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Spondyloarthropathies Phase 3 Binary Endpoint NCT01087762

Certolizumab Pegol in Subjects With Active Axial Spondyloarthritis: Complete Statistical Analysis

This analysis examines a randomized, double-blind Phase 3 trial of certolizumab pegol versus placebo in active axial spondyloarthritis. It focuses on ASAS20 response at Week 12, the registry’s reported analyses, and the precision and limitations of the posted results.

Trial start: 2010-03  ·  Enrollment: 325  ·  Sponsor: UCB BIOSCIENCES GmbH
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 Certolizumab Pegol in Subjects With Active Axial Spondyloarthritis (NCT01087762), a randomized phase 3 study. The primary outcome is Assessment in Axial Spondyloarthritis International Society 20 % (ASAS20) Response Criteria at Week 12.

325
Enrollment
Phase 3
4
Arms
In the primary outcome
+19.3 pts
Risk difference
CZP 200 mg Q2W (FAS)
6.3 to 32.4 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01087762
PhasePhase 3
ConditionSpondyloarthropathies
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment325
Arms in the primary outcome4
Lead sponsorUCB BIOSCIENCES GmbH
Results postedYes

2. Clinical Question

Population

Participants with active axial spondyloarthritis were enrolled in a multicenter study. The registry lists spondyloarthropathies as the condition and reports total enrollment of 325. The primary endpoint analysis used the Randomized Set, with non-responder imputation described in the registry record.

Intervention

Two certolizumab pegol regimens were studied: 200 mg Q2W and 400 mg Q4W. Both regimens began with 400 mg subcutaneous loading doses on Weeks 0, 2 and 4. The 200 mg Q2W schedule continued from Week 6; the 400 mg Q4W schedule continued from Week 8.

Comparator

The comparator was matching placebo. Participants assigned to placebo who did not meet predefined response criteria at both Weeks 14 and 16 left the placebo group on Week 16. After 24 weeks, participants were randomized to active treatment.

Primary question

At Week 12, what percentage of participants in each group met ASAS20 response criteria, and how did the active-treatment groups compare with placebo? ASAS20 requires improvement across specified disease activity domains while also requiring no deterioration in the remaining domain. The trial record reports percentages, 95% confidence intervals, and sponsor analyses for two active-versus-placebo comparisons.

The question is about the observed response proportions and their uncertainty in this trial. It does not, by itself, establish how the regimens compare with one another or how the findings apply beyond the population and study conditions recorded.

3. Trial Design

This was a Phase 3, multicenter, randomized, double-blind, placebo-controlled, parallel-group study sponsored by UCB BIOSCIENCES GmbH. The registry reports that the study started in 2010-03, reached primary completion in 2011-10, and is completed. Enrollment was 325.

The randomized treatment groups were placebo, certolizumab pegol 200 mg Q2W, and certolizumab pegol 400 mg Q4W. Both active regimens used loading doses before their scheduled maintenance dosing. The registry describes placebo injections as matching active injections to maintain masking. The randomized double-blind design is intended to reduce systematic differences between groups and to limit the influence of participants’ and study personnel’s knowledge of assigned treatment on outcomes and their assessment.

The placebo group had a planned escape arrangement: participants who failed predefined response criteria at both Weeks 14 and 16 left placebo on Week 16 and received active treatment. After 24 weeks, all participants were randomized to active treatment. Consequently, the Week 12 primary endpoint falls before the described Week 16 escape, while later assessments occur in a study with treatment changes described in the record.

The primary endpoint is the percentage meeting ASAS20 response criteria at Week 12. The registry also lists Week 24 ASAS20 and several functional, disease activity, metrology, and imaging outcomes. The full original statistical plan, the trial’s original sample-size justification, and the procedures for any interim analyses are not reported in the registry record. The record includes a total enrollment figure, but that alone does not explain how the planned enrollment was selected or how the study was designed to address every listed outcome.

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: Patients with positive Tuberculosis (TB) tests within Screening Period, but no signs and symptoms of active TB had to be treated with prophylactic TB treatment for at least 4 weeks prior to first study drug administration.

Double Blind Period (Weeks 0-24)

StagePlaceboCZP 200 mg Q2WCZP 400 mg Q4WAll CZP 200 mgAll CZP 400 mg
STARTED10711110700
COMPLETED951059800
NOT COMPLETED126900

Reasons for not completing this period:

ReasonPlaceboCZP 200 mg Q2WCZP 400 mg Q4WAll CZP 200 mgAll CZP 400 mg
Lack of Efficacy20300
Protocol Violation60100
Lost to Follow-up12100
Withdrawal by Subject12100
SAE, non-fatal22300

Open-Label Period (Weeks 48-204)

StagePlaceboCZP 200 mg Q2WCZP 400 mg Q4WAll CZP 200 mgAll CZP 400 mg
STARTED000158157
COMPLETED00099100
NOT COMPLETED0005957

Reasons for not completing this period:

ReasonPlaceboCZP 200 mg Q2WCZP 400 mg Q4WAll CZP 200 mgAll CZP 400 mg
Lack of Efficacy000414
Protocol Violation00011
Lost to Follow-up00052
Withdrawal by Subject0002215
Other00024
SAE, non-fatal00074
AE, non-serious non-fatal0001613
SAE, non-fatal + AE, non-serious/fatal00024

Analysis population for the primary outcome, as defined in the registry: Intention-to-treat dataset was the Randomized Set (RS). RS with non-responder imputation: subjects who withdrew for any reason or placebo subjects who used escape medication are considered as non-responders from drop out timepoint or when escape therapy was initiated. Subjects with missing data at a visit are non-responders for that visit, too.

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: Baseline Characteristics refer to the Randomized Set (RS), which is an Intention-to-Treat (ITT) dataset.

CharacteristicUnitPlaceboCZP 200 mg Q2WCZP 400 mg Q4WTotal Title
Participants analysed107111107325
Age, Categorical: <=18 yearsParticipants0000
Age, Categorical: Between 18 and 65 yearsParticipants102110105317
Age, Categorical: >=65 yearsParticipants5128
Age, Continuous: Mean ageyears39.9 (SD 12.4)39.1 (SD 11.9)39.8 (SD 39.9)39.6 (SD 11.9)
Sex: Female, Male: FemaleParticipants424439125
Sex: Female, Male: MaleParticipants656768200
Weightkilogram (kg)82.142 (SD 18.147)79.305 (SD 18.599)83.893 (SD 18.855)81.757 (SD 18.576)
Heightcentimeter (cm)170.704 (SD 9.692)171.769 (SD 10.171)172.753 (SD 9.607)171.739 (SD 9.834)

6. Primary Endpoint

The registry lists the primary outcome as Assessment in Axial Spondyloarthritis International Society 20 % (ASAS20) Response Criteria at Week 12, measured over Week 12.

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

The primary endpoint is the percentage of participants meeting Assessment in SpondyloArthritis International Society 20% response criteria, or ASAS20, at Week 12. The registry defines response as improvement of at least 20% and an absolute improvement of at least 1 unit on a 0 to 10 Numeric Rating Scale in at least 3 of 4 domains: patient global assessment of disease activity, total spinal pain, function represented by BASFI, and inflammation represented by the mean of BASDAI questions 5 and 6. The remaining domain must not deteriorate by at least 20% and at least 1 unit.

This composite response definition combines several aspects of axial spondyloarthritis rather than relying on a single symptom or measurement. A binary responder endpoint is interpretable as the proportion of participants who meet the prespecified response definition by a particular visit. It also makes the threshold explicit: a participant either meets all required response conditions or does not.

That simplification has a trade-off. Participants just short of the response threshold and those with little improvement are both classified as nonresponders, even though their underlying measurements may differ. The response percentage therefore addresses the frequency of meeting the composite criterion; it does not describe the full distribution of changes in each domain or the size of improvement among responders.

The registry reports percentages and 95% confidence intervals for the Week 12 endpoint. Those estimates should be read in light of the stated analysis population and missing-data handling, rather than as a direct description of every enrolled participant’s observed course.

7. Results Posted in the Registry

Risk difference: CZP 200 mg Q2W (FAS)

+19.3

95% CI: 6.3 to 32.4 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals25.435.645.855.966.176.3Placebo (FAS) (n=107)CZP 200 mg Q2W (FAS) (n=111)CZP 400 mg Q4W (FAS) (n=107)CZP 200 mg Q2W and CZP 400 mg… (n=218)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)CZP 200 mg Q2W (FAS)CZP 400 mg Q4W (FAS)CZP 200 mg Q2W and CZP 400 mg…-3.065.8115243241risk 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
Assessment in Axial Spondyloarthritis International Society 20 % (ASAS20) Response Criteria at Week 24Binary EndpointRisk difference+37.7 pts (25.4 to 50.0)27 per arm
Change From Baseline in the Spine Ankylosing Spondylitis Spine Magnetic Resonance Imaging (MRI) Scoring System for Disease Activity (ASspiMRI-a) in the Berlin Modification at Week 12Continuous EndpointMean difference-3.78 (-5.74 to -1.82)26 per arm
Change From Baseline in Sacroiliac Spondyloarthritis Research Consortium of Canada (SPARCC) Score at Week 12Continuous EndpointMean difference-2.28 (-5.45 to 0.89)178 per arm

Assessment in Axial Spondyloarthritis International Society 20 % (ASAS20) Response Criteria at Week 24

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)CZP 200 mg Q2W (FAS)CZP 400 mg Q4W (FAS)-4.278.1120334558risk difference (percentage points) vs control (95% CI)

Change From Baseline in the Spine Ankylosing Spondylitis Spine Magnetic Resonance Imaging (MRI) Scoring System for Disease Activity (ASspiMRI-a) in the Berlin Modification at Week 12

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)CZP 200 mg Q2W (FAS)CZP 400 mg Q4W (FAS)-6.20-4.87-3.53-2.20-0.870.46mean difference vs control (95% CI)

Change From Baseline in Sacroiliac Spondyloarthritis Research Consortium of Canada (SPARCC) Score at Week 12

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)CZP 200 mg Q2W (FAS)CZP 400 mg Q4W (FAS)-7.67-5.83-3.99-2.15-0.321.52mean difference vs control (95% CI)

The posted secondary outcomes cover different dimensions of disease, including ASAS20 response at Week 24, functional and disease activity indices, metrology, and imaging-based scores. The overall pattern is that some secondary outcomes show differences between active-treatment groups and placebo, while the amount of information varies by outcome and the results do not all have identical statistical strength. The findings therefore offer supporting context rather than a single uniform confirmation across every measure.

Week 24 ASAS20 response is a later assessment of the same broad response construct as the primary endpoint. The other measures address distinct constructs or use continuous score changes, so they cannot be interpreted as interchangeable replications of the Week 12 binary endpoint. Imaging outcomes also have smaller analysis populations than the primary response groups, as reflected in their reported group counts. This can affect precision and limits direct comparison of apparent strength across outcomes.

Secondary analyses are typically less conclusive when many endpoints and comparisons are examined. The registry lists 10 outcome measures and 10 analyses overall, but a multiplicity adjustment strategy is not reported in the registry record. Without such information, unadjusted secondary p-values can overstate the strength of evidence when considered as a collection. Results should be read as exploratory or supportive unless the statistical plan establishes their confirmatory role.

These secondary findings do not replace the primary endpoint or establish that one active schedule is superior to the other. The registry does not report a direct active-versus-active test or a multiplicity-controlled interpretation across the secondary outcomes. The broader pattern can inform how the primary result fits with other measured domains, but each endpoint retains its own measurement scale, population, and uncertainty.

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

9. Statistical Interpretation

Clinical Biostats interpretation

At Week 12, the registry reports ASAS20 response in 38.3% of the placebo group, 57.7% of the CZP 200 mg Q2W group, and 63.6% of the CZP 400 mg Q4W group. The corresponding 95% confidence intervals are 29.1% to 47.5%, 48.5% to 66.8%, and 54.4% to 72.7%. The combined active-treatment group is reported at 60.6%, with a 95% confidence interval of 54.1% to 67.0%.

The sponsor’s posted comparisons report a mean difference in final values of 19.3 for CZP 200 mg Q2W versus placebo, with a 95% confidence interval of 6.3 to 32.4 and p = 0.004. For CZP 400 mg Q4W versus placebo, the reported mean difference is 25.2, with a 95% confidence interval of 12.3 to 38.2 and p < 0.001. The sponsor identifies these as two-sided Wald tests. These are sponsor analyses of the primary response outcome; the unadjusted recalculations are not a substitute for them. Because the record flags a discrepancy, the sponsor’s own analysis takes precedence.

The confidence intervals express uncertainty in the estimated response percentages and sponsor-reported contrasts. They are not ranges that contain every participant’s outcome, and they do not quantify the probability that a treatment effect is true. The reported p-values describe compatibility of the data with a specified null comparison under the test’s assumptions; they do not measure clinical importance, prove causation by themselves, or establish the probability that the null hypothesis is correct.

The posted data describe higher observed Week 12 response percentages in each active-treatment group than in placebo. The sponsor-reported comparisons also have confidence intervals whose bounds are above zero. Interpretation should remain tied to this endpoint, visit, analysis population, and study design. The results do not establish a direct statistical comparison between the two active regimens, because such a comparison is not reported in the registry record. Nor should the combined active-treatment estimate be taken as a separately randomized treatment arm: the registry presents it as a pooled grouping of the two active regimens.

The endpoint uses non-responder imputation, including classification of withdrawals and placebo participants using escape medication as nonresponders from the relevant time point. That approach affects what the response percentages represent. The registry’s description of the primary population is truncated, and further details about missing observations are not reported in the registry record. These limitations matter when judging how completely the percentages represent outcomes under the intended treatment assignments.

10. Statistical Methods Explained

Several statistical ideas help distinguish the quantities reported for this trial. The primary endpoint is binary at the participant level: a participant either meets the ASAS20 response definition at Week 12 or does not. The group-level percentage is the estimated proportion who meet that definition. It is not an average change in a symptom score.

What a confidence interval describes

A confidence interval gives a range of values reasonably compatible with the observed data under the method used to construct it. A narrower interval indicates greater precision in the estimate, while a wider interval indicates more uncertainty. In repeated use of the same method under its assumptions, intervals at a stated confidence level have a long-run coverage interpretation. A 95% confidence interval does not mean that 95% of participants fall within the interval, and it is not a probability statement about the particular treatment effect after the data have been observed.

For a response percentage, uncertainty reflects that the observed participants are one realization of the broader process that could generate responses. The trial reports 95% confidence intervals around the arm percentages. The sponsor also reports 95% confidence intervals for the active-versus-placebo contrasts. The two kinds of intervals address different estimates: one concerns a response proportion within a group, and the other concerns the difference between groups as reported by the sponsor.

Comparisons and tests

The sponsor labels the primary comparisons as two-sided Wald tests and reports mean differences in final values. A two-sided test assesses departures in either direction from its null value. The p-value is calculated under the null hypothesis and the assumptions of the test; a small p-value indicates that data at least as incompatible with that null were not common under those assumptions. It is not the probability that the null is true, nor does it show whether an observed difference is important to participants.

Recalculated comparisons in the statistical display are simple, unadjusted re-calculations from posted summary statistics. They use the available group counts and outcome summaries rather than the full participant-level data or necessarily the sponsor’s full modeling and analysis procedures. Such calculations can be useful as a transparent check, but they may not reproduce a sponsor’s model, handling of missing data, covariate adjustment, or other analysis choices. Here the record flags a discrepancy; the sponsor’s own analysis takes precedence.

Why analysis populations and missingness matter

The registry says the primary analysis used the Randomized Set and non-responder imputation. It states that participants who withdrew for any reason, and placebo participants who used escape medication, were considered nonresponders from the dropout time point or when escape therapy began. In general, non-responder imputation assigns a nonresponse status to specified missing or post-escape observations rather than analyzing only participants with observed endpoint data. This can preserve a conservative interpretation for those situations, but the resulting estimate depends on the rule and the reasons data are missing.

The posted primary population description ends before its full missing-data statement is complete. The detailed handling of other missing observations and the exact analysis procedures are not reported in the registry record. Accordingly, a reader cannot infer all analysis decisions from the brief description alone.

Over-dispersion and continuous outcomes

Over-dispersion is a general issue for count or binary data when outcomes vary more than a chosen statistical model expects. If unaccounted for, standard errors can be too small and confidence intervals too narrow. The primary endpoint is reported as a binary response percentage, but the registry does not state that an over-dispersion adjustment was used; that detail is not reported in the registry record. The secondary results also include continuous outcomes, such as changes in imaging scores. Their interpretation is different: means and standard deviations describe numerical score changes, not the proportion meeting a threshold. Standard deviations describe variation among observations, whereas confidence intervals around a mean or contrast describe uncertainty in an estimated quantity.

Finally, the record lists numerous outcomes and analyses. When many hypotheses are tested, the chance of at least one nominally small p-value can increase. Adjustment procedures can address that issue, but multiplicity handling for the reported outcomes is not reported in the registry record. That is why isolated unadjusted secondary p-values should not be treated as definitive evidence.

11. Confidence Intervals and Precision

The Week 12 response estimates are accompanied by 95% confidence intervals. For placebo, the reported interval is 29.1% to 47.5%; for CZP 200 mg Q2W, it is 48.5% to 66.8%; and for CZP 400 mg Q4W, it is 54.4% to 72.7%. The combined active-treatment estimate has an interval from 54.1% to 67.0%. These intervals communicate uncertainty in the estimated response proportions, not variation in individual outcomes.

The sponsor’s 95% confidence interval for the reported CZP 200 mg Q2W comparison is 6.3 to 32.4, and the interval for CZP 400 mg Q4W is 12.3 to 38.2. Both reported intervals are on the positive side of zero for the mean difference. The record’s discrepancy flag is important: the sponsor’s analyses are the governing results, while recalculated estimates are unadjusted checks based on posted summaries.

Precision depends in part on the number of observations contributing to an estimate and on variation in the data. The primary response groups include 107 participants for placebo, 111 for CZP 200 mg Q2W, and 107 for CZP 400 mg Q4W. The record reports the total enrolled population separately from the group sizes used for this endpoint. The endpoint’s non-responder imputation and the registry’s incomplete description of other missing-data handling also affect what can be inferred about the estimates.

Confidence intervals should be considered alongside the estimated response proportions and the study context. They do not account for every possible source of uncertainty, including unreported analysis choices or multiplicity. No confidence interval can establish that a finding will recur in a different population or under different study conditions.

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 effect104139
75% of the observed effect184246
50% of the observed effect411550
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect1002005001,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, pooled-variance normal approximation for two proportions. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: CZP 200 mg Q2W (FAS).

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

The 80% power column gives the estimated number of participants per arm for a hypothetical study to have an 80% chance of rejecting the null hypothesis under the stated assumptions if the chosen effect were the true effect. The 90% power column uses a higher target chance of detecting that effect. These are design calculations; they do not say what power the completed trial actually had. This is not observed power.

Each planning scenario uses a fraction of the observed contrast: 100%, 75%, or 50%. The smaller the effect targeted for detection, the more participants are generally needed to distinguish it from random variation under the same assumptions. For instance, the primary comparison of CZP 200 mg Q2W with placebo lists 104 participants per arm for 80% power at 100% of the observed effect, 184 at 75%, and 411 at 50%. These values are examples of the planning pattern, not a recommendation or a reconstruction of the original protocol.

The figures depend on assumptions that may not match the original trial design or later research. They do not account for issues not included in the stated calculation, such as the trial’s full analysis plan or the handling of multiple outcomes. The planning values should therefore be read as conditional illustrations rather than guarantees about the sample size needed in another study.

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 = 0.383; treatment proportion p1 = 0.577; average p̄ = 0.480.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.7065 = 1.3848.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6932 = 0.5834.
  4. n = (1.3848 + 0.5834)2 / (0.1934)2 = 103.6, rounded up to 104 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 <- 0.383177570093458                          # control proportion
p1 <- 0.576576576576577                          # 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(1087762)
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 = 104 (80% power), 139 (90% power)
 75% of observed effect: n per arm = 184 (80% power), 246 (90% power)
 50% of observed effect: n per arm = 411 (80% power), 550 (90% power)
power.prop.test: 103.6 
Simulated power at n = 104 per arm: 0.789 (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
Wald-test, 2-sidedMean Difference (Final Values) 19.36.3 to 32.4=0.004
Wald-test, 2-sidedMean Difference (Final Values) 25.212.3 to 38.2< 0.001
Where the two analyses differ, rely on the sponsor's. The simple re-calculation above reaches a different conclusion from the sponsor's analysis, usually because the sponsor adjusts for covariates, stratification or repeated measures, or (for event rates) uses a negative binomial model that allows for over-dispersion and so gives wider intervals.

The registry reports sponsor analyses for the two primary active-versus-placebo comparisons. For CZP 200 mg Q2W versus placebo, the sponsor reports a mean difference in final values of 19.3, a 95% confidence interval of 6.3 to 32.4, and p = 0.004. For CZP 400 mg Q4W versus placebo, the corresponding reported mean difference is 25.2, with a 95% confidence interval of 12.3 to 38.2 and p < 0.001. Both are identified as two-sided Wald tests.

Recalculated comparisons are unadjusted calculations from posted summary statistics. They are useful as checks on the direction and approximate scale of the posted group results, but they are not equivalent to the sponsor’s analysis and may not reflect its full methods. The record explicitly flags a discrepancy. In that circumstance, the sponsor’s own analysis takes precedence; the recalculation should not be used to replace or reinterpret the sponsor-reported result.

The sponsor’s reported analyses concern active treatment versus placebo. A direct comparison between the two active schedules is not reported in the registry record. The sponsor’s p-values also should not be read as establishing clinical importance or as accounting for multiplicity across the trial’s other outcomes; multiplicity handling is not reported in the registry record.

15. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when a study evaluates multiple outcomes, time points, treatment comparisons, or statistical tests. Even if each test uses a conventional threshold, repeated testing increases the chance that at least one result appears statistically significant by chance alone. Methods such as hierarchical testing or other adjustment procedures can control error across a defined family of hypotheses. The registry record does not report whether such procedures were used for the primary and secondary analyses, how tests were grouped, or whether any results were designated as confirmatory beyond identifying the primary endpoint.

The record lists 10 outcome measures and 10 analyses. It reports sponsor p-values for the two active-versus-placebo primary comparisons and posts additional secondary results. Without a stated multiplicity strategy, the primary comparisons and the collection of secondary results should not be treated as though they necessarily share the same error control. Unadjusted p-values are evidence about individual tests under their assumptions, not an automatic correction for the number of questions examined.

The primary analysis population is described as the Randomized Set, with non-responder imputation. The registry states that participants who withdrew for any reason, and placebo participants who used escape medication, were considered nonresponders from the dropout time point or when escape therapy began. This is material to interpretation because the endpoint percentage is not simply the proportion among participants with observed Week 12 data.

The primary population description is incomplete in the registry record, ending after the statement about subjects with missing data. Further details about missing observations, sensitivity analyses, and the full analysis plan are not reported in the registry record. The record also does not report the original sample-size justification, interim-analysis procedures, or whether any planned statistical procedures changed. These omissions limit independent assessment of how the posted analyses relate to the complete protocol and all prespecified analyses.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
All CZP 200 mg (Safety Analysis)3515822.2%
All CZP 400 mg (Safety Analysis)3415721.7%
All CZP 200 mg + 400 mg6931521.9%
Placebo51074.7%
Participants with at least one serious adverse event
Serious adverse events by armAll CZP 200 mg (Safety Analys…22.2%All CZP 400 mg (Safety Analys…21.7%All CZP 200 mg + 400 mg21.9%Placebo4.7%% of participants with at least one serious adverse event

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
All CZP 200 mg (Safety Analysis)142 of 158
All CZP 400 mg (Safety Analysis)127 of 157
All CZP 200 mg + 400 mg269 of 315
Placebo28 of 107

Most frequent serious adverse event terms

Event termOrgan systemAll CZP 200 mg (Safety Analysis)All CZP 400 mg (Safety Analysis)All CZP 200 mg + 400 mgPlacebo
ColitisGastrointestinal disorders0 of 1583 of 1573 of 3150 of 107
Non-cardiac chest painGeneral disorders2 of 1580 of 1572 of 3152 of 107
PneumoniaInfections and infestations3 of 1580 of 1573 of 3150 of 107
OsteoarthritisMusculoskeletal and connective tissue disorders3 of 1580 of 1573 of 3150 of 107
DiarrhoeaGastrointestinal disorders0 of 1582 of 1572 of 3150 of 107
Chest painGeneral disorders1 of 1581 of 1572 of 3150 of 107
CholelithiasisHepatobiliary disorders0 of 1582 of 1572 of 3150 of 107
Mycobacterial infectionInfections and infestations1 of 1581 of 1572 of 3150 of 107
Back painMusculoskeletal and connective tissue disorders1 of 1581 of 1572 of 3150 of 107
Transient ischaemic attackNervous system disorders2 of 1580 of 1572 of 3150 of 107

Most frequent non-serious adverse event terms

Event termOrgan systemAll CZP 200 mg (Safety Analysis)All CZP 400 mg (Safety Analysis)All CZP 200 mg + 400 mgPlacebo
NasopharyngitisInfections and infestations47 of 15843 of 15790 of 3157 of 107
Upper respiratory tract infectionInfections and infestations35 of 15828 of 15763 of 3153 of 107
BronchitisInfections and infestations24 of 15817 of 15741 of 3150 of 107
HeadacheNervous system disorders17 of 15818 of 15735 of 3157 of 107
PharyngitisInfections and infestations24 of 15811 of 15735 of 3150 of 107
ArthralgiaMusculoskeletal and connective tissue disorders22 of 15811 of 15733 of 3150 of 107
HypertensionVascular disorders20 of 15811 of 15731 of 3154 of 107
Blood creatine phosphokinase increasedInvestigations14 of 15817 of 15731 of 3152 of 107
DiarrhoeaGastrointestinal disorders10 of 15820 of 15730 of 3150 of 107
RashSkin and subcutaneous tissue disorders11 of 15814 of 15725 of 3152 of 107

Serious events with the highest arm-level rate: colitis (1.9%), pneumonia (1.9%), osteoarthritis (1.9%), non-cardiac chest pain (1.9%), diarrhoea (1.3%).

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 events for 158 participants in the all-CZP 200 mg safety group, 157 in the all-CZP 400 mg group, 315 in the combined CZP group, and 107 in placebo. Serious adverse events affected 35, 34, 69, and 5 participants in those groups, respectively. The combined CZP group overlaps the two dose-group summaries and should not be treated as a separate randomized arm alongside them.

Other adverse events are reported for 142 participants in the all-CZP 200 mg group, 127 in the all-CZP 400 mg group, 269 in the combined CZP group, and 28 in placebo. These are participant counts, not counts of individual event episodes. The registry lists colitis, pneumonia, osteoarthritis, and non-cardiac chest pain at 1.9% each among the top serious-event terms, and diarrhoea and cholelithiasis at 1.3% each.

These summaries describe events recorded in the registry; they do not establish that treatment caused a particular event or permit a complete safety comparison by themselves. Death counts are not reported in the registry record. Detailed event definitions, exposure-adjusted rates, and further context needed for a full safety assessment are not reported in the registry record.

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

The posted primary data show that the reported Week 12 ASAS20 response percentages were higher in each certolizumab pegol group than in placebo. The sponsor’s reported active-versus-placebo comparisons have positive mean differences and confidence intervals above zero. These findings describe the trial’s measured response outcome under its stated analysis approach; they do not amount to a general statement about every participant or every outcome.

ASAS20 is a composite threshold. It indicates whether participants met defined improvement and non-deterioration conditions across disease activity, pain, function, and inflammation domains. It does not show the amount of improvement for each person, and the same response percentage could arise from different patterns of change among those domains. The secondary measures address some of those other dimensions, but multiplicity and missing-data details are not fully reported.

The result does not establish a direct comparison between CZP 200 mg Q2W and CZP 400 mg Q4W. Although each regimen is compared with placebo in the sponsor analyses, a statistically tested difference between the active regimens is not reported in the registry record. The combined active estimate also does not constitute a separate randomized group.

Nor do the results prove that the observed differences are clinically important for every participant, guarantee similar findings in other settings, or resolve uncertainties about longer-term outcomes. The study’s double-blind randomized design supports interpretation of the assigned-group comparison, but conclusions remain bounded by the recorded population, endpoint, visit, analysis methods, and available reporting. Statistical significance is not a substitute for clinical judgment, and these results are not medical advice.

18. Why This Trial Matters Statistically

This trial illustrates why a clinical result should be read through several linked statistical choices. The endpoint is a defined binary response rather than a continuous change score, the comparison is between randomized groups, and the primary analysis applies non-responder imputation for specified withdrawals and placebo escape. Each choice shapes what the resulting percentage estimates.

It also provides a useful distinction between sponsor-reported analyses and unadjusted recalculations from posted summaries. The registry supplies sponsor Wald-test comparisons and flags a discrepancy with recalculated estimates. Recognizing that the sponsor analysis takes precedence prevents a transparent summary-based check from being mistaken for the trial’s own inferential procedure.

The study further shows why confidence intervals and p-values answer different questions. Intervals communicate precision around estimated quantities, while p-values summarize compatibility with a null hypothesis under test assumptions. Neither alone establishes clinical importance, and neither resolves questions that depend on unreported multiplicity or missing-data procedures.

Finally, the record spans multiple outcome domains and follow-up times, alongside a placebo escape and later active treatment. These design features make it important to tie each interpretation to the specific endpoint, population, and assessment time. A statistically careful reading keeps the primary result distinct from secondary findings and from safety counts, while acknowledging where the registry record does not document enough detail for a fuller audit.

19. Limitations

The primary population description in the registry record is truncated, so the full missing-data rules cannot be assessed. The record does specify non-responder imputation for withdrawals and placebo participants using escape medication, but other details about missing observations and sensitivity analyses are not reported. This limits evaluation of how robust the primary result is to alternative assumptions.

The registry does not report the original sample-size justification, interim-analysis procedures, or a complete statistical analysis plan. It also does not report multiplicity handling for the several outcomes and analyses. As a result, the posted secondary p-values cannot be assumed to have adjusted error rates, and the relationship between all reported tests and any prespecified hierarchy is unclear.

The primary comparisons are active treatment versus placebo; no direct statistical comparison between the active regimens is reported. The later treatment changes described for placebo participants also mean that later assessments should be interpreted in the context of escape and subsequent active treatment, rather than as an uninterrupted placebo comparison.

The registry’s safety summary gives participant counts and selected serious-event terms, but deaths are not reported and further information such as exposure-adjusted rates is not reported in the registry record. The record is sufficient to describe the posted event counts, but not to conduct a comprehensive safety assessment. These reporting limitations are specific to what can be established from the registry record and do not themselves determine the validity of analyses not posted there.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

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23. Record Summary

NCT01087762 is a completed, randomized, double-blind, parallel-group Phase 3 study of certolizumab pegol in active axial spondyloarthritis, sponsored by UCB BIOSCIENCES GmbH. The registry reports enrollment of 325 and primary completion in 2011-10.

The primary endpoint was ASAS20 response at Week 12. The registry reports response percentages and 95% confidence intervals for placebo and two active dosing regimens, as well as sponsor-reported two-sided Wald-test comparisons. The record flags a discrepancy with simple unadjusted recalculations, so the sponsor’s analyses take precedence.

Secondary outcomes span response, functional and disease activity indices, metrology, and imaging. Safety summaries report serious and other adverse-event counts. Multiplicity procedures, the original sample-size justification, interim analyses, and complete missing-data details are not reported in the registry record.

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