Study of Efficacy and Safety of Brodalumab in Subjects With Psoriatic Arthritis: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Study of Efficacy and Safety of Brodalumab in Subjects With Psoriatic Arthritis (NCT02024646), a randomized phase 3 study. The primary outcome is ACR20 (American College of Rheumatology 20% Improvement) Response Rate Through Week 16.

2. Clinical Question

3. Trial Design

This was a randomized, parallel-group, placebo-controlled phase 3 study of brodalumab in people with psoriatic arthritis. The registry lists quadruple masking. That label indicates that masking was recorded at that level, but the roles included in the masking are not reported in the registry record. The parallel design means participants were assigned to one of the treatment arms rather than crossing between treatments as part of the stated comparison.

The intervention arms were 210 mg brodalumab and 140 mg brodalumab, administered by subcutaneous injection. The comparator was subcutaneous placebo, described as continuing until week 24. The registry lists enrollment of 484. The primary endpoint is framed around baseline and 16 weeks, and the primary analysis set is described as randomized subjects who had the opportunity to complete the week 16 visit before study termination.

The registry identifies the study as completed and lists its start as 2014-03 and primary completion as 2015-10. These dates describe the registry record; they do not, by themselves, establish when every participant was assessed or how follow-up was handled. The registry record does not report the trial’s original sample-size justification, detailed allocation procedures, or which people were masked. It also does not report a detailed statistical analysis plan or a sponsor-reported inferential analysis for the primary endpoint. The efficacy comparisons discussed in the results are unadjusted recalculations from the posted summary information, rather than a substitute for an unreported sponsor analysis.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Analysis population for the primary outcome, as defined in the registry: The Primary Analysis Set consists of all randomized subjects who had the opportunity to complete the week 16 visit prior to termination of the study. The numbers in the outcome measure data table reflect the percentage of subjects achieving ACR20.

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as ACR20 (American College of Rheumatology 20% Improvement) Response Rate Through Week 16, measured over Baseline and 16 Weeks.

The primary endpoint is the ACR20 response rate through week 16, expressed as the percentage of participants. The registry describes ACR20 as the proportion of subjects reaching a 20% improvement in tender and swollen joint counts. It states that a higher percentage reaching an improvement indicates greater success on this measure. The timeframe is listed as baseline and 16 weeks.

A response-rate endpoint turns a participant-level outcome into a proportion: each person is classified according to whether the specified response was reached, and the percentage reports how common that response was in the analysis group. In general, a binary endpoint can be straightforward to interpret because it distinguishes whether the criterion was met, but it does not show the size of improvement for each individual or capture all dimensions of a condition. Those are general properties of binary endpoints, not additional findings from this trial.

The registry record does not provide further detail about how the component measures were collected, how borderline or unavailable assessments were classified, or whether additional clinical measures were part of the primary endpoint. The reported rates were 41.8% for 210 mg brodalumab, 48.9% for 140 mg brodalumab, and 24.7% for placebo. Those percentages describe the endpoint as posted; they do not, on their own, quantify uncertainty or establish why participants did or did not respond.

7. Results Posted in the Registry

• 210 mg Brodalumab: 41.8% (61/146) versus 24.7% (36/146) on control; risk difference 17.1 percentage points (95% CI 6.5 to 27.7), risk ratio 1.69 (1.20–2.39); unadjusted two-proportion z-test p = 0.002.
• 140 mg Brodalumab: 48.9% (69/141) versus 24.7% (36/146) on control; risk difference 24.3 percentage points (95% CI 13.5 to 35.1), risk ratio 1.98 (1.43–2.76); unadjusted two-proportion z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry record provides binary response percentages by arm and comparison summaries that are identified as recalculated, unadjusted results. The method explanations below are general descriptions of what these statistics mean; they do not establish which complete analysis procedure the trial sponsor used.

What does a response percentage describe?

For a binary endpoint such as ACR20, each participant is represented as having met or not met the response criterion. The arm percentage describes the fraction of assessed participants who met that criterion, expressed as a percentage. The posted outcome gives 41.8% for 210 mg brodalumab, 48.9% for 140 mg brodalumab, and 24.7% for placebo. The outcome record also identifies the numbers of participants in the arm summaries: 146 for 210 mg brodalumab, 141 for 140 mg brodalumab, and 146 for placebo. These are endpoint denominators, not a restatement of overall enrollment.

In general, a percentage is easier to interpret when its denominator and analysis population are clear. Here, the registry describes the primary analysis set as randomized subjects who had the opportunity to complete the week 16 visit before study termination. It does not give further detail about how missing endpoint values were treated or whether all randomized participants contributed to the posted outcome. The stated analysis-set definition and the arm denominators should therefore be kept together when interpreting the percentages.

What is a risk difference?

In general, a risk difference is the absolute difference between two event proportions. For this binary endpoint, the event is reaching ACR20. The recalculated unadjusted estimates are 0.171 for the comparison of 210 mg brodalumab with placebo and 0.243 for the comparison of 140 mg brodalumab with placebo. An estimate above zero indicates a higher response proportion in the brodalumab arm under the comparison’s stated direction. These figures are recalculations from posted summary statistics, not adjusted estimates.

A risk difference is measured on the probability scale. It differs from a relative risk, which compares proportions as a ratio, and an odds ratio, which compares odds. The comparison record includes recalculated relative measures as well, but the absolute rates and risk differences provide direct context for the response proportions. These measures answer different statistical questions and should not be treated as interchangeable.

What do the p values say?

The unadjusted p values are 0.002 for 210 mg brodalumab versus placebo and <0.001 for 140 mg brodalumab versus placebo. In general, a p value describes how unusual data at least this discrepant from a specified null comparison would be if that null model and its assumptions held. It is not the probability that the null hypothesis is true, a measure of the size of an effect, or a direct measure of clinical importance.

These p values are explicitly unadjusted. The registry record does not report a multiplicity procedure for the two dose comparisons or the sponsor’s own inferential analysis. Without that information, the p values should not be interpreted as adjusted for testing multiple comparisons. Their interpretation also depends on the statistical assumptions used in the recalculation.

Why does uncertainty matter?

A confidence interval gives a range of values compatible with the observed data under a specified method and its assumptions. In general, a narrower interval indicates greater precision, while a wider interval indicates more uncertainty about the size of the estimate. The recalculated intervals for both risk differences lie above zero. Their limits are not repeated because the posted limits include more than three decimal places. The interval’s position and width should be considered alongside the estimate, the response percentages, and the analysis limitations.

For a binary endpoint, uncertainty depends on the number of observations and the distribution of responses, among other factors. General statistical reasoning also cautions that a confidence interval does not account for every potential source of bias, such as issues in outcome ascertainment, missing data, or analysis choices that are not described in the record. The registry does not report enough detail to evaluate all such features.

What analysis details are not available?

The registry record does not report the original sample-size justification, detailed handling of missing outcomes, a multiplicity adjustment, interim analyses, or a complete statistical analysis plan. It also does not report a sponsor inferential analysis in the posted analysis count. These absences limit reconstruction of the full analysis pathway. The recalculated unadjusted comparisons remain useful summaries of the posted arm data, but they should not be mistaken for a complete account of the trial’s prespecified methods.

In general, a randomized design supports comparisons between assigned groups, while masking can reduce some forms of knowledge-related influence on treatment or assessment. The record lists randomization and quadruple masking, but does not report the implementation details necessary to assess those processes. These general design principles do not resolve the specific questions left undocumented in this record.

10. Confidence Intervals and Precision

The posted response percentages are point estimates: 41.8% for 210 mg brodalumab, 48.9% for 140 mg brodalumab, and 24.7% for placebo. A point estimate summarizes the observed group result, but it does not show how much the estimate might vary across comparable studies. The comparison record adds confidence intervals for the recalculated unadjusted risk differences. Both intervals lie above zero, indicating that the reported interval ranges do not include no difference under the recalculation method.

A confidence interval is a range constructed by a statistical procedure that, in general, would cover the target quantity at its stated confidence level in repeated use if the model assumptions hold. It is not a guarantee that the true effect lies within a particular interval, and it does not represent uncertainty from every possible source. The registry record does not specify the confidence level in the comparison summary, so no level is asserted.

The exact interval bounds in the record have more than three decimal places and are therefore not reproduced. The estimates themselves are recalculated risk differences of 0.171 and 0.243 for the 210 mg and 140 mg comparisons, respectively. Their precision should be judged from the associated interval width as well as their location, not from the number of digits in an estimate. More digits do not make an estimate more certain.

The arm denominators are 146 for the 210 mg arm, 141 for the 140 mg arm, and 146 for placebo. In general, response-rate precision is influenced by the amount of information and by how responses are distributed. The record’s description of the primary analysis set and the absence of detailed missing-data handling are also relevant: uncertainty intervals quantify sampling variability under a method, but do not automatically account for uncertainty introduced by unreported analysis decisions.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning illustrations give participants per arm for 80% power and participants per arm for 90% power. They are not totals across arms and are not event counts. The registry’s planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each illustration targets a stated fraction of the observed effect. The trial’s own original design assumptions and sample-size justification are not reported in the registry record.

For the 210 mg brodalumab comparison, planning for 100% of the observed effect gives 118 participants per arm for 80% power and 157 participants per arm for 90% power. Planning for 75% of the observed effect gives 203 participants per arm for 80% power and 271 participants per arm for 90% power. Planning for 50% of the observed effect gives 440 participants per arm for 80% power and 588 participants per arm for 90% power.

For the 140 mg brodalumab comparison, planning for 100% of the observed effect gives 61 participants per arm for 80% power and 81 participants per arm for 90% power. Planning for 75% of the observed effect gives 105 participants per arm for 80% power and 140 participants per arm for 90% power. Planning for 50% of the observed effect gives 226 participants per arm for 80% power and 302 participants per arm for 90% power.

In plain terms, the 80% column gives the modeled number per arm for a design with an 80% chance of detecting the chosen effect under the stated assumptions; the 90% column gives the corresponding number for a higher target chance. Smaller effects need more participants, as the 50% observed-effect scenarios illustrate. These are planning illustrations based on the observed effect, not observed power and not evidence that the trial was designed using these assumptions. The curve should be read as the same planning relationship across effect sizes, not as a record of trial enrollment or a new analysis of the trial.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.247; treatment proportion p₁ = 0.418; average p̄ = 0.332.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6661 = 1.3055.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6550 = 0.5513.
4. n = (1.3055 + 0.5513)² / (0.1712)² = 117.6, rounded up to 118 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 <- 0.246575342465753                          # control proportion
p1 <- 0.417808219178082                          # 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(2024646)
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 = 118 (80% power), 157 (90% power)
 75% of observed effect: n per arm = 203 (80% power), 271 (90% power)
 50% of observed effect: n per arm = 440 (80% power), 588 (90% power)
power.prop.test: 117.6 
Simulated power at n = 118 per arm: 0.805 (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.

13. Multiplicity, Missing Data and Analysis Populations

The registry record posts one primary outcome measure and no posted secondary outcomes in the available results. It identifies the primary endpoint as ACR20 response through week 16. It does not report a multiplicity adjustment for the comparisons of the two brodalumab doses with placebo, nor does it describe a hierarchy, gatekeeping procedure, or other control of the overall chance of false-positive findings across multiple tests. The recalculated p values are unadjusted.

In general, multiplicity arises when multiple statistical questions are tested in the same study. If each is assessed separately without adjustment, the chance of at least one nominally significant result can be higher than for a single test. This is a general statistical consideration; the record does not establish which testing strategy the sponsor prespecified or used. The unadjusted results should therefore be understood as individual comparisons rather than evidence of a documented multiplicity-controlled testing plan.

The registry describes the primary analysis set as all randomized subjects who had the opportunity to complete the week 16 visit prior to termination of the study. It does not report the number excluded from that set, the number with unavailable endpoint assessments, or the method used to handle missing outcomes. It also does not provide a detailed intention-to-treat definition or explain whether any imputation or sensitivity analysis was performed. Missing-data methods can affect a binary response rate because they determine how participants without an observed endpoint contribute to the analysis; that is a general methodological point, not a claim about what happened in this trial.

The posted arm denominators are reported as 146, 141, and 146 for the 210 mg, 140 mg, and placebo arms, respectively. The registry does not explain in detail how these denominators relate to all randomized participants or to the stated analysis-set eligibility. This limits assessment of the flow from randomization to analysis.

The record also does not report interim analyses or the complete statistical analysis plan. Without those details, readers cannot verify whether endpoint definitions, exclusions, testing order, or missing-data procedures were specified before results were known. These omissions do not change the posted rates, but they constrain how fully the analysis can be audited.

14. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: myocardial infarction (1.2%), abortion induced (0.6%), cerebrovascular accident (0.6%), haemorrhoidal haemorrhage (0.6%), alt increased (0.6%).

The registry reports serious adverse events in 5 of 163 participants at risk in the 210 mg brodalumab arm, 3 of 160 in the 140 mg arm, and 5 of 161 in the placebo arm. It reports other adverse events in 91 of 163, 85 of 160, and 83 of 161 participants, respectively. These are counts with the corresponding at-risk denominators, not efficacy response rates.

The serious-event terms listed include Myocardial Infarction at 1.2%, Abortion Induced at 0.6%, Cerebrovascular Accident at 0.6%, Haemorrhoidal haemorrhage at 0.6%, ALT increased at 0.6%, and AST Increased at 0.6%. The record does not provide further context for these terms in the listed summary, such as treatment attribution or a comparative analysis for each event. The death fields are not reported in the registry record.

In general, adverse-event counts describe events recorded under a trial’s definitions and observation procedures; they do not establish that an intervention caused an event. The available summary supports description of the reported counts only. It does not, by itself, establish comparative safety, account for event timing or duration, or resolve how individual events were assessed.

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

The primary result describes the proportion of participants reaching ACR20 through week 16. The posted rates were higher in each brodalumab arm than in the placebo arm: 41.8% for 210 mg brodalumab, 48.9% for 140 mg brodalumab, and 24.7% for placebo. The recalculated unadjusted risk differences were 0.171 and 0.243, and the associated intervals lie above zero. These findings concern this endpoint, these arms, and this time point.

The results do not establish what happened to every participant, how long responses lasted, or whether outcomes differed on measures not reported in the posted results. A group-level response proportion does not give the size or character of improvement for each responder. The registry record does not post secondary outcome analyses, so the primary endpoint should not be taken as a summary of every possible clinical outcome.

Statistical significance and clinical importance are different questions. A p value describes compatibility with a null comparison under specified assumptions; it does not establish the practical importance of a difference. The record does not provide a threshold for a clinically important ACR20 difference, so none is applied. Nor do the unadjusted comparisons document control of multiplicity across the dose comparisons.

The registry describes a randomized, quadruple-masked study, features that are intended in general to support fair comparisons and reduce some forms of bias. However, the registry record does not report implementation details for randomization or masking, full missing-data methods, or a detailed analysis plan. The results therefore should be interpreted with those reporting limits in mind.

The safety summaries give serious and other adverse-event counts for each arm, but the listed counts alone do not establish causation or provide a complete comparative safety assessment. The death fields are not reported in the registry record. Overall, the evidence described is a week 16 response-rate comparison with accompanying unadjusted recalculations and limited safety summaries; it does not support conclusions beyond the recorded outcomes and methods.

16. Why This Trial Matters Statistically

This trial raises several useful statistical questions in a compact setting: how to interpret binary response rates, how absolute and relative comparisons differ, and how to read uncertainty when a registry presents arm summaries alongside recalculated comparisons. ACR20 reduces a multidimensional clinical assessment to a responder status, making the endpoint proportion easy to communicate while leaving the details of individual response outside that summary.

The three posted arm percentages make clear why the comparator matters. A response percentage on its own is not the same as a treatment contrast; the placebo arm provides the reference for the recalculated risk differences. Reporting both arm rates and an absolute contrast allows readers to see the underlying proportions as well as the comparison estimate. The confidence intervals add a further dimension by conveying uncertainty, rather than presenting the contrast as a fixed exact quantity.

The record also illustrates the difference between an observed trial result and a planning exercise. The sample-size illustrations scale the observed effects under explicit assumptions, but they do not reveal the trial’s original design justification and are not observed power. Separating planning calculations from the trial’s actual design history prevents a retrospective illustration from being mistaken for a prospective protocol decision.

Finally, interpretability depends on more than a point estimate. The analysis-set description, missing-data reporting, multiplicity handling, and sponsor analysis details affect how completely readers can evaluate the comparison. Several of those details are not reported in the registry record. Making that boundary clear is statistically important: it preserves what the posted data show while avoiding claims about methods or conclusions that the record cannot substantiate.

17. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

The primary endpoint is limited to ACR20 response through week 16. The record does not post secondary outcome analyses, so the available efficacy summary does not show whether patterns were similar for other outcomes or at later time points. Although the study’s brief summary identifies a safety objective and the record lists adverse events, the posted efficacy result addresses only the stated primary measure.

The analysis population is described as randomized participants who had the opportunity to complete the week 16 visit before study termination. The record does not explain in detail how participants without an observed endpoint were handled, how many were unavailable for assessment, or how the outcome denominators relate to all randomized participants. These omissions limit assessment of missing-data effects and the completeness of the analysis population.

The comparisons are unadjusted recalculations from posted summary statistics. The record does not report multiplicity control, the complete statistical analysis plan, or a sponsor inferential analysis for the primary endpoint. Therefore, the recalculated p values and confidence intervals should not be read as a substitute for an unreported prespecified analysis. No discrepancy is flagged in the registry record.

The registry lists quadruple masking but does not specify the roles masked or describe implementation. It also does not report details sufficient to assess the randomization process. The serious-event summary provides counts and selected terms, but the death fields are not reported in the registry record, and event attribution and timing are not detailed in the posted summary. These are reporting limitations; they do not establish that any particular bias or safety issue occurred.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Study of Efficacy and Safety of Brodalumab in Subjects With Psoriatic Arthritis — NCT02024646.
• Registry record last updated 2020-08-20; status last verified 2020-08.
• Results first posted 2020-08-20.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

The registry record describes a completed phase 3, randomized, parallel, placebo-controlled study of brodalumab in psoriatic arthritis, with quadruple masking listed. The intervention arms were 210 mg and 140 mg brodalumab by subcutaneous injection; placebo was also administered by subcutaneous injection. Enrollment is recorded as 484.

The primary endpoint was the ACR20 response rate through week 16. Posted rates were 41.8% for 210 mg brodalumab, 48.9% for 140 mg brodalumab, and 24.7% for placebo. Recalculated unadjusted risk differences were 0.171 and 0.243, with unadjusted p values of 0.002 and <0.001. The registry record does not report secondary outcome analyses or the trial’s complete statistical analysis plan.

Serious and other adverse-event counts are listed by arm, but the death fields are not reported in the registry record. The posted results support interpretation of the specified week 16 endpoint and the reported safety summaries, with the analysis and reporting limitations described in the registry kept in view.