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Crohn's Disease Phase 2 Binary Endpoint NCT00771667

A Study of Safety and Effectiveness of Ustekinumab in Patients With Moderate to Severe Active Crohn's Disease Who Have Been Previously Treated With Anti-TNF Therapy: Complete Statistical Analysis

This Phase 2b randomized trial compared intravenous ustekinumab doses with placebo for clinical response at Week 6 in adults with moderately to severely active Crohn’s disease previously treated with TNF antagonist therapy. The interpretation covers the registry’s primary result, its statistical uncertainty, secondary outcomes, and safety reporting.

Trial start: 2008-12  ·  Enrollment: 526  ·  Sponsor: Centocor, Inc.
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 of Safety and Effectiveness of Ustekinumab in Patients With Moderate to Severe Active Crohn's Disease Who Have Been Previously Treated With Anti-TNF Therapy (NCT00771667), a randomized phase 2 study. The primary outcome is Number of Participants With Clinical Response at Week 6.

526
Enrollment
Phase 2
4
Arms
In the primary outcome
+13.2 pts
Risk difference
Ustekinumab 1 mg/kg (IP)
2.2 to 24.1 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00771667
PhasePhase 2
ConditionCrohn's Disease
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment526
Arms in the primary outcome4
Lead sponsorCentocor, Inc.
Results postedYes

2. Clinical Question

Population

Adults with moderately to severely active Crohn’s disease who had previously been treated with TNF antagonist therapy. The primary analysis population included all randomized participants, regardless of whether they received study agent.

Intervention

Intravenous ustekinumab at 1 mg/kg, 3 mg/kg, or 6 mg/kg.

Comparator

Placebo administered intravenously.

Primary question

How many participants in each group had a clinical response by Week 6, as measured by a reduction in Crohn’s Disease Activity Index (CDAI) score?

The primary endpoint was the number of participants with clinical response from baseline to Week 6. Clinical response was defined as a reduction from baseline of at least 100 CDAI points. For participants whose baseline CDAI was at least 220 and at most 248, response instead required reaching a CDAI score below 150. The registry describes CDAI scores as ranging from 0 points, representing minimal disease activity, to over 600 points, representing severe disease activity.

The posted primary results report response counts of 31 among 132 participants receiving placebo, 48 among 131 receiving ustekinumab 1 mg/kg, 45 among 132 receiving 3 mg/kg, and 52 among 131 receiving 6 mg/kg. These are event counts at the Week 6 assessment, not measures of change in average CDAI. They describe how many participants met the endpoint definition in each group.

The trial asks about a short-term clinical response in a population with prior TNF antagonist treatment. It does not, through this endpoint alone, answer questions about longer-term remission, sustained response, or outcomes in patients outside the described population. The registry record does not report further details about the specific prior treatments or the duration of Crohn’s disease.

3. Trial Design

The registry describes a Phase 2b, multicenter, randomized, double-blind, placebo-controlled, parallel-group study. The official title identifies the population as subjects with moderately to severely active Crohn’s disease previously treated with TNF antagonist therapy. The trial status is completed. The registry lists a start of 2008-12 and primary completion of 2010-05, with enrollment of 526.

For the primary endpoint, the listed comparison arms were placebo, ustekinumab 1 mg/kg, ustekinumab 3 mg/kg, and ustekinumab 6 mg/kg, all identified as intravenous in the intervention descriptions. The primary outcome timeframe was baseline to Week 6. The registry states that the primary analysis population consisted of all participants randomized, whether or not they received study agent. The arm counts and response counts for this outcome are reported alongside the comparison statistics.

The registry also lists later treatment sequences involving intravenous response status and subsequent subcutaneous placebo or ustekinumab. These include responder and nonresponder groups. Their presence indicates that the record contains later treatment and safety information beyond the initial four-arm primary comparison. The arm descriptions are blank, however, and the registry record does not report enough detail to reconstruct the full sequence, decision rules, or timing of those later assignments.

The record identifies double masking but does not report which study personnel or participants were masked. It also does not report the method used to generate the randomization sequence, allocation concealment procedures, the planned sample-size justification, interim analyses, or the trial’s original statistical analysis plan. Those design details cannot be inferred from the reported primary outcome or from the posted comparisons.

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.

Only the first 6 of 10 groups are shown.

Induction Phase

StagePlacebo (IP)Ustekinumab 1 mg/kg (IP)Ustekinumab 3 mg/kg (IP)Ustekinumab 6 mg/kg (IP)Placebo IV -> Responder -> Placebo SC (MP)Placebo IV -> Nonresponder -> Ustekinumab 270/90 mg SC (MP)
STARTED13213113213100
COMPLETED11312112012300
NOT COMPLETED191012800

Reasons for not completing this period:

ReasonPlacebo (IP)Ustekinumab 1 mg/kg (IP)Ustekinumab 3 mg/kg (IP)Ustekinumab 6 mg/kg (IP)Placebo IV -> Responder -> Placebo SC (MP)Placebo IV -> Nonresponder -> Ustekinumab 270/90 mg SC (MP)
Adverse Event524100
Lack of Efficacy924300
Lost to Follow-up101000
Other463400

Maintenance Phase

StagePlacebo (IP)Ustekinumab 1 mg/kg (IP)Ustekinumab 3 mg/kg (IP)Ustekinumab 6 mg/kg (IP)Placebo IV -> Responder -> Placebo SC (MP)Placebo IV -> Nonresponder -> Ustekinumab 270/90 mg SC (MP)
STARTED00002885
COMPLETED00002678
NOT COMPLETED000027

Reasons for not completing this period:

ReasonPlacebo (IP)Ustekinumab 1 mg/kg (IP)Ustekinumab 3 mg/kg (IP)Ustekinumab 6 mg/kg (IP)Placebo IV -> Responder -> Placebo SC (MP)Placebo IV -> Nonresponder -> Ustekinumab 270/90 mg SC (MP)
Adverse Event000013
Lack of Efficacy000013
Other000001

Analysis population for the primary outcome, as defined in the registry: All participants who were randomized, regardless of whether they received study agent.

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.

CharacteristicUnitPlacebo (IP)Ustekinumab 1 mg/kg (IP)Ustekinumab 3 mg/kg (IP)Ustekinumab 6 mg/kg (IP)Total
Participants analysed132131132131526
Age Continuousyears39.5 (SD 13.05)38.8 (SD 11.95)38.2 (SD 12.63)39.4 (SD 13.21)39 (SD 12.69)
Sex: Female, Male: FemaleParticipants68837583309
Sex: Female, Male: MaleParticipants64485748217

6. Primary Endpoint

The registry lists the primary outcome as Number of Participants With Clinical Response at Week 6, measured over Baseline to Week 6.

ElementRegistry entry
Result typeNumber
Measure of spreadnot applicable
UnitParticipants
Endpoint classificationBinary Endpoint

The primary endpoint counts participants who met the trial’s clinical-response definition by Week 6. The definition was based on change in CDAI from baseline: a reduction of at least 100 points qualified as response, except for participants with a baseline CDAI of at least 220 and at most 248, for whom a score below 150 was required. CDAI is a disease-activity index; the registry describes its range from 0 points for minimal disease activity to over 600 points for severe disease activity.

A binary response endpoint is useful for presenting the proportion of participants who cross a prespecified clinical threshold. It is relatively straightforward to interpret: each participant either met the endpoint definition or did not, and the reported group result is the number meeting it. The outcome does not show the size of each participant’s CDAI change beyond whether it reached the response criterion. It therefore differs from an analysis of average score change, which could describe the magnitude and distribution of changes across participants.

The Week 6 outcome captures a specific assessment window, not the duration of response. By itself, it does not establish whether response continued, whether participants achieved clinical remission, or whether other health outcomes changed. Those questions require separate outcomes and timeframes. The registry lists several secondary outcomes at later or earlier visits, but the primary endpoint remains the Week 6 clinical-response count.

The population definition also matters for interpretation. The registry says the analysis included all randomized participants, regardless of receipt of study agent, and the trial focused on people previously treated with TNF antagonist therapy. The record does not report additional eligibility details that would support extending the result to other populations.

7. Results Posted in the Registry

Risk difference: Ustekinumab 1 mg/kg (IP)

+13.2

95% CI: 2.2 to 24.1 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals13.921.428.936.443.951.4Placebo (IP) (n=132)Ustekinumab 1 mg/kg (IP) (n=131)Ustekinumab 3 mg/kg (IP) (n=132)Ustekinumab 6 mg/kg (IP) (n=131)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ustekinumab 1 mg/kg (IP)Ustekinumab 3 mg/kg (IP)Ustekinumab 6 mg/kg (IP)-2.443.9410172329risk 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
Number of Participants With Clinical Remission at Week 6Binary EndpointRisk difference+5.4 pts (-2.8 to 13.6)615 per arm
Number of Participants With Clinical Response at Week 4Binary EndpointRisk difference+10.8 pts (0.9 to 20.8)230 per arm
Number of Participants With Clinical Response at Week 8Binary EndpointRisk difference+14.6 pts (4.4 to 24.9)136 per arm

Number of Participants With Clinical Remission at Week 6

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ustekinumab 1 mg/kg (IP)Ustekinumab 3 mg/kg (IP)-4.17-0.353.477.291115risk difference (percentage points) vs control (95% CI)

Number of Participants With Clinical Response at Week 4

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ustekinumab 1 mg/kg (IP)Ustekinumab 3 mg/kg (IP)-2.474.6912192633risk difference (percentage points) vs control (95% CI)

Number of Participants With Clinical Response at Week 8

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ustekinumab 1 mg/kg (IP)Ustekinumab 3 mg/kg (IP)-1.993.799.57152127risk difference (percentage points) vs control (95% CI)

The secondary outcomes cover clinical response at Week 4 and Week 8, clinical remission at Week 6 and Week 8, and response and remission at Week 22 among participants who responded at Week 6. The available detailed secondary results include Week 4 response, Week 8 response, and Week 6 remission. The registry record lists the later outcomes, but their detailed results are not reported in the registry record.

At a broad level, the posted Week 4 and Week 8 response comparisons tend to show more responses in the ustekinumab arms than in placebo. The Week 6 remission findings are less consistent with a clear separation from placebo in the reported comparisons. This differs from the primary endpoint, which is clinical response at Week 6, not remission. Response and remission use distinct outcome definitions, so their results should not be treated as interchangeable or as direct confirmation of one another.

The secondary outcomes provide context about timing and other dimensions of disease activity, but they do not replace the primary endpoint. Their interpretation is also limited because the registry does not report a multiplicity plan for the set of secondary analyses. When many outcomes and treatment comparisons are examined, some nominally notable results can arise by chance. The secondary p-values are therefore less persuasive when considered in isolation, particularly without a reported adjustment strategy or a prespecified hierarchy.

Some secondary estimates are recalculated from posted counts, while the registry also reports sponsor analyses for selected comparisons. Those analyses do not cover every listed secondary endpoint in the material available in the registry record. The Week 22 outcomes specifically condition on Week 6 response, which defines a selected subgroup; the record does not report their results or sufficient detail to assess those analyses. Overall, the secondary findings can be read as supportive context for the pattern of early response, but they cannot establish effects on unreported endpoints or resolve questions about durability.

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

9. Statistical Interpretation

Clinical Biostats interpretation

At Week 6, the registry reports 31 clinical responses among 132 participants in the placebo group, compared with 48 among 131 receiving ustekinumab 1 mg/kg, 45 among 132 receiving 3 mg/kg, and 52 among 131 receiving 6 mg/kg. The raw counts show more participants meeting the response definition in each ustekinumab arm than in the placebo arm. Counts alone do not convey the precision of those group differences, so the risk-difference estimates and confidence intervals are also important.

The unadjusted recalculated risk difference for ustekinumab 1 mg/kg versus placebo is 0.132, with a 95% confidence interval from 0.022 to 0.241 and an unadjusted p-value of 0.02. For 3 mg/kg, the estimated risk difference is 0.106, with a 95% confidence interval from -0.002 to 0.214 and an unadjusted p-value of 0.057. For 6 mg/kg, the estimated risk difference is 0.162, with a 95% confidence interval from 0.051 to 0.273 and an unadjusted p-value of 0.005. These recalculations are simple, unadjusted comparisons from the posted group summaries.

The 3 mg/kg interval includes zero, so the recalculated data are compatible with no difference as well as with a positive difference of varying size. The intervals for 1 mg/kg and 6 mg/kg are above zero in these recalculations. This describes the statistical uncertainty of the unadjusted estimates; it is not a claim about clinical importance. The registry’s reported analyses use the Cochran-Mantel-Haenszel method and report p-values of 0.021 for 1 mg/kg, 0.057 for 3 mg/kg, and 0.005 for 6 mg/kg. Where these differ from the unadjusted recalculations, the sponsor’s own analysis takes precedence.

The study’s primary findings concern a threshold-defined response at Week 6 in a selected population previously treated with TNF antagonist therapy. They do not establish a treatment effect on every measure of Crohn’s disease, longer-term outcomes, or outcomes in populations not described by the record. The registry’s primary comparison also does not provide a formal statement about clinical importance. Assessment of that question would require a meaningful clinical threshold and context not reported in the registry record.

Interpretation should also account for the number of arms and outcomes examined. The record reports multiple dose comparisons and secondary outcomes, while a multiplicity adjustment plan is not reported in the registry record. The recalculated p-values are explicitly unadjusted; they should not be read as if they accounted for all comparisons in the trial. The posted estimates and intervals are most useful when considered together with the sponsor’s reported analysis, the endpoint definition, and the limits of the registry record.

10. Statistical Methods Explained

The primary outcome is binary: each participant either met the Week 6 clinical-response definition or did not. The registry reports counts by randomized treatment arm. A comparison of binary outcomes can be expressed as a risk difference, which is the estimated difference between the response risks in two groups. A positive risk difference indicates a higher observed response risk in the ustekinumab group than in placebo in that comparison. The recalculated estimates use the posted event counts and arm denominators and are unadjusted.

What does a risk difference describe?

A risk difference expresses the contrast on an absolute scale. It is not the same as a risk ratio or an odds ratio, which describe the contrast using relative scales. Absolute differences can be useful for understanding the size of a group-level contrast, while relative measures answer a different question. Neither type of measure establishes that an observed contrast is clinically important. The recalculated risk differences and their confidence intervals are simple unadjusted re-calculations; they do not replace the trial’s reported analysis.

What does the confidence interval add?

A confidence interval describes uncertainty around an estimated effect under the assumptions of the statistical method. A narrower interval indicates greater precision than a wider interval, but neither width nor position alone establishes clinical relevance. For the primary recalculated comparison at 3 mg/kg, the interval extends from -0.002 to 0.214 and includes zero. For 1 mg/kg and 6 mg/kg, the intervals are 0.022 to 0.241 and 0.051 to 0.273, respectively. These intervals show that the estimated effects are not known with exact precision.

A p-value describes how compatible the observed data are with a specified null hypothesis under the assumptions of the analysis. It does not measure the probability that the null hypothesis is true, nor does it describe the magnitude or clinical importance of an effect. The unadjusted recalculated p-values are 0.02, 0.057, and 0.005 for the comparisons of 1 mg/kg, 3 mg/kg, and 6 mg/kg with placebo. The sponsor’s reported Cochran-Mantel-Haenszel p-values are 0.021, 0.057, and 0.005 for those comparisons. With the discrepancy flag recorded, the sponsor’s own analysis takes precedence over the simple recalculations.

Why can the reported and recalculated analyses differ?

The recalculated comparisons use unadjusted summary-statistic methods. The registry identifies the sponsor’s reported analyses as Cochran-Mantel-Haenszel tests. This method can account for stratification in an analysis, whereas the simple recalculation from aggregate group counts does not reproduce any stratified analysis. The registry record does not report the strata or enough detail to reconstruct the sponsor’s analysis. A difference in analysis method can lead to different p-values; it does not, by itself, establish an error in either result.

For general context, stratified methods combine information across defined strata while accounting for the grouping structure. They may be useful when the trial’s design or analysis specifies strata, but the registry record does not explain whether or how stratification was implemented. The sponsor’s own analysis is the relevant reported trial analysis, and the recalculations are best treated as descriptive, unadjusted checks based on the posted counts.

What is the role of the outcome definition?

The endpoint is not simply any CDAI decrease. It applies the trial’s stated threshold, including a special rule for the baseline CDAI range of at least 220 and at most 248. This creates a binary outcome from a clinical index. The analysis compares the number meeting the criterion in each arm, rather than modeling the full CDAI score distribution. The registry does not report how missing Week 6 outcome measurements were handled, so assumptions about imputation or other missing-data methods cannot be made.

More generally, analysis-population choices can affect interpretation. The registry states that all randomized participants were included regardless of whether they received study agent. That is the available description of the primary population. It does not report adherence-based or per-protocol definitions, nor does it state how participants with unavailable endpoint data were treated in the analysis.

Finally, statistical interpretation must consider the full set of comparisons. Multiple dose arms and multiple outcomes create opportunities for chance findings across tests. The registry record does not report whether the primary comparisons or secondary analyses were adjusted for multiplicity. The recalculated p-values are unadjusted, and the outcome-specific estimates should not be interpreted as if they were a single isolated test. The registry’s reported sponsor analyses and any multiplicity plan beyond what is stated are not recoverable from the posted record.

11. Confidence Intervals and Precision

The confidence intervals for the recalculated Week 6 risk differences describe uncertainty in the absolute comparisons with placebo. For ustekinumab 1 mg/kg, the estimate is 0.132, with a 95% confidence interval from 0.022 to 0.241. For 3 mg/kg, the estimate is 0.106, with a 95% confidence interval from -0.002 to 0.214. For 6 mg/kg, the estimate is 0.162, with a 95% confidence interval from 0.051 to 0.273.

Each interval spans a range of effect sizes compatible with the observed data under the method’s assumptions. The 3 mg/kg interval includes zero, so it does not rule out no difference under this unadjusted calculation. The other two intervals are above zero, but they still cover a range of possible positive differences. These are not guarantees that the true effect lies within the interval, and they do not indicate whether an effect is clinically important.

The posted counts and denominators also matter for precision: less information generally produces more uncertainty. The primary arm sizes are reported as 132 for placebo, 131 for 1 mg/kg, 132 for 3 mg/kg, and 131 for 6 mg/kg. These are the denominators associated with the primary endpoint, not a statement about how many participants contributed to every other outcome or safety analysis.

The sponsor’s reported analyses provide p-values but do not include confidence-interval estimates in the reported-analysis entries. The risk-difference intervals are therefore the unadjusted recalculated intervals, not the sponsor’s stratified intervals. The discrepancy flag means the sponsor’s own analysis takes precedence for the trial’s reported inferential result. The registry record does not report additional details needed to assess precision under the sponsor’s analysis.

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 effect190254
75% of the observed effect327437
50% of the observed effect711951
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect2005001,0002,00040%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 (control proportion held at the observed value). Calculated for the comparison: Ustekinumab 1 mg/kg (IP).

The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design justification. For these binary outcomes, the figures are participants per arm. 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. The trial’s own original sample-size assumptions are not reported in the registry record.

The 80% power column gives the planned participants per arm under those assumptions for an analysis with an 80% chance of detecting the specified effect if that effect were true. The 90% power column gives the corresponding participants per arm for a 90% chance. These are design-planning probabilities under the assumed effect and statistical model, not probabilities that a particular trial result is correct.

Rows for planning at 100%, 75%, and 50% of the observed effect illustrate how sample-size requirements change when the effect assumed for planning is smaller. The smaller-effect scenarios require more participants per arm to maintain the same target power. For example, the primary comparison planning figures vary by dose because the observed risk differences differ, and each comparison has its own planning illustration.

These figures are not observed power. They are hypothetical planning calculations derived from the observed effect and stated assumptions, and they should not be treated as the original enrollment target or as evidence that the completed trial was adequately or inadequately powered. They also do not account for design features or analysis choices not included in the stated planning assumptions.

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 = 0.235; treatment proportion p1 = 0.366; average p̄ = 0.301.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6485 = 1.2710.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6418 = 0.5401.
  4. n = (1.2710 + 0.5401)2 / (0.1316)2 = 189.5, rounded up to 190 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 <- 0.234848484848485                          # control proportion
p1 <- 0.366412213740458                          # 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(771667)
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 = 190 (80% power), 254 (90% power)
 75% of observed effect: n per arm = 327 (80% power), 437 (90% power)
 50% of observed effect: n per arm = 711 (80% power), 951 (90% power)
power.prop.test: 189.5 
Simulated power at n = 190 per arm: 0.807 (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-Haenszelnot reported0.005
Cochran-Mantel-Haenszelnot reported0.057
Cochran-Mantel-Haenszelnot reported0.021
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 using the Cochran-Mantel-Haenszel method. For the primary comparisons, the reported p-values are 0.021 for ustekinumab 1 mg/kg versus placebo, 0.057 for 3 mg/kg versus placebo, and 0.005 for 6 mg/kg versus placebo. These are the trial’s reported analysis results in the registry record.

The recalculated comparisons use unadjusted risk differences derived from the posted response counts and denominators. Their p-values are 0.02, 0.057, and 0.005 for the same dose comparisons. The close agreement in some comparisons does not make the methods identical, and the record flags a discrepancy between sponsor results and recalculations. Under that circumstance, the sponsor’s own analysis takes precedence.

The registry does not give enough information to reproduce the sponsor’s method, including details of any strata or other analysis specifications. Consequently, the recalculated estimates and intervals are useful as simple summaries of the posted group counts, but they should not be described as a reproduction of the sponsor’s analysis. Where a reported sponsor result and an unadjusted recalculation differ, interpretation should be anchored in the sponsor’s reported analysis while recognizing that the exact source of the discrepancy is not reported in the registry record.

15. Multiplicity, Missing Data and Analysis Populations

The trial includes several randomized treatment arms, a primary endpoint, and multiple secondary outcomes at different visits. Each additional comparison can increase the chance of obtaining a nominally notable result even when there is no underlying effect. Statistical methods for multiplicity can control or organize this issue, for example by adjusting significance thresholds or specifying an ordered testing strategy. The registry record does not report whether such a plan was used for the primary dose comparisons or secondary outcomes.

The reported sponsor comparisons use the Cochran-Mantel-Haenszel method, but that method description does not itself establish that multiplicity was addressed. The recalculated p-values are unadjusted. Accordingly, their interpretation should remain tied to the individual comparisons and should not imply that a family-wise error rate or other multiplicity criterion was controlled. The record does not report a prespecified hierarchy among the three dose comparisons.

The primary population is described as all participants randomized, regardless of whether they received study agent. That provides a useful statement about the intended population for the primary outcome, but it does not resolve missing outcome data. The registry record does not report the number of missing Week 6 assessments, the handling of participants without endpoint data, or whether imputation or another missing-data approach was used. Nor does it report sensitivity analyses examining alternative assumptions about missing outcomes.

The registry also does not report a detailed analysis plan, interim-analysis plan, stopping rules, or full protocol specifications. These details could affect how results are interpreted, but they cannot be inferred from the arm counts or reported p-values. The record’s stated primary population should be distinguished from an assumption that every randomized participant had an observed endpoint; the handling of unavailable measurements is not reported.

Because the endpoint is binary, missingness can matter if the probability of an unobserved response differs across treatment groups or relates to participants’ disease status. General statistical practice is to describe missingness and assess whether conclusions depend on plausible assumptions. The registry record does not provide the information needed to assess that issue for this trial.

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 (IP)111328.3%
Ustekinumab 1 mg/kg (IP)61304.6%
Ustekinumab 3 mg/kg (IP)81336.0%
Ustekinumab 6 mg/kg (IP)91316.9%
Placebo IV -> Responder -> Placebo SC (MP)82828.6%
Placebo IV -> Nonresponder -> Ustekinumab 270/90 mg SC (MP)168518.8%
Ustekinumab IV -> Responder -> Placebo SC (MP)127316.4%
Ustekinumab IV -> Responder -> Ustekinumab 90mg SC (MP)97212.5%
Ustekinumab IV -> Nonresponder -> Placebo SC (MP)2111019.1%
Ustekinumab IV -> Nonresponder -> Ustekinumab 90mg SC (MP)2210920.2%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo (IP)8.3%Ustekinumab 1 mg/kg (IP)4.6%Ustekinumab 3 mg/kg (IP)6.0%Ustekinumab 6 mg/kg (IP)6.9%Placebo IV -> Responder -> Pl…28.6%Placebo IV -> Nonresponder ->…18.8%Ustekinumab IV -> Responder -…16.4%Ustekinumab IV -> Responder -…12.5%% 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
Placebo (IP)53 of 132
Ustekinumab 1 mg/kg (IP)51 of 130
Ustekinumab 3 mg/kg (IP)50 of 133
Ustekinumab 6 mg/kg (IP)47 of 131
Placebo IV -> Responder -> Placebo SC (MP)18 of 28
Placebo IV -> Nonresponder -> Ustekinumab 270/90 mg SC (MP)47 of 85

Most frequent serious adverse event terms

Event termOrgan systemPlacebo (IP)Ustekinumab 1 mg/kg (IP)Ustekinumab 3 mg/kg (IP)Ustekinumab 6 mg/kg (IP)Placebo IV -> Responder -> Placebo SC (MP)Placebo IV -> Nonresponder -> Ustekinumab 270/90 mg SC (MP)
Crohn's diseaseGastrointestinal disorders5 of 1322 of 1304 of 1332 of 1313 of 288 of 85
Anal abscessInfections and infestations2 of 1320 of 1300 of 1331 of 1310 of 280 of 85
Abdominal painGastrointestinal disorders0 of 1320 of 1301 of 1330 of 1310 of 281 of 85
ConstipationGastrointestinal disorders1 of 1320 of 1300 of 1330 of 1311 of 280 of 85
Small intestinal obstructionGastrointestinal disorders1 of 1320 of 1301 of 1330 of 1310 of 280 of 85
Decreased appetiteMetabolism and nutrition disorders0 of 1320 of 1300 of 1330 of 1311 of 281 of 85
Suicidal ideationPsychiatric disorders0 of 1321 of 1300 of 1331 of 1310 of 280 of 85
Abdominal massGastrointestinal disorders0 of 1320 of 1300 of 1331 of 1310 of 280 of 85
Anal stenosisGastrointestinal disorders0 of 1320 of 1301 of 1330 of 1310 of 280 of 85
GastritisGastrointestinal disorders0 of 1320 of 1301 of 1330 of 1310 of 280 of 85

Most frequent non-serious adverse event terms

Event termOrgan systemPlacebo (IP)Ustekinumab 1 mg/kg (IP)Ustekinumab 3 mg/kg (IP)Ustekinumab 6 mg/kg (IP)Placebo IV -> Responder -> Placebo SC (MP)Placebo IV -> Nonresponder -> Ustekinumab 270/90 mg SC (MP)
HeadacheNervous system disorders8 of 1328 of 1309 of 13313 of 1311 of 285 of 85
NasopharyngitisInfections and infestations6 of 1327 of 1307 of 1338 of 1311 of 2812 of 85
NauseaGastrointestinal disorders11 of 1329 of 1301 of 1338 of 1313 of 288 of 85
Crohn's diseaseGastrointestinal disorders8 of 1325 of 1303 of 1333 of 13110 of 289 of 85
ArthralgiaMusculoskeletal and connective tissue disorders4 of 1328 of 1308 of 1336 of 1312 of 287 of 85
Abdominal painGastrointestinal disorders9 of 1325 of 1308 of 1337 of 1311 of 284 of 85
PyrexiaGeneral disorders3 of 1325 of 1304 of 1333 of 1311 of 288 of 85
CoughRespiratory, thoracic and mediastinal disorders3 of 1326 of 1304 of 1333 of 1314 of 282 of 85
Back painMusculoskeletal and connective tissue disorders3 of 1325 of 1304 of 1334 of 1312 of 282 of 85
Upper respiratory tract infectionInfections and infestations0 of 1325 of 1304 of 1335 of 1312 of 282 of 85

Serious events with the highest arm-level rate: crohn's disease (10.7%), constipation (3.6%), perirectal abscess (3.6%), decreased appetite (3.6%), intervertebral disc disorder (3.6%).

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 safety results list serious adverse events by treatment sequence and group. In the initial four arms, the registry reports serious adverse events in 11 of 132 participants receiving placebo, 6 of 130 receiving ustekinumab 1 mg/kg, 8 of 133 receiving 3 mg/kg, and 9 of 131 receiving 6 mg/kg. These are counts and group denominators as reported for the safety information; they should not be confused with the primary endpoint denominators, which are slightly different for some arms.

The registry also lists serious adverse events in later groups defined by intravenous response status and subsequent subcutaneous treatment. Those groups have different treatment histories and should not be read as equivalent to the initial randomized comparisons. Their counts are descriptive and do not, without further design and analysis details, establish a causal comparison between later sequences.

The listed serious-event terms include Crohn’s disease at 10.7%, along with constipation, perirectal abscess, decreased appetite, intervertebral disc disorder, and ovarian cyst at 3.6% each. The registry does not report deaths in the safety record; the death entries are not populated. These adverse-event summaries alone do not establish comparative safety, and the registry record does not provide enough detail to assess event timing, severity beyond the serious classification, or causal attribution.

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

The posted primary data show Week 6 clinical-response counts in each of the four treatment arms. More participants met the response definition in each ustekinumab arm than in the placebo arm, while the recalculated risk differences and confidence intervals describe uncertainty around those observed contrasts. The sponsor’s reported analyses provide the registry’s primary inferential results, and the sponsor’s own analysis takes precedence over the simple recalculations where the discrepancy flag applies.

These findings address a defined endpoint in a defined population: adults with moderately to severely active Crohn’s disease previously treated with TNF antagonist therapy, assessed for response from baseline to Week 6. They do not establish what happened for every possible clinical outcome. In particular, a Week 6 response count is not equivalent to remission, sustained response, long-term disease control, or a change in quality of life. Outcomes that are listed but lack detailed results are not reported in the registry record.

Statistical evidence also does not by itself determine clinical importance. The estimates describe the direction and magnitude of group contrasts on the risk-difference scale, while confidence intervals describe their uncertainty. A clinical threshold for deciding whether a difference is important is not reported in the registry record. Nor can a p-value say whether a result is meaningful to an individual participant.

The record does not report the original sample-size justification, missing-data handling, multiplicity plan, or detailed protocol and analysis specifications. These omissions limit evaluation of the trial’s design assumptions and the full context for the reported results. Safety counts are descriptive, and the later treatment-sequence groups are not the same as the initial randomized dose comparisons.

Thus, the most defensible reading is limited to the registry’s stated primary comparison and the reported endpoint, methods, and uncertainty. The posted results should not be extended to unreported outcomes or populations, and they are not individualized medical guidance.

18. Why This Trial Matters Statistically

This trial illustrates why an endpoint definition is central to interpreting clinical research. Clinical response was not an informal judgment: it was defined by a CDAI reduction threshold, with a separate rule for a specified baseline-score range. That creates a reproducible binary outcome, but it also means the result describes whether participants crossed a threshold rather than the full pattern of score changes.

It also shows the value of distinguishing raw counts, effect estimates, confidence intervals, and p-values. Counts make the observed events concrete, while risk differences express the absolute contrast and confidence intervals show its uncertainty. P-values alone would not communicate either the size or precision of the comparison. The 3 mg/kg recalculated interval includes zero, whereas the other two recalculated intervals do not; those distinctions are more informative when read alongside the estimates and the sponsor’s analysis.

The record provides a practical example of why the analysis method matters. The sponsor reports Cochran-Mantel-Haenszel tests, while the recalculations use unadjusted comparisons from aggregate counts. Even when the results are similar, they are not identical analyses. The discrepancy flag makes clear that a simple re-analysis should not be presented as if it supersedes the sponsor’s reported method.

Finally, multiple doses, visits, and outcomes raise questions about multiplicity and selective emphasis. A significant-looking secondary result cannot be interpreted in isolation when the analysis plan for multiple testing is not reported. Statistical literacy requires recognizing both what the registry can establish and what remains unknown, including missing-data handling, original design assumptions, and detailed methods.

19. Limitations

The registry record does not report the original sample-size justification, so the planning illustrations based on observed effects should not be mistaken for the trial’s design calculations. The statistical analysis plan, interim analyses, randomization sequence method, and allocation concealment procedures are also not reported in the registry record.

Details of the sponsor’s Cochran-Mantel-Haenszel analyses are not sufficient to reproduce them. The record does not identify the relevant strata or provide sponsor confidence intervals for the primary comparisons. The recalculated risk differences are unadjusted and should not be treated as substitutes for the sponsor’s reported results.

Missing outcome data are another limitation. The primary population is described as all randomized participants, but the registry record does not report missing Week 6 measurements or how they were handled. The same lack of detail prevents assessment of sensitivity to missing-data assumptions. A multiplicity plan for the dose comparisons and secondary outcomes is not reported, so the posted p-values cannot be assumed to account for all testing.

The detailed secondary results are incomplete in the registry record. Week 22 outcomes are listed but their results are not reported there. The record also gives blank arm descriptions for the interventions, limiting reconstruction of the full sequence of later treatments. The later safety groups reflect response status and subsequent treatment, making them different from the initial randomized dose arms.

Finally, the primary endpoint measures a Week 6 response threshold in the stated prior-TNF-antagonist population. It does not directly answer questions about longer-term outcomes, remission for every dose comparison, or patients outside that population. The safety summary gives serious-event counts and selected event terms, but the registry record does not report deaths, event timing, or sufficient causal detail for a comprehensive comparative safety assessment.

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23. Record Summary

NCT00771667 is a completed Phase 2b randomized, double-blind, placebo-controlled, parallel-group study of ustekinumab in adults with moderately to severely active Crohn’s disease previously treated with TNF antagonist therapy. The registry lists enrollment of 526, a start of 2008-12, and primary completion of 2010-05.

The primary endpoint was the number of participants with clinical response at Week 6, defined using CDAI change from baseline. The posted results report 31 responses among 132 participants receiving placebo, 48 among 131 receiving 1 mg/kg, 45 among 132 receiving 3 mg/kg, and 52 among 131 receiving 6 mg/kg.

The sponsor reported Cochran-Mantel-Haenszel analyses, while the risk differences and confidence intervals discussed in the recalculations are unadjusted. Because the record flags a discrepancy, the sponsor’s own analysis takes precedence. The registry does not report the original sample-size rationale, multiplicity plan, or missing-data handling.

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