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 BI 655066 Versus Placebo & Active Comparator (Ustekinumab) in Patients With Moderate to Severe Chronic Plaque Psoriasis (NCT02684357), a randomized phase 3 study. The primary outcome is Percentage of Participants Achieving 90% Improvement in Psoriasis Area and Severity Index (PASI) Score (PASI90) at Week 16 in Participants Who Received Risankizumab Compared With Placebo (Part A).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02684357 |
| Phase | Phase 3 |
| Condition | Psoriasis |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 577 |
| Arms in the primary outcome | 2 |
| Lead sponsor | AbbVie |
| Results posted | Yes |
2. Clinical Question
Population
Adults with moderate to severe chronic plaque psoriasis were enrolled. The primary endpoint used the intent-to-treat population, defined in the registry record as all randomized participants. Overall enrollment was 577.
Intervention
For the primary Part A comparison, participants assigned to risankizumab received 150 mg by subcutaneous injection at Weeks 0 and 4. The registry describes the study as double blind and double dummy.
Comparator
The primary comparator was placebo. In Part A, the placebo group received double-blind placebo by subcutaneous injection at Weeks 0 and 4. Ustekinumab was also included as an active comparator in the trial, but it is not the comparator for the primary endpoint.
Primary question
The primary question was what percentage of participants achieved PASI90 at Week 16 with risankizumab compared with placebo. PASI90 means at least a 90% reduction from baseline in the Psoriasis Area and Severity Index score. The endpoint therefore measures the proportion meeting a defined improvement threshold, rather than the average change in PASI score.
3. Trial Design
This was a Phase 3, randomized, double-blind, parallel-group trial of BI 655066, also called risankizumab, with placebo and ustekinumab comparators. The registry record describes the study as double dummy as well as double blind. The brief summary says the study assessed safety and efficacy to support registration for treatment of moderate to severe chronic plaque psoriasis in adult patients. The trial is listed as completed.
Enrollment was 577. Part A included placebo, ustekinumab, and risankizumab groups. The primary endpoint compares the risankizumab and placebo groups at Week 16; the reported endpoint denominators were 294 and 98, respectively. The Part A arm descriptions specify risankizumab 150 mg at Weeks 0 and 4, placebo at Weeks 0 and 4, and ustekinumab 45 or 90 mg based on screening weight at Weeks 0 and 4. The posted primary endpoint results do not compare risankizumab directly with ustekinumab.
The registry record lists study start as 2016-03 and primary completion as 2016-12. It reports 20 outcome measures and 20 analyses, and identifies 18 secondary outcomes as posted. Those counts describe the record, not the number of outcomes used in the primary comparison. The original protocol’s full statistical analysis plan, including its sample-size justification and any planned interim analyses, is not reported in the registry record. The sample-size figures discussed separately are planning illustrations based on the observed result, not the trial’s documented design rationale.
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: A total of 577 subjects were enrolled; 86 subjects failed screening and are excluded from the analyses.
Part A
| Stage | Placebo (Part A) | Ustekinumab (Part A) | Risankizumab (Part A) | Placebo/Risankizumab (Part B) | Ustekinumab/Ustekinumab (Part B) | Risankizumab/Risankizumab (Part B) |
|---|---|---|---|---|---|---|
| STARTED | 98 | 99 | 294 | 0 | 0 | 0 |
| COMPLETED | 94 | 96 | 292 | 0 | 0 | 0 |
| NOT COMPLETED | 4 | 3 | 2 | 0 | 0 | 0 |
Reasons for not completing this period:
| Reason | Placebo (Part A) | Ustekinumab (Part A) | Risankizumab (Part A) | Placebo/Risankizumab (Part B) | Ustekinumab/Ustekinumab (Part B) | Risankizumab/Risankizumab (Part B) |
|---|---|---|---|---|---|---|
| Adverse Event (Worsening of Disease) | 1 | 0 | 0 | 0 | 0 | 0 |
| Lost to Follow-up | 0 | 2 | 2 | 0 | 0 | 0 |
| Withdrawal by Subject | 3 | 0 | 0 | 0 | 0 | 0 |
| Other | 0 | 1 | 0 | 0 | 0 | 0 |
Part B
| Stage | Placebo (Part A) | Ustekinumab (Part A) | Risankizumab (Part A) | Placebo/Risankizumab (Part B) | Ustekinumab/Ustekinumab (Part B) | Risankizumab/Risankizumab (Part B) |
|---|---|---|---|---|---|---|
| STARTED | 0 | 0 | 0 | 94 | 94 | 291 |
| COMPLETED | 0 | 0 | 0 | 91 | 90 | 278 |
| NOT COMPLETED | 0 | 0 | 0 | 3 | 4 | 13 |
Reasons for not completing this period:
| Reason | Placebo (Part A) | Ustekinumab (Part A) | Risankizumab (Part A) | Placebo/Risankizumab (Part B) | Ustekinumab/Ustekinumab (Part B) | Risankizumab/Risankizumab (Part B) |
|---|---|---|---|---|---|---|
| Adverse Event (Other) | 0 | 0 | 0 | 1 | 1 | 1 |
| Lost to Follow-up | 0 | 0 | 0 | 1 | 1 | 7 |
| Withdrawal by Subject | 0 | 0 | 0 | 0 | 2 | 4 |
| Other | 0 | 0 | 0 | 1 | 0 | 1 |
Analysis population for the primary outcome, as defined in the registry: Intent-to-treat (ITT) population: all randomized participants.
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) population: all randomized participants
| Characteristic | Unit | Placebo (Part A) | Ustekinumab (Part A) | Risankizumab (Part A) | Total |
|---|---|---|---|---|---|
| Participants analysed | 98 | 99 | 294 | 491 | |
| Age, Continuous | years | 46.3 (SD 13.26) | 48.6 (SD 14.81) | 46.2 (SD 13.68) | 46.7 (SD 13.84) |
| Sex: Female, Male: Female | Participants | 31 | 33 | 91 | 155 |
| Sex: Female, Male: Male | Participants | 67 | 66 | 203 | 336 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 19 | 12 | 44 | 75 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 79 | 87 | 250 | 416 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 1 | 0 | 2 | 3 |
| Race (NIH/OMB): Asian | Participants | 7 | 4 | 25 | 36 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 1 | 1 | 0 | 2 |
| Race (NIH/OMB): Black or African American | Participants | 2 | 2 | 10 | 14 |
| Race (NIH/OMB): White | Participants | 87 | 91 | 255 | 433 |
| Race (NIH/OMB): More than one race | Participants | 0 | 1 | 2 | 3 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 |
6. Primary Endpoint
The registry lists the primary outcome as Percentage of Participants Achieving 90% Improvement in Psoriasis Area and Severity Index (PASI) Score (PASI90) at Week 16 in Participants Who Received Risankizumab Compared With Placebo (Part A), measured over Week 16.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | percentage of participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint is the percentage of participants achieving PASI90 at Week 16. PASI combines assessments of psoriasis-affected body surface area with ratings of lesion redness, thickness, and scaling. Each sign is assessed on a five-point scale, and the resulting PASI score ranges from 0 to 72, with 0 indicating no psoriasis and 72 indicating very severe psoriasis.
PASI90 is defined as at least a 90% reduction in PASI score compared with baseline. This is a binary endpoint: each participant is classified as meeting or not meeting the threshold, and the trial result is the proportion meeting it in each group. It does not describe the average PASI score or the range of individual changes. Participants with missing data were handled using non-responder imputation, so missing outcomes were treated as non-response for this endpoint.
A threshold endpoint is useful for communicating how many participants reached a prespecified level of improvement. It also discards information about the size of changes that fall short of the threshold and about differences among participants who cross it. The registry record defines the endpoint and its calculation, but the original justification for selecting this endpoint is not reported in the registry record.
7. Results Posted in the Registry
- Risankizumab (Part A): 74.8% (220/294) versus 2.0% (2/98) on control; risk difference 72.8 percentage points (95% CI 67.1 to 78.5), risk ratio 36.67 (9.29–144.77); unadjusted two-proportion z-test p = <0.001.
Risk difference: Risankizumab (Part A)
95% CI: 67.1 to 78.5 percentage points
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Percentage of Participants Achieving sPGA Score of Clear at Week 16 in Participants Who Received Risankizumab Compared With Placebo (Part A) | Binary Endpoint | Risk difference | +48.0 pts (41.3 to 54.6) | 13 per arm |
| Percentage of Participants Achieving PASI100 at Week 16 in Participants Who Received Risankizumab Compared With Placebo (Part A) | Binary Endpoint | Risk difference | +48.6 pts (42.3 to 55.0) | 12 per arm |
| Percentage of Participants Achieving a Dermatology Life Quality Index (DLQI) Score of 0 or 1 at Week 16 in Participants Who Received Risankizumab Compared With Placebo (Part A) | Binary Endpoint | Risk difference | +62.6 pts (55.9 to 69.2) | 8 per arm |
Percentage of Participants Achieving sPGA Score of Clear at Week 16 in Participants Who Received Risankizumab Compared With Placebo (Part A)
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Risankizumab (Part A): 51.0% (150/294) versus 3.1% (3/98) on control; risk difference 48.0 percentage points (95% CI 41.3 to 54.6), risk ratio 16.67 (5.44–51.07); unadjusted two-proportion z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Risankizumab (Part A) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Percentage of Participants Achieving PASI100 at Week 16 in Participants Who Received Risankizumab Compared With Placebo (Part A)
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Risankizumab (Part A): 50.7% (149/294) versus 2.0% (2/98) on control; risk difference 48.6 percentage points (95% CI 42.3 to 55.0), risk ratio 24.83 (6.27–98.35); unadjusted two-proportion z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Risankizumab (Part A) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Percentage of Participants Achieving a Dermatology Life Quality Index (DLQI) Score of 0 or 1 at Week 16 in Participants Who Received Risankizumab Compared With Placebo (Part A)
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Risankizumab (Part A): 66.7% (196/294) versus 4.1% (4/98) on control; risk difference 62.6 percentage points (95% CI 55.9 to 69.2), risk ratio 16.33 (6.23–42.79); unadjusted two-proportion z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Risankizumab (Part A) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The registry lists secondary outcomes covering several dimensions: other PASI response thresholds, investigator-rated clear or almost clear status, skin-related quality of life, and psoriasis symptoms. The detailed secondary results available for the placebo comparisons show a consistent direction across the three reported measures: the risankizumab group had higher percentages than the placebo group. These outcomes complement the primary PASI90 comparison by examining different response thresholds and patient- or investigator-relevant measures, rather than repeating exactly the same endpoint.
The registry record identifies 18 secondary outcomes as posted. The numerical results for the remaining listed secondary outcomes are not reported in the registry record in the results used for this analysis. Consequently, the overall pattern is limited to the detailed secondary comparisons available and should not be generalized to every listed secondary outcome.
Secondary outcomes can help assess whether a primary endpoint result is accompanied by a broader pattern, but they usually carry less confirmatory weight than a designated primary endpoint. In general, testing many outcomes increases the chance that at least one result will appear statistically notable by chance. A prespecified multiplicity procedure can address that issue, but such a procedure is not reported in the registry record. The unadjusted secondary comparisons therefore should be read as supportive descriptive evidence, not as independent confirmation equivalent to the primary analysis.
These secondary results also do not answer the same question as a direct active-comparator analysis. Some listed outcomes compare risankizumab with ustekinumab, but numerical results for those comparisons are not reported in the registry record in the results used for this analysis. The placebo comparisons should not be used to infer the relative result against ustekinumab.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Percentage of Participants Achieving sPGA Score of Clear at Week 16 in Participants Who Received Risankizumab Compared With Placebo (Part A)
- Percentage of Participants Achieving PASI100 at Week 16 in Participants Who Received Risankizumab Compared With Placebo (Part A)
- Percentage of Participants Achieving a Dermatology Life Quality Index (DLQI) Score of 0 or 1 at Week 16 in Participants Who Received Risankizumab Compared With Placebo (Part A)
- Percentage of Participants Achieving a Psoriasis Symptom Scale (PSS) Score of 0 at Week 16 in Participants Who Received Risankizumab Compared With Placebo (Part A)
- Percentage of Participants Achieving PASI90 at Week 16 in Participants Who Received Risankizumab Compared With Ustekinumab (Part A)
- Percentage of Participants Achieving sPGA Score of Clear or Almost Clear at Week 16 in Participants Who Received Risankizumab Compared With Ustekinumab (Part A)
- Percentage of Participants Achieving PASI100 at Week 16 in Participants Who Received Risankizumab Compared With Ustekinumab (Part A)
- Percentage of Participants Achieving sPGA Score of Clear at Week 16 in Participants Who Received Risankizumab Compared With Ustekinumab (Part A)
9. Statistical Interpretation
At Week 16, PASI90 was recorded for 74.8% of participants in the risankizumab group and 2.0% in the placebo group. The corresponding reported counts were 220 of 294 and 2 of 98. These are the posted group-level proportions under the registry’s non-responder imputation approach; they do not describe every participant’s individual course.
The registry’s sponsor analysis used the Cochran-Mantel-Haenszel method and reported an adjusted percentage difference of 72.5, with a 95% confidence interval from 66.8 to 78.2 and p < 0.001. A separate simple, unadjusted recalculation from the posted counts gives a risk difference of 0.728, with an interval from 0.671 to 0.785 and p < 0.001. The recalculation and sponsor estimate are close but not identical; the adjusted sponsor analysis is the primary reported analysis and takes precedence over the unadjusted recalculation.
The p-value is evidence about compatibility of the observed data with a null comparison under the method used; it is not a measure of the size or importance of the difference. The estimated difference and its interval convey magnitude and precision more directly. The reported interval indicates that the analysis is compatible with a range of adjusted percentage differences, rather than identifying one exact value. It should not be read as a range containing every individual participant’s outcome.
The result is a comparison of group proportions at a specified follow-up time. It does not establish the duration of any response beyond Week 16, describe outcomes for every secondary endpoint, or by itself establish a complete benefit-risk profile. Nor does a statistically small p-value resolve questions about missingness, multiplicity, generalizability, or how the outcome was selected and analyzed. These matters depend on design and reporting details, some of which are not reported in the registry record.
The study also included an ustekinumab active-comparator group, but the primary result is risankizumab versus placebo. The primary endpoint figures should not be interpreted as a direct comparison with ustekinumab. Safety figures are reported for multiple groups and trial parts and require separate interpretation; they do not change the primary endpoint’s definition or comparison.
10. Statistical Methods Explained
The main outcome is binary because each participant either met the PASI90 threshold at Week 16 or did not. The group percentages are the proportions classified as responders. A risk difference expresses the absolute separation between those proportions. The simple recalculation uses the posted response counts and denominators without the adjustment used in the sponsor’s analysis. It is a useful way to check the scale of the observed contrast, but it does not replace the prespecified analysis, whose full details are not reported in the registry record.
What does the adjusted comparison do?
The sponsor reports a Cochran-Mantel-Haenszel analysis and an adjusted percentage difference. In general, this method can estimate a comparison while accounting for stratification factors. The particular factors used, how they were defined, and the model details are not reported in the registry record. Therefore, the adjusted estimate can be described as the registry-reported result, but the specific adjustments cannot be reconstructed from the available record details.
The sponsor’s estimate is 72.5, with a 95% confidence interval from 66.8 to 78.2 and p < 0.001. The unadjusted recalculation is a risk difference of 0.728, with an interval from 0.671 to 0.785 and p < 0.001. These estimates use different analytic approaches and scales: the sponsor reports an adjusted percentage difference, while the recalculation is an unadjusted difference based on the posted group summaries. Their close values do not make the methods interchangeable.
What does non-responder imputation mean?
The registry states that non-responder imputation was used for missing primary endpoint data. In general, this approach classifies participants with missing outcome data as not meeting the response threshold. It gives a defined rule for handling missing endpoint assessments and retains missing participants in the response calculation as non-responders. This rule can affect the estimated response proportions, and it does not reveal why data were missing or whether missingness was related to outcome. Reasons for missing data, the amount of missingness, and sensitivity analyses using alternative assumptions are not reported in the registry record.
What does the intent-to-treat population mean?
The primary analysis population is described as all randomized participants. In general, an intent-to-treat analysis preserves the comparison created by random assignment by analyzing participants according to their randomized group, regardless of later treatment exposure. The registry’s definition supports that broad interpretation. Further details about exclusions, analysis-set implementation, and deviations from assigned treatment are not reported in the registry record.
How should the p-value be read?
The posted primary p-value is less than 0.001 for the sponsor analysis, and the unadjusted recalculation also reports p < 0.001. In general, a p-value describes how unusual data at least as inconsistent with a null hypothesis would be under the assumptions of the test if that null hypothesis were true. It is not the probability that the null hypothesis is true, nor does it measure the probability that the result will recur. Interpretation also depends on the analysis plan and the number of comparisons made.
The registry record does not report enough information to reconstruct every assumption and analysis decision behind the sponsor’s test. It identifies the method, the adjusted estimate, its confidence interval, and the p-value. Details such as the stratification variables and any multiplicity procedure are not reported in the registry record. General statistical interpretation should therefore distinguish what the reported analysis states from what would require additional protocol or analysis-plan documentation.
11. Confidence Intervals and Precision
The sponsor’s adjusted percentage difference is 72.5, and its 95% confidence interval runs from 66.8 to 78.2. The interval describes uncertainty in the estimated group comparison under the sponsor’s analysis. It is not a range of observed participant responses, and it does not mean that 95% of participants had outcomes within those limits. In general, a confidence interval is a method-based range of values compatible with the data and assumptions at a stated confidence level.
The interval has limits on both sides of the point estimate, indicating that the result is not known with exact precision. Its position and span matter alongside the point estimate: the endpoints convey the scale of uncertainty, while the estimate gives the central reported comparison. The interval is for the adjusted group difference, not for each arm’s response percentage separately.
The unadjusted recalculation gives a risk difference of 0.728, with interval limits of 0.671 and 0.785. These limits accompany a different calculation from the sponsor’s adjusted percentage difference. They should not be substituted for the sponsor’s 95% interval when describing the sponsor analysis. The registry entries identify the sponsor interval as 95%; the recalculated interval is reported as computed for the unadjusted comparison.
Confidence intervals do not account for every source of uncertainty. They do not resolve the consequences of missing-data assumptions, possible multiplicity, unreported analysis choices, or limitations in applying the findings outside the enrolled population. The registry record does not report alternative missing-data analyses or a multiplicity plan, so the intervals should be read as precision measures for the stated analyses rather than as a complete account of uncertainty.
12. Planning a Similar Trial: Sample Size
This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 6 | 8 |
| 75% of the observed effect | 10 | 13 |
| 50% of the observed effect | 18 | 24 |
The planning illustrations are expressed as participants per arm, not total events. They use the observed primary comparison as a starting point and consider planning for 100%, 75%, and 50% of that observed effect. For the primary endpoint, the entries are 6 and 8 participants per arm for 80% and 90% power when planning for 100% of the observed effect; 10 and 13 when planning for 75%; and 18 and 24 when planning for 50%.
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. In plain terms, the 80% power column gives the illustrative number of participants per arm under those assumptions for an 80% chance of detecting the specified effect if that effect were the true one. The 90% column describes the corresponding planning target for 90% power.
Smaller effects are harder to distinguish from random variation, so planning to detect a smaller fraction of the observed difference requires more participants per arm in these illustrations. These counts are not a reconstruction of the trial’s original enrollment target. The registry record does not report the trial’s original sample-size assumptions or justification. These figures are planning illustrations, not observed power; observed power is not a way to measure how convincing the completed trial result is.
Interpret the entries conditionally: they depend on the observed effect used as a reference and on the listed assumptions. If the true effect differs from that reference, or if the analysis design and assumptions differ, the planning numbers may not describe the sample size needed for that setting. The registry record’s enrollment of 577 should not be confused with these per-arm illustrations.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
n is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.
Worked calculation for this trial
- Control proportion p0 = 0.020; treatment proportion p1 = 0.748; average p̄ = 0.384.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6879 = 1.3483.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.4564 = 0.3842.
- n = (1.3483 + 0.3842)2 / (0.7279)2 = 5.7, rounded up to 6 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 <- 0.0204081632653061 # control proportion
p1 <- 0.748299319727891 # 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(2684357)
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 = 6 (80% power), 8 (90% power)
75% of observed effect: n per arm = 10 (80% power), 13 (90% power)
50% of observed effect: n per arm = 18 (80% power), 24 (90% power)
power.prop.test: 5.7
Simulated power at n = 6 per arm: 0.910 (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
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Cochran-Mantel-Haenszel | Adjusted percentage difference 72.5 | 66.8 to 78.2 | < 0.001 |
The registry reports the sponsor’s primary comparison as a Cochran-Mantel-Haenszel adjusted percentage difference of 72.5, with a 95% confidence interval from 66.8 to 78.2 and p < 0.001. This is the trial’s reported analysis and is the appropriate result to lead with when describing the sponsor’s conclusion from the primary endpoint.
The simple recalculation from the posted response counts is unadjusted. It gives a risk difference of 0.728, with an interval from 0.671 to 0.785 and p < 0.001. It serves as a transparent comparison based on the group summaries, but it does not reproduce the sponsor’s adjusted method. The estimates are close, yet they are not identical because they are not the same analysis.
The registry record does not report the details needed to independently reconstruct the sponsor’s adjustment, including the factors used in the Cochran-Mantel-Haenszel analysis. The recalculation should therefore be treated as a descriptive check, not as a correction to or replacement for the sponsor’s result. No discrepancy is flagged between the posted outcome data and the sponsor analysis.
15. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when more than one hypothesis is tested. With a primary endpoint and numerous secondary outcomes, the chance of at least one apparently positive result can increase if each test is interpreted independently. In general, trial analysis plans may address this through a prespecified testing sequence or another adjustment. The registry record lists 20 outcome measures and 20 analyses and identifies 18 secondary outcomes as posted, but a multiplicity strategy is not reported in the registry record.
The primary result is reported with a Cochran-Mantel-Haenszel analysis and p < 0.001. The registry record does not state whether or how that result was incorporated into a broader testing hierarchy. The secondary outcome entries include analyses with their own reported p-values, but their adjustment status is not stated in the record details. They should not automatically be treated as multiplicity-adjusted evidence.
For the primary endpoint, non-responder imputation was used for missing data. In general, this assigns missing endpoint outcomes to the non-responder category. The registry record does not report the number of missing primary endpoint assessments, the reasons for missingness, or sensitivity analyses under alternative missing-data assumptions. As a result, the robustness of the primary estimate to other missing-data approaches cannot be assessed from the registry record.
The primary analysis population is described as the intent-to-treat population, consisting of all randomized participants. The registry does not provide additional detail on analysis exclusions or the implementation of that population. The original statistical analysis plan, planned interim analyses, and original sample-size justification are also not reported in the registry record. These missing details limit how fully an external reader can evaluate the prespecification of analyses and the treatment of all possible sources of uncertainty.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Placebo (Part A) | 1 | 98 | 1.0% |
| Ustekinumab (Part A) | 3 | 99 | 3.0% |
| Risankizumab (Part A) | 6 | 294 | 2.0% |
| Placebo/Risankizumab (Part B) | 4 | 94 | 4.3% |
| Ustekinumab/Ustekinumab (Part B) | 3 | 94 | 3.2% |
| Risankizumab/Risankizumab (Part B) | 13 | 291 | 4.5% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Placebo (Part A) | 0 of 98 |
| Ustekinumab (Part A) | 0 of 99 |
| Risankizumab (Part A) | 1 of 294 |
| Placebo/Risankizumab (Part B) | 0 of 94 |
| Ustekinumab/Ustekinumab (Part B) | 0 of 94 |
| Risankizumab/Risankizumab (Part B) | 1 of 291 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Placebo (Part A) | 8 of 98 |
| Ustekinumab (Part A) | 14 of 99 |
| Risankizumab (Part A) | 29 of 294 |
| Placebo/Risankizumab (Part B) | 27 of 94 |
| Ustekinumab/Ustekinumab (Part B) | 26 of 94 |
| Risankizumab/Risankizumab (Part B) | 67 of 291 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo (Part A) | Ustekinumab (Part A) | Risankizumab (Part A) | Placebo/Risankizumab (Part B) | Ustekinumab/Ustekinumab (Part B) | Risankizumab/Risankizumab (Part B) |
|---|---|---|---|---|---|---|---|
| Cardiac failure congestive | Cardiac disorders | 0 of 98 | 0 of 99 | 1 of 294 | 0 of 94 | 0 of 94 | 1 of 291 |
| Coronary artery disease | Cardiac disorders | 0 of 98 | 0 of 99 | 1 of 294 | 0 of 94 | 1 of 94 | 0 of 291 |
| Herpes zoster | Infections and infestations | 0 of 98 | 1 of 99 | 1 of 294 | 0 of 94 | 0 of 94 | 0 of 291 |
| Pneumonia | Infections and infestations | 0 of 98 | 0 of 99 | 0 of 294 | 0 of 94 | 0 of 94 | 2 of 291 |
| Basal cell carcinoma | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 0 of 98 | 0 of 99 | 1 of 294 | 0 of 94 | 0 of 94 | 1 of 291 |
| Atrial fibrillation | Cardiac disorders | 0 of 98 | 0 of 99 | 0 of 294 | 0 of 94 | 0 of 94 | 1 of 291 |
| Atrial flutter | Cardiac disorders | 0 of 98 | 0 of 99 | 0 of 294 | 0 of 94 | 1 of 94 | 0 of 291 |
| Cardiac aneurysm | Cardiac disorders | 0 of 98 | 0 of 99 | 0 of 294 | 0 of 94 | 0 of 94 | 1 of 291 |
| Cardiac ventricular thrombosis | Cardiac disorders | 0 of 98 | 0 of 99 | 0 of 294 | 0 of 94 | 0 of 94 | 1 of 291 |
| Glaucoma | Eye disorders | 0 of 98 | 0 of 99 | 0 of 294 | 1 of 94 | 0 of 94 | 0 of 291 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo (Part A) | Ustekinumab (Part A) | Risankizumab (Part A) | Placebo/Risankizumab (Part B) | Ustekinumab/Ustekinumab (Part B) | Risankizumab/Risankizumab (Part B) |
|---|---|---|---|---|---|---|---|
| Viral upper respiratory tract infection | Infections and infestations | 2 of 98 | 5 of 99 | 10 of 294 | 17 of 94 | 14 of 94 | 34 of 291 |
| Upper respiratory tract infection | Infections and infestations | 2 of 98 | 4 of 99 | 11 of 294 | 9 of 94 | 8 of 94 | 24 of 291 |
| Diarrhoea | Gastrointestinal disorders | 3 of 98 | 5 of 99 | 3 of 294 | 2 of 94 | 3 of 94 | 6 of 291 |
| Influenza | Infections and infestations | 1 of 98 | 0 of 99 | 6 of 294 | 2 of 94 | 5 of 94 | 4 of 291 |
Serious events with the highest arm-level rate: atrial flutter (1.1%), coronary artery disease (1.1%), glaucoma (1.1%), colitis (1.1%), muscular weakness (1.1%).
Serious adverse events are reported by group for Part A and Part B. In Part A, the registry records 1 serious adverse event among 98 participants in the placebo group, 3 among 99 in the ustekinumab group, and 6 among 294 in the risankizumab group. The recorded deaths in those groups were 0, 0, and 1, respectively. These are counts as posted, not estimates of causal treatment effects.
Part B safety groups are also listed, including participants who switched from placebo to risankizumab and participants continuing assigned treatments. Their reported serious adverse event counts are 4 among 94, 3 among 94, and 13 among 291, respectively; deaths are 0, 0, and 1. Part B groups reflect different treatment sequences from Part A, so they should not be combined casually with Part A for a simple between-group comparison.
In general, serious adverse event counts describe events recorded during the reported study experience; they do not by themselves establish whether an event was caused by a study drug. The registry record does not provide an inferential comparison or a causal assessment alongside these counts. Small counts can also leave substantial uncertainty about comparative rates. The listed serious event terms and percentages should be interpreted as recorded safety information, not as proof of a treatment relationship or as a complete safety assessment.
17. What the Result Does, and Does Not, Mean
The primary result means that, in the randomized Part A groups and under the registry’s specified handling of missing outcomes, the proportion achieving PASI90 at Week 16 was higher in the risankizumab group than in the placebo group. The sponsor’s adjusted estimate is 72.5 percentage points, with a 95% confidence interval from 66.8 to 78.2. The unadjusted recalculation is similar in direction and magnitude, but the sponsor’s adjusted result remains the primary reported analysis.
This finding concerns a defined threshold at one follow-up time. It does not describe the average degree of improvement, establish how long the response lasted, or show what happened after Week 16. It also does not tell the reader which individual participants improved, whether a participant experienced other outcomes, or how the result applies to people outside the trial population.
The comparison is against placebo, not ustekinumab. Although ustekinumab was an active comparator in the study, the primary figures do not establish a comparative result between risankizumab and ustekinumab. The registry’s listed secondary endpoints include active-comparator questions, but numerical results for those comparisons are not reported in the registry record in the results used for this analysis.
A statistically small p-value does not resolve the limitations of the design record or establish clinical importance on its own. The result must be interpreted alongside its endpoint definition, the non-responder imputation rule, the confidence interval, and the analysis plan. The registry record does not report a multiplicity plan or several details needed to assess missing-data sensitivity and analytic prespecification fully.
Safety information is a separate part of interpretation. Serious adverse event counts and deaths are reported, but counts alone do not establish causation or quantify a complete benefit-risk balance. The posted data support a description of the observed endpoint comparison; they do not justify medical advice or a broad claim about treatment for an individual.
18. Why This Trial Matters Statistically
This trial illustrates how a clinical endpoint can turn a multidimensional measurement into a clinically interpretable response threshold. PASI combines affected body surface area and lesion characteristics, while PASI90 classifies participants according to whether they reached a substantial reduction from baseline. The binary result is easy to compare between randomized groups, but it does not preserve all information in the underlying PASI scores.
It also illustrates why the analysis method matters. The sponsor reported an adjusted percentage difference using the Cochran-Mantel-Haenszel method, while the simple recalculation uses the posted counts without adjustment. The estimates are close, but the distinction between adjusted and unadjusted comparisons should remain clear. A calculation from summary counts is a useful check, not a substitute for the trial’s reported analysis.
The result further shows the importance of handling missing outcomes and interpreting multiple endpoints. Non-responder imputation supplies a definite rule for missing primary outcomes, but the amount and reasons for missingness and the results of alternative assumptions are not reported. The trial also has many listed outcomes, while its multiplicity procedure is not reported. Those omissions do not erase the posted primary comparison, but they limit a full assessment of how robust the evidence is.
Finally, planning calculations based on the observed result are not a record of the original design. They show how assumed effect size and target power relate to illustrative participants-per-arm requirements under stated assumptions. Keeping that planning exercise separate from the completed trial’s enrollment prevents post hoc sample-size illustrations from being mistaken for evidence about the trial’s design or its observed power.
19. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
- Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.
The registry record gives the primary endpoint definition, group results, and sponsor analysis, but it does not report the full statistical analysis plan. The particular adjustment factors in the Cochran-Mantel-Haenszel analysis are not stated. The original sample-size justification, planned interim analyses, and multiplicity strategy are not reported, limiting assessment of how the analyses were prespecified and coordinated.
Missing primary endpoint data were handled by non-responder imputation. The registry record does not give the amount or reasons for missingness or sensitivity analyses using other assumptions. Although the primary population is described as all randomized participants, further details about exclusions and analysis-set implementation are not reported.
The primary comparison is at Week 16 and is against placebo. The trial included an ustekinumab group, but the primary estimate cannot answer the active-comparator question. Numerical results for the other listed secondary outcomes are not reported in the registry record in the results used for this analysis. The secondary findings that are available therefore provide only a partial view of the trial’s other outcome questions.
Safety counts are reported across treatment groups and trial parts, but the registry record does not supply a causal assessment alongside those counts. Part B includes different treatment sequences from Part A, so the group counts are not a straightforward extension of the primary randomized comparison. The results also do not describe long-term outcomes beyond the stated Week 16 primary endpoint. These limitations constrain interpretation of precision, generalizability, and the broader balance of outcomes.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: BI 655066 Versus Placebo & Active Comparator (Ustekinumab) in Patients With Moderate to Severe Chronic Plaque Psoriasis — NCT02684357.
- Registry record last updated 2021-08-23; status last verified 2021-07.
- Results first posted 2019-07-15.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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23. Record Summary
The registry record describes a completed Phase 3 randomized, double-blind, parallel-group trial of risankizumab, placebo, and ustekinumab in adults with moderate to severe chronic plaque psoriasis. Enrollment was 577. The primary endpoint was the percentage achieving PASI90 at Week 16 in the intent-to-treat population, with non-responder imputation for missing data.
The sponsor reported an adjusted percentage difference of 72.5, with a 95% confidence interval from 66.8 to 78.2 and p < 0.001 for risankizumab versus placebo. The unadjusted recalculation from posted counts was similar but uses a different method. The registry also reports secondary outcomes and safety counts. Multiplicity procedures, the original sample-size justification, and several details needed to assess missing-data sensitivity are not reported in the registry record.