.2 pts (11.8 to 30.6)54 per arm
Percentage of Participants With Psoriasis Response of IGA (Score: 0[Cleared] or 1[Minimal] and >=2 Grade Reduction From Baseline) at Week 24 Among Participants With >=3% Body Surface Area (BSA) Psoriatic Involvement and IGA Score of >=2 (Mild) at BaselineBinary EndpointRisk difference+41.9 pts (28.6 to 55.3)20 per arm
Percentage of Participants Who Achieved an American College of Rheumatology (ACR) 20 Response at Week 16Binary EndpointRisk difference+26.6 pts (15.0 to 38.1)52 per arm

Percentage of Participants Who Achieved an American College of Rheumatology (ACR) 50 Response at Week 24

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Guselkumab 100 mg q8wGuselkumab 100 mg q4w-2.955.6014233140risk difference (percentage points) vs control (95% CI)

Percentage of Participants With Psoriasis Response of IGA (Score: 0[Cleared] or 1[Minimal] and >=2 Grade Reduction From Baseline) at Week 24 Among Participants With >=3% Body Surface Area (BSA) Psoriatic Involvement and IGA Score of >=2 (Mild) at Baseline

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Guselkumab 100 mg q8wGuselkumab 100 mg q4w-5.751128446178risk difference (percentage points) vs control (95% CI)

Percentage of Participants Who Achieved an American College of Rheumatology (ACR) 20 Response at Week 16

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Guselkumab 100 mg q8wGuselkumab 100 mg q4w-3.697.0118283950risk difference (percentage points) vs control (95% CI)

Across the posted secondary outcomes, the broad pattern is that the guselkumab groups have higher response percentages than placebo on several response measures, including ACR measures and psoriasis response. The secondary outcomes also include changes in physical function and disease activity, and a health-related quality-of-life measure. Considered together, these outcomes provide context around the primary ACR 20 finding: the observed pattern is not limited to the primary response definition alone.

Secondary endpoints differ in what they measure, their assessment time, and the participants eligible for analysis. The psoriasis response outcome, for example, is restricted to participants meeting the stated baseline body-surface-area and IGA criteria. ACR 50 and ACR 70 use more demanding response thresholds than ACR 20, while change scores and disease-activity measures have different scales and interpretations. These differences mean that results should be considered outcome by outcome, rather than combined as if every measure represented the same clinical construct.

The secondary findings carry less inferential weight than a prespecified primary result when the record does not establish how testing across outcomes was handled. Repeated testing across many outcomes can increase the chance of at least one apparently noteworthy result arising by chance. The registry record does not report a multiplicity-control procedure or a hierarchy defining which secondary tests were confirmatory. The posted secondary comparisons should therefore be treated as supportive or exploratory evidence, not as independent confirmation equivalent to the primary analysis.

The secondary outcomes generally relate to the primary result by assessing other dimensions of symptoms, function, skin involvement, disease activity, or quality of life. They can help show whether the pattern is coherent across domains, but they do not replace the primary endpoint or resolve limitations in its population, measurement, or analysis. The record’s many outcomes also make selective emphasis a concern; interpretation should account for the full outcome set rather than focus only on favorable findings.

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

9. Statistical Interpretation

Clinical Biostats interpretation

At Week 24, the posted response percentages were 22.2 for placebo, 52.0 for guselkumab 100 mg q8w, and 59.4 for guselkumab 100 mg q4w. These are the percentages for the primary endpoint, ACR 20 response. They describe the trial groups under the registry’s classification rule, including the rule that missing observations and specified treatment failures count as non-response. They should not be read as the probability of response for a particular person.

The sponsor’s reported comparison of guselkumab q8w with placebo gives a difference in percentage of 29.8, with a 95% confidence interval from 18.6 to 41.1 and p < 0.001. For guselkumab q4w compared with placebo, the reported difference is 37.1, with a 95% confidence interval from 26.1 to 48.2 and p < 0.001. The registry labels both analyses as superiority comparisons and identifies the Cochran-Mantel-Haenszel method. The posted results therefore show higher ACR 20 response percentages in each guselkumab group than in the placebo group at this assessment point.

Unadjusted recalculations from the posted arm summaries express the risk difference on the proportion scale. For q8w versus placebo, the estimate is 0.297, with a 95% interval from 0.184 to 0.411. For q4w versus placebo, it is 0.371, with a 95% interval from 0.260 to 0.483. These recalculations are not identical to the sponsor’s reported analysis because they are simple unadjusted calculations from the posted summaries, whereas the sponsor reports a Cochran-Mantel-Haenszel analysis. The sponsor’s own analysis is the primary reported analysis; the recalculations are useful as a transparent comparison based on the displayed group data.

The p-values indicate that the observed contrasts would be unusual under the null hypothesis used for each analysis, subject to that analysis’s assumptions. They do not quantify the size or clinical importance of an effect, and they do not establish that all uncertainty has been resolved. The confidence intervals describe a range of effect estimates compatible with the analysis and data under its assumptions. Both sponsor-reported intervals are above zero, consistent with the reported superiority tests.

The study also reports higher percentages for the active groups across the listed secondary outcomes, including ACR response measures, psoriasis response, disease activity, physical function, and health-related quality of life. The secondary results add context but should not be treated as equivalent to the designated primary analysis. The record does not report whether or how multiplicity was controlled across the many outcomes and analyses. The conclusions are also specific to the Week 24 endpoint, the study population, and the response and missing-data rules recorded for this analysis.

10. Statistical Methods Explained

The primary outcome is binary: a participant either met the ACR 20 response definition at Week 24 or did not, according to the registry’s analysis rules. The arm percentages summarize the proportion classified as responders. For this endpoint, the registry says participants who met treatment-failure criteria before Week 24 or had missing data were classified as non-responders. That rule is part of the estimand being described: the posted percentages are not simply the observed response among participants with complete measurements.

What does a risk difference describe?

A risk difference compares the event proportions in two groups by subtracting one proportion from the other. Here, the event is ACR 20 response, and the comparisons use placebo as the control. A positive risk difference means the response proportion is higher in the guselkumab group in that comparison. The recalculated estimates are 0.297 for q8w versus placebo and 0.371 for q4w versus placebo. Their respective unadjusted 95% confidence intervals are 0.184 to 0.411 and 0.260 to 0.483. These are simple recalculations from the posted arm summaries, not replacements for the sponsor’s analysis.

A risk difference is an absolute contrast on the proportion scale. It answers how far apart the group response proportions are, rather than expressing the contrast as a relative change. Other effect measures, such as a risk ratio or odds ratio, answer different questions and can give a different impression of the same data. Measures should therefore be interpreted according to their scale and should not be treated as interchangeable.

Why is the sponsor’s method different?

The registry identifies the sponsor’s primary comparisons as Cochran-Mantel-Haenszel analyses of the difference in percentage. The reported q8w contrast is 29.8, with a 95% confidence interval from 18.6 to 41.1; the reported q4w contrast is 37.1, with a 95% confidence interval from 26.1 to 48.2. Both have p < 0.001. A Cochran-Mantel-Haenszel analysis is a general method for comparing categorical outcomes while accounting for defined strata. The registry does not report the specific stratification details in the registry record for this analysis, so those details should not be inferred.

The unadjusted recalculations use the posted group summaries directly. The sponsor’s reported method may incorporate analysis features not reproduced by a simple calculation from aggregate percentages. Since the registry reports no discrepancy, the sponsor’s reported analysis remains the main trial analysis, and the unadjusted results serve as a check and a complementary description rather than a competing primary result.

What do the p-values say?

A p-value is a measure of how incompatible the observed data are with a specified null hypothesis, assuming the analysis model and other conditions hold. The registry reports p < 0.001 for each primary comparison. This is evidence against the null hypothesis used in those comparisons; it is not the probability that the null hypothesis is true. It also does not measure the probability that the finding will replicate, nor does it express clinical importance.

The registry labels the sponsor analyses as superiority tests. A superiority test evaluates whether the outcome differs in the direction of a higher response in the intervention group compared with the control under the stated framework. The record does not report further details of the testing hierarchy, allocation of significance levels across endpoints, or any multiplicity adjustment. Interpretation of the primary p-values is therefore distinct from interpretation of the many secondary analyses.

Why do endpoint rules matter?

ACR 20 requires improvement in both joint-count measures and a threshold of improvement in three of five additional assessments. ACR 20 therefore does not mean that every component improved, nor does it convey the size of change beyond meeting the response thresholds. The non-responder rule for missing data and treatment failure also affects the classification. Such rules can be conservative in some settings, but their impact depends on why observations are missing and how missingness relates to outcomes; that information is not reported in the registry record.

General statistical context: randomization supports comparison of assigned groups by reducing systematic differences at assignment, while blinding can help limit differences in care or assessment related to knowledge of allocation. These design features do not remove all uncertainty, guarantee that every potential source of bias is absent, or ensure that results apply to populations outside the trial. The registry identifies the trial as randomized and double-blind but does not report all operational details needed to assess implementation.

11. Confidence Intervals and Precision

A confidence interval communicates uncertainty around an estimated group contrast. In general, a narrower interval indicates greater precision under the analysis assumptions, while a wider interval indicates less precision. A confidence interval is not a range containing every participant’s response, and it is not a guarantee that the true effect lies within its endpoints. Its interpretation depends on the method used and the assumptions underlying that method.

For the sponsor’s q8w comparison, the estimated difference in percentage is 29.8 and the 95% confidence interval runs from 18.6 to 41.1. For q4w, the estimate is 37.1 and the interval runs from 26.1 to 48.2. Each interval lies above zero, in line with the reported p < 0.001 superiority result. The interval widths also show that the point estimates should not be treated as exact values: a range of effect sizes remains compatible with the data and analysis.

The unadjusted recalculated intervals are reported on the proportion scale: 0.184 to 0.411 for q8w and 0.260 to 0.483 for q4w. These intervals accompany simple calculations from the posted summaries, not the sponsor’s Cochran-Mantel-Haenszel method. The two sets of estimates and intervals should be read on their stated scales and in light of their different methods, rather than compared as though they were generated by an identical analysis.

Precision is affected by the amount of information in the data, the event frequency, and the analysis method. Confidence intervals do not address unmeasured bias, incomplete reporting, endpoint selection, or whether the study population represents other populations. The registry record does not provide enough information to evaluate all such issues. Nor do the intervals establish that the difference is clinically important; the registry does not state a threshold for clinical importance.

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 effect4154
75% of the observed effect6992
50% of the observed effect147197
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect5010020050040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
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: Guselkumab 100 mg q8w.

The sample-size illustrations use the observed effect as a starting point and show planning examples for detecting the full observed effect, 75% of the observed effect, or 50% of the observed effect. For these binary outcomes, the entries are participants per arm, not total events. The assumptions listed for the illustrations are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The stated effect to detect is the selected fraction of the observed effect. The original trial’s own design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the illustrative number of participants per arm for a design that, under those assumptions and a specified effect, would have an 80% chance of producing a statistically significant result if that effect were the true one. The 90% power column describes the corresponding planning target for a 90% chance under the same kind of assumptions. These are design calculations, not statements about the probability that the trial’s observed result is correct. The displayed figures are planning illustrations, not observed power.

The effect-size scenarios matter: when planning to detect a smaller effect, more participants are generally needed to distinguish it from random variation, all else being equal. Thus the rows representing 75% or 50% of the observed effect require larger per-arm planning figures than the row based on the full observed effect. Such illustrations are sensitive to the assumed event rates, allocation, statistical method, and other design choices. They do not establish what the trial originally planned or whether its enrolled sample was adequate for every outcome.

A curve accompanying the sample-size material should be read as a visual representation of the same planning relationship, not as a new result from the trial. The registry record does not report that these calculations were used to choose the trial’s enrollment target.

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 = 0.222; treatment proportion p1 = 0.520; average p̄ = 0.371.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6832 = 1.3389.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6500 = 0.5470.
  4. n = (1.3389 + 0.5470)2 / (0.2975)2 = 40.2, rounded up to 41 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 <- 0.222222222222222                          # control proportion
p1 <- 0.519685039370079                          # 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(3162796)
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 = 41 (80% power), 54 (90% power)
 75% of observed effect: n per arm = 69 (80% power), 92 (90% power)
 50% of observed effect: n per arm = 147 (80% power), 197 (90% power)
power.prop.test: 40.2 
Simulated power at n = 41 per arm: 0.816 (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
Cochran-Mantel-HaenszelDifference in percentage 29.818.6 to 41.1< 0.001
Cochran-Mantel-HaenszelDifference in percentage 37.126.1 to 48.2< 0.001

The registry reports the sponsor’s primary analyses using the Cochran-Mantel-Haenszel method. For q8w compared with placebo, the sponsor reports a difference in percentage of 29.8, with a 95% confidence interval from 18.6 to 41.1 and p < 0.001. For q4w compared with placebo, the corresponding reported difference is 37.1, with a 95% confidence interval from 26.1 to 48.2 and p < 0.001.

The unadjusted recalculations use the posted arm summaries and give risk differences of 0.297 and 0.371, respectively. Their intervals are 0.184 to 0.411 and 0.260 to 0.483. These are simple recalculations on the proportion scale and are not the sponsor’s reported stratified-method estimates. Small differences between an aggregate-data recalculation and the sponsor’s analysis can arise from differences in method and analysis details. The registry record does not describe all details needed to reproduce the sponsor’s calculation from individual-level data.

The registry marks no discrepancy between the reported analyses and the recalculations. The sponsor’s own analysis therefore remains the principal reported analysis; the recalculations are supplementary checks based on the posted summaries. They should not be interpreted as a correction to, or a substitute for, the registered analysis. Both forms of analysis point in the same direction, but their estimates and confidence intervals should be associated with the method that produced them.

15. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when statistical tests are conducted across multiple outcomes, comparisons, or time points. If each test is interpreted in isolation, the chance of at least one false-positive result across the set can be greater than the nominal error rate for an individual test. Common approaches include a prespecified testing sequence, adjustment of significance thresholds, or clearly distinguishing confirmatory from exploratory analyses. These are general statistical options, not procedures that can be assumed for this trial.

The registry reports 100 outcome measures, 28 analyses, and 99 posted secondary outcomes. It identifies the primary endpoint and reports sponsor p-values for the primary comparisons, but a multiplicity adjustment, testing hierarchy, or family-wise error procedure is not reported in the registry record. Accordingly, the primary findings can be interpreted as the trial’s stated primary comparison, while the secondary p-values should be read with caution. The record does not establish that the nominal p-values for secondary outcomes control the chance of false-positive findings across all analyses.

The endpoint population is named full analysis set 1 (FAS1). The registry describes the responder classification for that population, but a complete membership definition for FAS1 is not reported in the registry record. Participants who met one or more listed treatment-failure criteria before Week 24 or had missing data were considered non-responders. This rule is reported for the primary endpoint; further missing-data methods, including sensitivity analyses or alternative assumptions, are not reported in the registry record.

Missing-data handling can matter because the conclusions may depend on whether unavailable measurements are related to treatment response. Classifying missing observations as non-response is explicit and makes the analysis rule transparent, but it does not reveal the reasons observations were missing or how alternative rules would affect estimates. The record also does not report interim analyses, a full statistical analysis plan, or additional details of the randomization procedure. Those omissions limit assessment of analysis choices beyond the methods stated for the posted results.

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 (CP)51264.0%
Guselkumab 100 mg q8w (CP)41273.1%
Guselkumab 100 mg q4w (CP)01280.0%
Placebo to Guselkumab 100 mg q4w (ACP Through Week 60)41143.5%
Guselkumab 100 mg q8w (Through Week 60)81276.3%
Guselkumab 100 mg q4w (Through Week 60)41283.1%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo (CP)4.0%Guselkumab 100 mg q8w (CP)3.1%Guselkumab 100 mg q4w (CP)0.0%Placebo to Guselkumab 100 mg …3.5%Guselkumab 100 mg q8w (Throug…6.3%Guselkumab 100 mg q4w (Throug…3.1%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Placebo (CP)2 of 126
Guselkumab 100 mg q8w (CP)0 of 127
Guselkumab 100 mg q4w (CP)0 of 128
Placebo to Guselkumab 100 mg q4w (ACP Through Week 60)0 of 114
Guselkumab 100 mg q8w (Through Week 60)0 of 127
Guselkumab 100 mg q4w (Through Week 60)0 of 128

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 (CP)25 of 126
Guselkumab 100 mg q8w (CP)38 of 127
Guselkumab 100 mg q4w (CP)28 of 128
Placebo to Guselkumab 100 mg q4w (ACP Through Week 60)25 of 114
Guselkumab 100 mg q8w (Through Week 60)48 of 127
Guselkumab 100 mg q4w (Through Week 60)41 of 128

Most frequent serious adverse event terms

Event termOrgan systemPlacebo (CP)Guselkumab 100 mg q8w (CP)Guselkumab 100 mg q4w (CP)Placebo to Guselkumab 100 mg q4w (ACP Through Week 60)Guselkumab 100 mg q8w (Through Week 60)Guselkumab 100 mg q4w (Through Week 60)
Arrhythmia SupraventricularCardiac disorders0 of 1261 of 1270 of 1280 of 1141 of 1270 of 128
Mechanical IleusGastrointestinal disorders0 of 1261 of 1270 of 1280 of 1141 of 1270 of 128
Plasma Cell MyelomaNeoplasms benign, malignant and unspecified (incl cysts and polyps)0 of 1261 of 1270 of 1280 of 1141 of 1270 of 128
Cervical DysplasiaReproductive system and breast disorders0 of 1261 of 1270 of 1280 of 1141 of 1270 of 128
Atrial FibrillationCardiac disorders0 of 1260 of 1270 of 1281 of 1140 of 1270 of 128
Cardiac FailureCardiac disorders1 of 1260 of 1270 of 1280 of 1140 of 1270 of 128
PainGeneral disorders1 of 1260 of 1270 of 1280 of 1140 of 1270 of 128
Abscess LimbInfections and infestations1 of 1260 of 1270 of 1280 of 1140 of 1270 of 128
BronchitisInfections and infestations0 of 1260 of 1270 of 1280 of 1141 of 1270 of 128
CellulitisInfections and infestations0 of 1260 of 1270 of 1280 of 1141 of 1270 of 128

Most frequent non-serious adverse event terms

Event termOrgan systemPlacebo (CP)Guselkumab 100 mg q8w (CP)Guselkumab 100 mg q4w (CP)Placebo to Guselkumab 100 mg q4w (ACP Through Week 60)Guselkumab 100 mg q8w (Through Week 60)Guselkumab 100 mg q4w (Through Week 60)
NasopharyngitisInfections and infestations8 of 12616 of 1277 of 12813 of 11421 of 12714 of 128
Upper Respiratory Tract InfectionInfections and infestations8 of 1267 of 12711 of 1288 of 11410 of 12716 of 128
Alanine Aminotransferase IncreasedInvestigations3 of 1268 of 1275 of 1284 of 1149 of 1279 of 128
Aspartate Aminotransferase IncreasedInvestigations3 of 1269 of 1273 of 1284 of 11411 of 1276 of 128
EnthesopathyMusculoskeletal and connective tissue disorders6 of 1266 of 1276 of 1280 of 1147 of 1278 of 128
BronchitisInfections and infestations1 of 1265 of 1271 of 1283 of 1149 of 1272 of 128

Serious events with the highest arm-level rate: atrial fibrillation (0.9%), pyelonephritis (0.9%), urosepsis (0.9%), head injury (0.9%), cardiac failure (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.

For the placebo-controlled period, the registry lists serious adverse events in 5 participants in the placebo group, 4 in the guselkumab 100 mg q8w group, and 0 in the guselkumab 100 mg q4w group. The corresponding groups at risk are listed as 126, 127, and 128. Deaths are listed as 2 for placebo and 0 for each guselkumab group during this period. These are counts from the posted safety record; they should be read with the stated groups and period, not as estimates of an individual’s risk.

The record also lists safety data through Week 60, including groups that reflect crossover from placebo to guselkumab. Those later group descriptions do not represent the same original placebo-controlled comparison, because participants assigned to placebo were scheduled to begin guselkumab at Week 24. Serious adverse event counts through Week 60 are 4 for the placebo-to-guselkumab q4w group, 8 for the q8w group, and 4 for the q4w group. Deaths in those groups are listed as 0.

Serious adverse event counts alone do not establish whether an event was caused by treatment, and low counts provide limited precision for comparing uncommon outcomes. The registry lists serious-event terms, but event counts and percentages should be interpreted alongside follow-up period, exposure, and the complete safety record. The posted counts do not support a causal conclusion by themselves.

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

The primary result describes group-level ACR 20 response at Week 24 under the endpoint rules recorded for the trial. The posted percentages were 22.2 for placebo, 52.0 for guselkumab 100 mg q8w, and 59.4 for guselkumab 100 mg q4w. The sponsor’s reported comparisons favored each guselkumab schedule over placebo, with p < 0.001 for each comparison and confidence intervals above zero. This is evidence about the relative response percentages in this randomized, double-blind trial at the specified assessment point.

The result does not mean that every participant receiving guselkumab responded, that every participant receiving placebo did not respond, or that an individual can know their likely outcome from the group percentage. ACR 20 is a threshold-based composite measure. It requires improvement in specified joint counts and additional assessments, but it does not show how much each component changed or whether every symptom or disease feature improved. The registry’s non-responder rule also counts missing data and specified treatment failures as non-response.

The result does not by itself establish the size of a clinically important benefit. The record does not state a threshold for clinical importance, and statistical significance is not the same as clinical importance. Nor does it establish that the observed contrast will be identical in other populations, settings, or periods of follow-up. The trial includes participants with active psoriatic arthritis, including those previously treated with biologic anti-TNF alpha agents, but the registry record does not provide all details needed to judge how closely this group represents any particular clinical population.

Safety counts are descriptive and do not by themselves show causation or settle comparisons for uncommon events. Secondary results add information across other outcomes, but the registry does not report multiplicity control, so they warrant more cautious interpretation. The record also does not report the full statistical plan, FAS1 definition, or additional missing-data sensitivity analyses. These limits leave important questions about generalizability and robustness beyond the primary reported comparison.

18. Why This Trial Matters Statistically

This trial illustrates why a clinical result should be read through its endpoint definition, comparison, and analysis method rather than through a single percentage or p-value. ACR 20 is a composite response requiring improvement in joint counts plus improvement across additional assessments. The resulting responder proportion is interpretable as a threshold outcome, but it compresses multiple dimensions of disease response into a yes-or-no classification. That distinction matters when translating a statistical comparison into a broader description of patient experience.

The trial also makes the contrast between an adjusted sponsor analysis and an unadjusted recalculation visible. The registry reports Cochran-Mantel-Haenszel comparisons, while the recalculations use posted aggregate summaries. The estimates are close in direction, but they arise from different methods and should be reported with their own confidence intervals and scales. This is a useful example of why independent arithmetic checks can support transparency without replacing a trial’s stated analysis.

Finally, the study’s multiple secondary outcomes show how evidence accumulates across domains while also creating multiplicity concerns. A consistent broad pattern can be informative, but it does not eliminate the need to distinguish a primary test from secondary findings whose testing framework is not reported. The record’s explicit handling of missing values and treatment failures also demonstrates that outcome classification rules are part of the statistical question, not a technical afterthought.

For biostatisticians and clinical researchers, the central lesson is to connect effect estimates to their denominator, endpoint rule, analysis population, time point, and uncertainty. Doing so clarifies what the observed data support, what is a supplementary analysis, and what remains unreported. It also prevents statistical significance from being mistaken for a complete account of benefit, safety, or applicability.

19. Limitations

The registry record does not report the full definition of FAS1, the original sample-size justification, the complete statistical analysis plan, or the trial’s detailed randomization procedures. Those omissions make it difficult to assess whether the posted analyses follow all prespecified decisions or to reproduce the sponsor’s method fully from the record. The sample-size illustrations based on observed effects cannot substitute for the original design rationale.

The primary endpoint is a thresholded composite. It does not preserve the full scale of change in its component measures, and an ACR 20 classification does not indicate which components drove response. Missing data and treatment-failure criteria were counted as non-response, but reasons for missingness and sensitivity analyses under alternative assumptions are not reported. These details matter when judging robustness of the responder percentages.

The study reports many outcomes and analyses, but the registry does not report multiplicity control or a testing hierarchy. This limits the strength of confirmatory interpretation for secondary findings and makes selective emphasis a risk. The posted results also include secondary outcomes with different eligibility criteria and time points, so they should not be treated as a uniform set of interchangeable measures.

Placebo crossover at Week 24 limits interpretation of later follow-up as a continued placebo-controlled comparison. Safety counts through Week 60 include groups after crossover, so the randomized comparison is clearest during the placebo-controlled period. Serious adverse events and deaths are relatively sparse in the posted counts, which limits precision for comparing uncommon outcomes. The record does not provide enough detail to draw causal conclusions about individual events.

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23. Record Summary

The registry identifies NCT03162796 as a completed Phase 3, multicenter, randomized, double-blind, parallel-group, placebo-controlled study of subcutaneous guselkumab in active psoriatic arthritis, including participants previously treated with biologic anti-TNF alpha agents. Enrollment is listed as 383. The primary completion date is 2019-03-14.

The primary outcome is ACR 20 response at Week 24. Posted response percentages were 22.2 for placebo, 52.0 for guselkumab 100 mg q8w, and 59.4 for guselkumab 100 mg q4w. The sponsor reports Cochran-Mantel-Haenszel differences of 29.8 and 37.1 percentage points, respectively, with p < 0.001 for each comparison.

The registry also posts secondary outcomes and safety counts. The trial’s original sample-size rationale, multiplicity procedure, full FAS1 definition, and further missing-data analyses are not reported in the registry record.

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