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Axial Spondyloarthritis Phase 3 Binary Endpoint NCT02437162

A Study to Evaluate the Efficacy and Safety of Ustekinumab in the Treatment of Anti-TNFα Naive Participants With Active Radiographic Axial Spondyloarthritis: Complete Statistical Analysis

This analysis examines the Week 24 ASAS 40 response in a randomized, placebo-controlled study of ustekinumab in anti-TNFα-naive adults with active radiographic axial spondyloarthritis. It places the reported treatment comparisons, their uncertainty, secondary outcomes, and safety counts in statistical context.

Trial start: 2015-09-03  ·  Enrollment: 347  ·  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 to Evaluate the Efficacy and Safety of Ustekinumab in the Treatment of Anti-TNFα Naive Participants With Active Radiographic Axial Spondyloarthritis (NCT02437162), a randomized phase 3 study. The primary outcome is Percentage of Participants Who Achieved an Assessment of Spondyloarthritis International Society (ASAS) 40 Response at Week 24.

347
Enrollment
Phase 3
3
Arms
In the primary outcome
+2.6 pts
Risk difference
Ustekinumab 45 Milligram (mg)
-9.2 to 14.3 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT02437162
PhasePhase 3
ConditionAxial Spondyloarthritis
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment347
Arms in the primary outcome3
Lead sponsorJanssen Research & Development, LLC
Results postedYes

2. Clinical Question

Population

Adults with active radiographic axial spondyloarthritis who had not previously received anti-TNF alpha agents. The primary analysis population was the full analysis set: randomized participants who received at least one administration of study agent, analyzed according to randomized group.

Intervention

Ustekinumab 45 mg or ustekinumab 90 mg. The registry describes dosing at Weeks 0 and 4 followed by dosing every 12 weeks, with the last administration at Week 100 for the ustekinumab groups.

Comparator

Placebo. The design also lists a golimumab 50 mg intervention, but the posted primary endpoint comparisons are against placebo.

Primary question

At Week 24, what percentage of participants in each group achieved an ASAS 40 response, and how uncertain were the differences between each ustekinumab dose and placebo?

The study asked whether ustekinumab was associated with a different Week 24 response rate from placebo in this specific population. ASAS 40 is a threshold-based response: a participant needed substantial improvement in at least three of four specified domains, together with no worsening in the remaining domain. The outcome is therefore a response proportion, not an average change in symptoms or function.

The registry record lists a randomized, parallel-group, placebo-controlled study and reports results for placebo and both ustekinumab doses. Its primary comparisons concern the percentage achieving the response, rather than a direct comparison of the two ustekinumab doses. The posted results can describe the observed response proportions and their statistical uncertainty, but they do not by themselves establish why any response occurred or whether the result applies to people outside the trial population.

The record also lists secondary measures, including ASAS 20, BASDAI response, and change in BASFI. These outcomes offer other views of response and function, but they do not replace the prespecified primary endpoint. Details of the trial's original sample-size justification and full statistical plan are not reported in the registry record.

3. Trial Design

The registry identifies this as a Phase 3, randomized, quadruple-masked, parallel-group study. It lists placebo, ustekinumab 45 mg, ustekinumab 90 mg, and golimumab 50 mg as interventions. Enrollment is listed as 347. The primary endpoint results reported for Week 24 compare placebo with each ustekinumab dose.

The registry describes placebo injections at Weeks 0, 4, and 16 for the placebo group. It describes ustekinumab dosing at Weeks 0 and 4 followed by dosing every 12 weeks for the ustekinumab groups, with the last administration at Week 100. The placebo description also refers to re-randomization at Week 24, with exceptions for participants who qualified for early escape. The available arm descriptions are incomplete, so further details of later treatment assignments and the golimumab group are not reported in the registry record.

The stated primary outcome is the percentage of participants with an ASAS 40 response at Week 24. The full analysis set included randomized participants who received at least one administration of study agent, analyzed in the group to which they were randomized regardless of treatment received. This defines the population used for the reported primary outcome; the posted material does not give further detail about every analysis population used for other outcomes.

The registry lists a study start date of 2015-09-03, a primary completion date of 2017-03-22, and a status of terminated. The reason for termination and its implications for the planned study are not reported in the registry record. The record does not report the trial's original sample-size assumptions, interim analysis plan, or the reasons for any changes to study conduct. Those details should not be inferred from the posted endpoint results or from planning illustrations based on observed effects.

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 347 participants were randomized, and 346 participants were treated (116 participants to placebo, 116 participants to ustekinumab 45 mg, and 114 participants to 90 mg).

Overall Study

StagePlaceboUstekinumab 45 mgUstekinumab 90 mg
STARTED116116115
Treated116116114
Early Escape at Week 16262114
Cross Over at Week 248700
COMPLETED986
NOT COMPLETED107108109

Reasons for not completing this period:

ReasonPlaceboUstekinumab 45 mgUstekinumab 90 mg
Protocol Violation010
Randomized but not treated001
Study discontinued by Sponsor939897
Withdrawal by Subject1379
Adverse Event010
Lost to Follow-up101
Death010
Other001

Analysis population for the primary outcome, as defined in the registry: The full analysis set (FAS) included all participants who were randomized and received at least one administration of study agent. Participants analyzed based on randomized treatment group they were assigned to regardless of treatment received.

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) included all participants who were randomized and received at least one administration of study agent.

CharacteristicUnitPlaceboUstekinumab 45 mgUstekinumab 90 mgTotal
Participants analysed116116114346
Age, Continuousyears38.3 (SD 11.35)39.2 (SD 10.5)39.5 (SD 11.32)39 (SD 11.04)
Sex: Female, Male: FemaleParticipants15231452
Sex: Female, Male: MaleParticipants10193100294
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants4015
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants112116113341
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants0000
Race (NIH/OMB): American Indian or Alaska NativeParticipants0000
Race (NIH/OMB): AsianParticipants30323193
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants0000
Race (NIH/OMB): Black or African AmericanParticipants0011
Race (NIH/OMB): WhiteParticipants868482252
Race (NIH/OMB): More than one raceParticipants0000
Race (NIH/OMB): Unknown or Not ReportedParticipants0000
Race/Ethnicity, Customized: AsianParticipants30323193
Race/Ethnicity, Customized: Black or African AmericanParticipants0011
Race/Ethnicity, Customized: Hispanic or LatinoParticipants4015
Race/Ethnicity, Customized: White Non-HispanicParticipants828481247
Region of Enrollment: PolandParticipants19141750
Region of Enrollment: UkraineParticipants19202261
Region of Enrollment: United StatesParticipants2215
Region of Enrollment: RussiaParticipants323831101
Region of Enrollment: Korea, Democratic People'S Republic OfParticipants911929
Region of Enrollment: Taiwan, Province Of ChinaParticipants23212367
Region of Enrollment: Czech RepublicParticipants12101133

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants Who Achieved an Assessment of Spondyloarthritis International Society (ASAS) 40 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 ASAS 40 response at Week 24. Under the registry's definition, response required improvement from baseline of at least 40% and an absolute improvement of at least 2 on a 0-to-10 scale in at least three of four domains: the participant's global assessment, total back pain, BASFI, and inflammation. The remaining domain could not worsen from baseline.

This endpoint is useful because it expresses response as a clear threshold that combines several domains relevant to axial spondyloarthritis, rather than relying on a single symptom or an average score. It is a binary outcome: each participant is classified as a responder or non-responder for this analysis. The resulting group percentages communicate how often the defined response occurred, while a comparison between groups estimates the difference in those proportions.

Threshold outcomes have limits. Participants just on opposite sides of the response rule are classified differently even if their underlying measurements are similar, while participants with different degrees of improvement can be grouped together once they meet the threshold. The endpoint also depends on how missing responses and intercurrent events are handled. For this primary measure, the record describes imputation rules involving treatment failure, early escape, and non-responder imputation. The registry does not report further detail on how the clinical importance of this threshold was established for this trial.

7. Results Posted in the Registry

Risk difference: Ustekinumab 45 Milligram (mg)

+2.6

95% CI: -9.2 to 14.3 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals18.723.328.032.637.241.9Placebo (n=116)Ustekinumab 45 Milligram (mg) (n=116)Ustekinumab 90 mg (n=114)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ustekinumab 45 Milligram (mg)Ustekinumab 90 mg-14-8.01-1.894.221016risk 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 Assessment of Spondyloarthritis International Society (ASAS) 20 Response at Week 24Binary EndpointRisk difference+10.3 pts (-2.5 to 23.1)366 per arm
Percentage of Participants Who Achieved at Least a 50 Percent (%) Improvement From Baseline in Bath Ankylosing Spondylitis Disease Activity Index (BASDAI) at Week 24Binary EndpointRisk difference-2.6 pts (-13.9 to 8.7)4,548 per arm
Change From Baseline in Bath Ankylosing Spondylitis Functional Index (BASFI) Total Score at Week 24Continuous EndpointMean difference-0.26 (-0.90 to 0.38)1,128 per arm

Percentage of Participants Who Achieved an Assessment of Spondyloarthritis International Society (ASAS) 20 Response at Week 24

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ustekinumab 45 Milligram (mg)Ustekinumab 90 mg-10-3.034.13111826risk difference (percentage points) vs control (95% CI)

Percentage of Participants Who Achieved at Least a 50 Percent (%) Improvement From Baseline in Bath Ankylosing Spondylitis Disease Activity Index (BASDAI) at Week 24

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ustekinumab 45 Milligram (mg)Ustekinumab 90 mg-16-10-5.010.365.7411risk difference (percentage points) vs control (95% CI)

Change From Baseline in Bath Ankylosing Spondylitis Functional Index (BASFI) Total Score at Week 24

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Ustekinumab 45 Milligram (mg)Ustekinumab 90 mg-1.00-0.69-0.38-0.070.240.55mean difference vs control (95% CI)

The posted secondary outcomes do not show a uniform pattern across measures. ASAS 20 response percentages were higher in both ustekinumab groups than in the placebo group, while the BASDAI response percentages were lower in both ustekinumab groups. Mean change in BASFI was more negative in the ustekinumab groups than in the placebo group. These outcomes measure different aspects of response and function, so their directions need not match.

This mixed pattern does not overturn or confirm the primary ASAS 40 result. The primary outcome remains the designated Week 24 comparison, and its sponsor-reported confidence intervals include zero. Secondary endpoints can add context about other dimensions of the condition, but consistency across them cannot be assumed, and they should not be selectively treated as decisive evidence.

The registry lists additional secondary measures, including ASDAS-CRP inactive disease, hsCRP, MASES, BASMI, and ASQoL. Numerical results for those outcomes are not reported in the registry record in the results summarized for this analysis. The registry lists 35 posted secondary outcomes, but only the outcomes with numerical data can contribute to the descriptive pattern.

Unadjusted secondary comparisons carry less inferential weight because many outcomes and comparisons can create opportunities for apparently notable results by chance. The registry record does not report a multiplicity adjustment or a prespecified hierarchy for interpreting the secondary findings. Their estimates are therefore best read as exploratory context, with attention to their uncertainty and the fact that the primary result did not show a clearly distinguishable difference from placebo.

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

9. Statistical Interpretation

Clinical Biostats interpretation

At Week 24, ASAS 40 response was reported for 28.4% of the placebo group, 31.0% of the ustekinumab 45 mg group, and 28.1% of the ustekinumab 90 mg group. The observed percentages were therefore close across the three groups. These descriptive values alone do not establish that the groups differ; the comparison estimates and their confidence intervals are important for judging the range of effects compatible with the data.

For ustekinumab 45 mg versus placebo, the sponsor-reported percentage difference was 2.586, with a 95% confidence interval from -9.138 to 14.310 and p = 0.669. For ustekinumab 90 mg versus placebo, the sponsor-reported percentage difference was -0.646, with a 95% confidence interval from -12.180 to 10.887 and p = 0.913. Both intervals include zero, so the reported analyses do not provide clear evidence of a difference in either direction under the sponsor's superiority comparisons. The intervals also span effects on either side of zero, so they do not establish equivalence or rule out potentially meaningful differences.

The unadjusted recalculations give the same broad picture. For the 45 mg comparison, the recalculated risk difference was 0.026, with a confidence interval from -0.092 to 0.143 and an unadjusted p-value of 0.667. For the 90 mg comparison, it was -0.004, with a confidence interval from -0.120 to 0.113 and an unadjusted p-value of 0.949. These simple calculations are not a substitute for the sponsor's reported analyses.

Other posted outcomes show a mixed pattern rather than a consistent shift in one direction across all measures. The ASAS 20 response percentages were higher in both ustekinumab groups than in the placebo group, whereas the BASDAI response percentages were slightly lower in both ustekinumab groups. Mean BASFI changes were numerically more negative in the ustekinumab groups than in the placebo group. These are secondary outcomes, and differences in outcome definition and analysis mean they should not be treated as confirmation of the primary result.

The statistical interpretation is limited to the measures and comparisons reported in the registry. The results describe observed responses in the analyzed groups; they do not establish a causal explanation for individual outcomes, prove that treatments are identical, or determine effects beyond the study population and observation period represented by the posted endpoint.

10. Statistical Methods Explained

The primary result is a binary response outcome: each participant either met the ASAS 40 definition or did not. For a binary outcome, the group percentage is the proportion classified as responders. A treatment comparison can be expressed as a difference between the two response proportions. A risk difference of zero corresponds to equal observed response proportions; a positive or negative estimate indicates which group had the larger observed proportion, based on the order of the comparison.

What does the confidence interval represent?

A confidence interval describes statistical uncertainty around an estimated group difference. It gives a range of values compatible with the observed data under the method used to construct the interval. It is not a range containing a specified proportion of individual participants' responses, nor does it assign a probability to the true effect after the data have been observed. For the primary comparisons, the sponsor reports 95% confidence intervals. Their inclusion of zero is consistent with the reported results not distinguishing the observed differences from no difference at the conventional level used in those analyses.

How do the two comparison approaches differ?

The registry reports sponsor analyses using the Cochran-Mantel-Haenszel method, with a percentage difference, a 95% confidence interval, and a p-value for each placebo comparison. The recalculations are simple, unadjusted comparisons derived from the posted group summaries. The sponsor's analysis and the recalculation can differ because they use different analysis approaches. The registry marks no discrepancy, and the sponsor's reported analysis remains the trial's own analysis. Details of any stratification variables or additional adjustment procedures are not reported in the registry record.

A p-value measures how incompatible the observed data are with a specified null hypothesis under the analysis assumptions. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of a difference. A large p-value does not prove that the groups are equivalent. Interpretation should therefore consider the estimated difference and confidence interval, not the p-value alone.

Why use a threshold-based response?

ASAS 40 translates several measurements into a responder classification, which makes a group response percentage straightforward to interpret. The trade-off is that a threshold discards some detail: the analysis does not retain all gradations of improvement in a single estimate. Participants' outcomes also depend on multiple domains and the no-worsening condition, so response is not determined by one score alone.

The record specifies that ASAS 40 response used imputed data. Participants were considered non-responders at and after treatment failure; early escape rules classified participants as non-responders at Week 20 and Week 24; and missing post-baseline responses were imputed as non-responses. These rules make the handling of certain missing or post-baseline situations explicit. The registry does not provide enough information to assess all assumptions behind the imputation or whether alternative missing-data analyses were performed.

What do the secondary-outcome calculations show?

For binary secondary outcomes, the posted group results are percentages, and the recalculations compare response proportions. BASFI is a continuous measure, so its results are reported as group mean changes with standard deviations. A mean difference compares the average changes between groups; a standard deviation describes variation among observations within a group. A confidence interval for a mean difference expresses uncertainty about that group-level contrast, not the range of individual changes. The registry does not list sponsor-reported analyses for these posted secondary outcomes, so the recalculations should be understood as unadjusted descriptive comparisons.

General statistical context: estimates from a study are subject to sampling variability, and the amount of uncertainty depends in part on the number of observations and the variability of the outcome. For binary outcomes, the number of responders and non-responders both contribute to precision. For continuous outcomes, both the sample size and spread of measurements matter. These general principles do not add conclusions about this particular trial beyond the reported estimates and intervals.

11. Confidence Intervals and Precision

The primary confidence intervals are broad enough to include both negative and positive differences. For ustekinumab 45 mg, the sponsor's 95% interval runs from -9.138 to 14.310 for the percentage difference. For ustekinumab 90 mg, it runs from -12.180 to 10.887. Each interval includes zero, indicating that the posted results are compatible with no difference as well as with differences in either direction under the reported analysis.

This uncertainty matters because a point estimate is only one value within a wider range of plausible effects. The 45 mg estimate is positive, while the 90 mg estimate is slightly negative, but neither point estimate should be read in isolation. The intervals do not identify a single precise effect, and the data do not establish that the response rates are equivalent. The registry does not report a prespecified equivalence or non-inferiority margin for these comparisons.

The unadjusted recalculations also have intervals that include zero: -0.092 to 0.143 for 45 mg, and -0.120 to 0.113 for 90 mg. They are close in direction and overall interpretation to the sponsor's reported estimates, but they arise from a different calculation approach. The sponsor's own analysis is the primary reference for the trial result.

Precision is also affected by the outcome definition and missing-data rules. ASAS 40 requires a participant to meet multiple criteria, and missing post-baseline responses are treated as non-responses under the stated NRI rule. The registry record does not report additional sensitivity analyses that would show how alternative missing-data assumptions might affect the estimates. Thus, the confidence intervals quantify sampling uncertainty under the reported analysis; they do not account for every possible source of uncertainty about trial conduct, endpoint assumptions, or generalizability.

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 effect4,9046,564
75% of the observed effect8,66311,596
50% of the observed effect19,36625,925
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect5,00010,00020,00050,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, pooled-variance normal approximation for two proportions. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: Ustekinumab 45 Milligram (mg).

The sample-size illustrations are planning calculations based on the observed effect, not the trial's original design assumptions. For these binary and continuous outcomes, the figures are participants per arm, not total participants across the study. The calculation assumptions listed in the registry are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The trial's own original sample-size assumptions are not reported in the registry record.

The 80% power column gives the illustrated number of participants per arm for a design with an 80% chance of detecting the specified effect under the listed assumptions, if that effect and assumptions were correct. The 90% power column gives the corresponding illustration for a 90% chance. These are planning concepts, not guarantees about what a study will find. This is not observed power.

The rows that plan for 100% of the observed effect use the full observed difference as the target; rows planning for 75% or 50% use smaller target effects. Smaller effects are harder to distinguish from random variation, so they require more participants under the same calculation assumptions. That pattern is particularly important when the observed effect is small: a large planning estimate can result from trying to detect a small difference, and does not mean that such a study would necessarily be informative about all clinically relevant effects.

The illustrations should not be read as evidence that the trial was underpowered or as a reconstruction of the sponsor's design process. They use effects estimated from the posted results, which are themselves uncertain. A planning calculation based on an uncertain observed effect can vary substantially with the target effect and assumptions. Any curve accompanying the planning values should be interpreted in the same way: it visualizes a planning relationship, not the trial's observed probability of success.

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 = 0.284; treatment proportion p1 = 0.310; average p̄ = 0.297.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6465 = 1.2670.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6462 = 0.5439.
  4. n = (1.2670 + 0.5439)2 / (0.0259)2 = 4,903.1, rounded up to 4,904 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 <- 0.28448275862069                          # control proportion
p1 <- 0.310344827586207                          # 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(2437162)
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 = 4,904 (80% power), 6,564 (90% power)
 75% of observed effect: n per arm = 8,663 (80% power), 11,596 (90% power)
 50% of observed effect: n per arm = 19,366 (80% power), 25,925 (90% power)
power.prop.test: 4903.1 
Simulated power at n = 4,904 per arm: 0.801 (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-HaenszelPercentage difference 2.586-9.138 to 14.3100.669
Cochran-Mantel-HaenszelPercentage difference -0.646-12.180 to 10.8870.913

The registry reports the sponsor's primary comparisons using the Cochran-Mantel-Haenszel method. For ustekinumab 45 mg versus placebo, the reported percentage difference is 2.586, with a 95% confidence interval from -9.138 to 14.310 and p = 0.669. For ustekinumab 90 mg versus placebo, the reported percentage difference is -0.646, with a 95% confidence interval from -12.180 to 10.887 and p = 0.913.

The unadjusted recalculations use the posted group summaries and produce risk-difference estimates of 0.026 and -0.004, respectively. Their confidence intervals and p-values are also reported as recalculated comparisons, not as the sponsor's model results. The registry does not mark a discrepancy between the recalculations and the sponsor analysis. The sponsor analysis is therefore the central reference for the trial's own reported inference; the recalculations are supplementary checks based on a simpler approach.

For the secondary outcomes described in the results, the registry does not list sponsor-reported analyses. The calculations accompanying those results should not be mistaken for sponsor analyses or for a full reconstruction of the trial's statistical plan. Details of adjustment, multiplicity control, and any additional sponsor analyses are not reported in the registry record.

15. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when several outcomes, time points, or treatment comparisons are evaluated. Each additional statistical test creates another opportunity for a result to appear noteworthy by chance, even if no true effect exists. The registry lists a range of secondary endpoints and results for more than one treatment comparison. A method for controlling the overall error rate across those comparisons is not reported in the registry record. The posted secondary results should therefore be treated as descriptive or exploratory unless a separate analysis plan establishes a different interpretation.

The primary outcome description does state how several situations were handled: participants were considered non-responders at and after treatment failure, early escape rules treated participants as non-responders at Week 20 and Week 24, and missing post-baseline responses were imputed as non-responses. These rules are part of the endpoint definition as analyzed. They do not eliminate all uncertainty about missing data, because the registry does not report further sensitivity analyses or the assumptions used to assess alternative missing-data scenarios.

The full analysis set included randomized participants who received at least one administration of study agent, analyzed according to their randomized group regardless of treatment received. This is the population specified for the primary endpoint. The registry does not report additional details about exclusions from this population or the analysis populations for all other outcomes.

The sponsor's primary analysis method is reported as Cochran-Mantel-Haenszel, but the registry record does not report the full statistical analysis plan, any stratification factors, interim analyses, or the original sample-size justification. Those omissions limit assessment of whether all analyses followed a prespecified strategy and how the reported primary and secondary results relate to the complete set of planned tests. These details should not be inferred from the posted p-values or planning illustrations.

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 Only21161.7%
Placebo to Golimumab0260.0%
Placebo to Ustekinumab 45mg2444.5%
Placebo to Ustekinumab 90mg2434.7%
Ustekinumab 45 mg Only31162.6%
Ustekinumab 45mg to Golimumab32114.3%
Ustekinumab 90 mg Only21141.8%
Ustekinumab 90mg to Golimumab0140.0%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo Only1.7%Placebo to Golimumab0.0%Placebo to Ustekinumab 45mg4.5%Placebo to Ustekinumab 90mg4.7%Ustekinumab 45 mg Only2.6%Ustekinumab 45mg to Golimumab14.3%Ustekinumab 90 mg Only1.8%Ustekinumab 90mg to Golimumab0.0%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Placebo Only0 of 116
Placebo to Golimumab0 of 26
Placebo to Ustekinumab 45mg0 of 44
Placebo to Ustekinumab 90mg0 of 43
Ustekinumab 45 mg Only0 of 116
Ustekinumab 45mg to Golimumab1 of 21

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 Only15 of 116
Placebo to Golimumab4 of 26
Placebo to Ustekinumab 45mg3 of 44
Placebo to Ustekinumab 90mg0 of 43
Ustekinumab 45 mg Only24 of 116
Ustekinumab 45mg to Golimumab7 of 21

Most frequent serious adverse event terms

Event termOrgan systemPlacebo OnlyPlacebo to GolimumabPlacebo to Ustekinumab 45mgPlacebo to Ustekinumab 90mgUstekinumab 45 mg OnlyUstekinumab 45mg to Golimumab
Ocular HypertensionEye disorders0 of 1160 of 260 of 441 of 430 of 1160 of 21
UveitisEye disorders0 of 1160 of 260 of 440 of 430 of 1161 of 21
CholelithiasisHepatobiliary disorders0 of 1160 of 261 of 440 of 430 of 1160 of 21
AppendicitisInfections and infestations0 of 1160 of 261 of 440 of 430 of 1160 of 21
Back InjuryInjury, poisoning and procedural complications0 of 1160 of 260 of 440 of 430 of 1161 of 21
ConcussionInjury, poisoning and procedural complications0 of 1160 of 261 of 440 of 430 of 1160 of 21
Ligament SprainInjury, poisoning and procedural complications0 of 1160 of 261 of 440 of 430 of 1160 of 21
Muscle StrainInjury, poisoning and procedural complications0 of 1160 of 261 of 440 of 430 of 1160 of 21
Intervertebral Disc DisorderMusculoskeletal and connective tissue disorders0 of 1160 of 260 of 440 of 431 of 1160 of 21
OsteoarthritisMusculoskeletal and connective tissue disorders0 of 1160 of 260 of 440 of 431 of 1160 of 21

Most frequent non-serious adverse event terms

Event termOrgan systemPlacebo OnlyPlacebo to GolimumabPlacebo to Ustekinumab 45mgPlacebo to Ustekinumab 90mgUstekinumab 45 mg OnlyUstekinumab 45mg to Golimumab
Alanine Aminotransferase IncreasedInvestigations6 of 1162 of 261 of 440 of 438 of 1162 of 21
Viral Upper Respiratory Tract InfectionInfections and infestations5 of 1161 of 261 of 440 of 439 of 1162 of 21
Aspartate Aminotransferase IncreasedInvestigations3 of 1162 of 260 of 440 of 438 of 1163 of 21
Upper Respiratory Tract InfectionInfections and infestations2 of 1161 of 260 of 440 of 433 of 1162 of 21
InfluenzaInfections and infestations1 of 1160 of 260 of 440 of 432 of 1160 of 21
HyperglycaemiaMetabolism and nutrition disorders0 of 1160 of 260 of 440 of 433 of 1160 of 21
Respiratory Tract Infection ViralInfections and infestations2 of 1160 of 260 of 440 of 430 of 1160 of 21
Ankylosing SpondylitisMetabolism and nutrition disorders0 of 1160 of 261 of 440 of 430 of 1160 of 21
Acute SinusitisInfections and infestations0 of 1160 of 260 of 440 of 430 of 1160 of 21
FasciitisMetabolism and nutrition disorders0 of 1160 of 260 of 440 of 430 of 1160 of 21

Serious events with the highest arm-level rate: uveitis (4.8%), back injury (4.8%), benign salivary gland neoplasm (4.8%), ocular hypertension (2.3%), calculus urinary (2.3%).

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

The registry reports serious adverse event counts by treatment-period group, with the number at risk and the number affected. For the groups labeled Placebo Only, Ustekinumab 45 mg Only, and Ustekinumab 90 mg Only, the serious adverse event counts were 2 of 116, 3 of 116, and 2 of 114, respectively. The record also lists groups that transitioned from placebo or ustekinumab to golimumab or ustekinumab, with their own at-risk counts and serious-event counts. These groups should be read as separate registry categories rather than combined into a new total.

The record reports one death in the Ustekinumab 45mg to Golimumab group and zero deaths in each of the other listed groups. It also lists serious-event terms and percentages, including uveitis, back injury, benign salivary gland neoplasm, ocular hypertension, calculus urinary, and cholelithiasis. The safety figures are counts as reported; the registry record does not provide enough information to determine causality or compare risk with an adjusted analysis.

Serious adverse event counts do not describe all adverse events or establish that an event was caused by treatment. Differences in follow-up or treatment transitions can also affect how group categories should be interpreted; further detail is not reported in the registry record. These figures should be considered descriptive safety information, not a standalone assessment of treatment risk.

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

The primary result describes the percentage of participants in each reported group who met the ASAS 40 response definition at Week 24. The sponsor-reported comparisons did not clearly distinguish either ustekinumab dose from placebo: both confidence intervals include zero, and both reported p-values are large. This is not proof that the response rates are identical, and it does not establish equivalence. The intervals remain compatible with differences in either direction.

The endpoint is specific to a trial population of anti-TNFα-naive adults with active radiographic axial spondyloarthritis and to a particular response definition and time point. It does not directly describe every possible symptom, functional outcome, longer-term result, or other population. Secondary outcomes provide additional descriptive information but have no reported multiplicity adjustment and do not supply a uniform pattern across all measures.

The results also depend on the stated analysis population and missing-response rules. The primary population required randomization and at least one administration of study agent, and the analysis followed randomized group. The ASAS 40 description treats specified missing or post-baseline circumstances as non-response. The registry does not report all details needed to evaluate alternative analytic assumptions.

These data do not provide medical advice, determine what an individual should receive, or establish effects outside the study. They report group-level statistical comparisons and their uncertainty. The reason the study was terminated, the full protocol history, and the original sample-size rationale are not reported in the registry record, so the posted endpoint results cannot answer questions about those aspects of the trial.

18. Why This Trial Matters Statistically

This trial illustrates why a treatment comparison should be read through its estimate and confidence interval, not a point estimate or p-value alone. The Week 24 ASAS 40 percentages are close across the placebo and ustekinumab groups, and the sponsor's confidence intervals include zero while spanning effects in both directions. The result is therefore not a precise demonstration of either a difference or equivalence.

It also shows how endpoint construction affects interpretation. ASAS 40 combines several domains and applies a responder threshold, while secondary outcomes use different definitions, including another binary response and a continuous functional score. Their patterns can differ without being contradictory, because they measure different features and classify change differently.

The registry provides an example of two analytical perspectives: the sponsor's Cochran-Mantel-Haenszel comparisons and simple unadjusted recalculations from posted group summaries. The latter can help readers understand the basic contrast, but they do not replace the sponsor's analysis or reconstruct the full statistical plan. The absence of reported multiplicity procedures and additional missing-data sensitivity analyses is also relevant when interpreting the broader set of secondary results.

Finally, sample-size illustrations based on observed effects are not evidence of observed power or of the study's original design rationale. They demonstrate how planning requirements depend on the target effect and assumptions. Together, these features make the record useful for learning to separate observed response, statistical uncertainty, analysis choices, and design information that is not reported.

19. Limitations

The registry marks the study as terminated, but the reason for termination is not reported in the registry record. The available arm descriptions are incomplete, and details of later treatment assignments and the golimumab group are not fully described in the record summarized for these results. This limits interpretation of treatment exposure beyond the primary Week 24 comparison.

The registry reports a primary analysis population and response-imputation rules, but does not report additional sensitivity analyses for missing data. It also does not report the full statistical analysis plan, original sample-size justification, interim analysis plan, or details of any multiplicity strategy. These omissions limit assessment of how the posted analyses relate to all planned outcomes and comparisons.

For the secondary outcomes discussed, sponsor-reported inferential analyses are not listed. The unadjusted recalculations are not a replacement for adjusted or prespecified analyses. The secondary measures that lack numerical results in the posted results cannot be assessed from the data, and the listed findings should not be treated as a complete account of every registered endpoint.

The primary endpoint is measured at Week 24 and relies on a multi-domain threshold with specified non-responder rules. The posted result does not by itself describe longer-term efficacy, individual trajectories, or outcomes outside the trial population. Safety counts are reported in several treatment-period categories, including transition groups; without additional details, they should not be combined or interpreted as adjusted comparative risks.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

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23. Record Summary

The registry describes a Phase 3, randomized, quadruple-masked, parallel-group study of ustekinumab in adults with active radiographic axial spondyloarthritis who were naive to anti-TNF alpha agents. Enrollment is listed as 347, and the study status is terminated. The primary endpoint was ASAS 40 response at Week 24.

Response percentages were 28.4% for placebo, 31.0% for ustekinumab 45 mg, and 28.1% for ustekinumab 90 mg. Sponsor-reported comparisons against placebo had 95% confidence intervals that included zero. The registry also reports secondary outcome results, serious adverse event counts, and planning illustrations based on observed effects. The reason for termination, original sample-size assumptions, and several details of the full statistical plan are not reported in the registry record.

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