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Crohn's Disease Phase 3 Binary Endpoint NCT00783692

Study of Vedolizumab (MLN0002) in Patients With Moderate to Severe Crohn's Disease: Complete Statistical Analysis

This analysis examines a randomized, blinded phase 3 study of vedolizumab for moderate to severe Crohn's disease. It focuses on clinical remission at Week 6 and the registry's reported maintenance outcomes through Week 52.

Trial start: 2008-12  ·  Enrollment: 1116  ·  Sponsor: Millennium Pharmaceuticals, 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 Study of Vedolizumab (MLN0002) in Patients With Moderate to Severe Crohn's Disease (NCT00783692), a randomized phase 3 study. The primary outcome is Induction Phase: Percentage of Participants Achieving Clinical Remission at Week 6.

1116
Enrollment
Phase 3
2
Arms
In the primary outcome
+7.8 pts
Risk difference
DB Vedolizumab
1.6 to 14.0 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00783692
PhasePhase 3
ConditionCrohn's Disease
AllocationRandomized
Design modelFactorial
MaskingTriple
Enrollment1116
Arms in the primary outcome2
Lead sponsorMillennium Pharmaceuticals, Inc.
Results postedYes

2. Clinical Question

Population

The primary analysis population was the Induction Study intention-to-treat population: randomized patients in Cohort 1 who received any amount of blinded study drug. The trial enrolled participants with moderate to severe Crohn's disease. The registry reports enrollment of 1116, but the primary endpoint population is more narrowly defined than the overall enrollment.

Intervention

During induction, participants assigned to vedolizumab received 300 mg by intravenous infusion at Week 0 and Week 2. The study also had a maintenance phase. Participants who demonstrated clinical response at Week 6 according to protocol-specified criteria were randomized in a 1:1:1 ratio for maintenance treatment.

Comparator

The induction comparator was placebo, administered by intravenous infusion at Week 0 and Week 2. The placebo group continued to receive placebo during maintenance regardless of induction response. The maintenance outcomes compare placebo with vedolizumab every 8 weeks and every 4 weeks.

Primary question

The primary question was whether the percentage of participants achieving clinical remission at Week 6 differed between vedolizumab and placebo during induction. Remission was defined using the Crohn's Disease Activity Index (CDAI), with a score at or below 150 points. The registry also describes maintenance questions about clinical response, corticosteroid-free remission, and durable remission at Week 52.

3. Trial Design

This was a phase 3, randomized, placebo-controlled, triple-masked, multicenter study with a factorial model. The registry describes the study as an investigation of induction and maintenance treatment in moderate to severe Crohn's disease. Enrollment was 1116. The study started in 2008-12, had primary completion in 2012-03, and is listed as completed.

The induction phase compared vedolizumab with placebo. The vedolizumab induction regimen was 300 mg by intravenous infusion at Week 0 and Week 2; placebo was administered on the same schedule. The primary endpoint was assessed at Week 6. Participants who showed a clinical response at Week 6 according to protocol-specified criteria entered the maintenance randomization described in the registry, which assigned participants in a 1:1:1 ratio. The registry's placebo arm description says participants assigned to placebo continued to receive placebo during maintenance regardless of their induction response.

The posted maintenance outcomes include comparisons of placebo with vedolizumab given every 8 weeks or every 4 weeks. Those outcomes are not simply further measurements of the full induction population: maintenance randomization depended on Week 6 response. The registry gives this response-based eligibility detail, but the full maintenance protocol and the original design assumptions are not reported in the registry record.

Millennium Pharmaceuticals, Inc. is listed as sponsor. The registry lists 7 outcome measures and 11 analyses. The posted results include the Week 6 primary outcome and maintenance outcomes at Week 52, as well as safety counts. The registry record does not report the full statistical analysis plan or explain how the factorial model informed each reported comparison.

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: In Cohort 1, eligible patients who met entry criteria were randomized to treatment with double-blind vedolizumab 300 mg or placebo in a 3:2 ratio. All Cohort 2 patients were treated with open-label vedolizumab. In the Maintenance Phase participants were assigned to treatment groups based on their Induction Phase treatment and response to therapy.

Only the first 6 of 7 groups are shown.

Induction Phase

StagePlaceboInduction Phase: DB VedolizumabInduction Phase: OL VedolizumabMaintenance Phase: PlaceboMaintenance Phase: Vedolizumab Q8WMaintenance Phase: Vedolizumab Q4W
STARTED148220748000
Treated148220747000
COMPLETED137199674000
NOT COMPLETED112174000

Reasons for not completing this period:

ReasonPlaceboInduction Phase: DB VedolizumabInduction Phase: OL VedolizumabMaintenance Phase: PlaceboMaintenance Phase: Vedolizumab Q8WMaintenance Phase: Vedolizumab Q4W
Adverse Event7924000
Protocol Violation001000
Lack of Efficacy1328000
Withdrawal by Subject3916000
Lost to Follow-up003000
Other002000

Maintenance Phase

StagePlaceboInduction Phase: DB VedolizumabInduction Phase: OL VedolizumabMaintenance Phase: PlaceboMaintenance Phase: Vedolizumab Q8WMaintenance Phase: Vedolizumab Q4W
STARTED13700153154154
COMPLETED4200647382
NOT COMPLETED9500898172

Reasons for not completing this period:

ReasonPlaceboInduction Phase: DB VedolizumabInduction Phase: OL VedolizumabMaintenance Phase: PlaceboMaintenance Phase: Vedolizumab Q8WMaintenance Phase: Vedolizumab Q4W
Adverse Event70015129
Protocol Violation000123
Lack of Efficacy7900645848
Withdrawal by Subject700769
Lost to Follow-up200132
Other000101

Analysis population for the primary outcome, as defined in the registry: Induction Study Intention to Treat (ITT) Population, which consisted of all randomized patients in Cohort 1 who received any amount of blinded study drug.

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: The Induction Phase Safety Population, defined as all participants, in both Cohort 1 and Cohort 2, who received any amount of study drug in the Induction Phase (Weeks 0 to 6), according to the actual study drug received.

CharacteristicUnitPlaceboInduction Phase: DB VedolizumabInduction Phase: OL VedolizumabTotal
Participants analysed1482207471115
Age, Continuousyears38.6 (SD 13.16)36.3 (SD 11.57)35.6 (SD 12.01)36.1 (SD 12.12)
Age, Customized: < 35 yearsparticipants67111404582
Age, Customized: ≥ 35 yearsparticipants81109343533
Age, Customized: < 65 yearsparticipants1422187321092
Age, Customized: ≥ 65 yearsparticipants621523
Sex: Female, Male: FemaleParticipants79115401595
Sex: Female, Male: MaleParticipants69105346520
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants521926
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants1392147121065
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants441624
Race/Ethnicity, Customized: Whiteparticipants124182689995
Race/Ethnicity, Customized: Blackparticipants331723
Race/Ethnicity, Customized: Asianparticipants19353589
Race/Ethnicity, Customized: Otherparticipants2068
Region of Enrollment: Australiaparticipants5103045
Region of Enrollment: Austriaparticipants43714
Region of Enrollment: Belgiumparticipants12174170
Region of Enrollment: Bulgariaparticipants57214
Region of Enrollment: Canadaparticipants2212103137
Region of Enrollment: Czech Republicparticipants11165380
Region of Enrollment: Denmarkparticipants02810
Region of Enrollment: Estoniaparticipants1236
Region of Enrollment: Franceparticipants433744
Region of Enrollment: Germanyparticipants014950
Body Weightkg68.7 (SD 18.90)67.1 (SD 19.07)70.8 (SD 19.56)69.8 (SD 19.42)
Body Mass Index (BMI)kg/m^223.7 (SD 5.77)23.1 (SD 5.62)24.2 (SD 6.02)23.9 (SD 5.93)
Duration of Crohn's Disease (CD)years8.2 (SD 7.80)9.2 (SD 8.18)9.2 (SD 7.63)9.0 (SD 7.77)
Duration of Crohn's Disease - Categorical: < 1 yearparticipants12124569
Duration of Crohn's Disease - Categorical: ≥ 1 to < 3 yearsparticipants2748126201
Duration of Crohn's Disease - Categorical: ≥ 3 to < 7 yearsparticipants4549191285
Duration of Crohn's Disease - Categorical: ≥ 7 yearsparticipants64111385560
Baseline Disease Activity - Crohn's Disease Activity Index (CDAI)units on a scale324.6 (SD 78.08)327.3 (SD 70.67)322.2 (SD 67.17)323.6 (SD 69.37)
Baseline Disease Activity - Categorical: CDAI ≤ 330participants81119418618
Baseline Disease Activity - Categorical: CDAI > 330participants66100325491
Baseline Disease Activity - Categorical: Missingparticipants1146
Baseline C-reactive Protein (CRP)mg/L23.6 (SD 27.85)24.1 (SD 27.23)20.4 (SD 27.40)21.5 (SD 27.45)

6. Primary Endpoint

The registry lists the primary outcome as Induction Phase: Percentage of Participants Achieving Clinical Remission at Week 6, measured over Week 6.

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

The primary endpoint is the percentage of participants who achieved clinical remission at Week 6 during induction. The registry defines remission as a CDAI score at or below 150 points. The CDAI is a symptom and disease-activity index for Crohn's disease, with a total score ranging from 0 to approximately 600; higher scores indicate greater disease activity.

The index combines eight factors: liquid or soft stools over 7 days, abdominal pain over 7 days, general well-being over 7 days, complications, use of Lomotil or opiates for diarrhea, an abdominal mass, hematocrit, and percentage deviation from standard weight. The daily stool, pain, and well-being assessments are accumulated over a week, while other components contribute to the weighted score. This approach combines several aspects of symptoms and clinical status rather than relying on a single symptom.

A threshold-based endpoint makes the result interpretable as the proportion meeting a stated remission definition at a specified assessment time. It does not describe the full distribution of CDAI scores or the size of any score change among participants who did not reach remission. The registry specifies that participants who discontinued prematurely for any reason were considered not to have achieved clinical remission. Thus, the primary percentage reflects both the remission definition and that discontinuation rule.

7. Results Posted in the Registry

Risk difference: DB Vedolizumab

+7.8

95% CI: 1.6 to 14.0 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals2.16.09.813.717.621.4Placebo (n=148)DB Vedolizumab (n=220)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)DB Vedolizumab-1.122.125.368.601215risk 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
Maintenance Phase: Percentage of Participants With Enhanced Clinical Response at Week 52Binary EndpointRisk difference+13.4 pts (2.8 to 24.1)201 per arm
Maintenance Phase: Percentage of Participants in Corticosteroid-free Clinical Remission at Week 52Binary EndpointRisk difference+15.9 pts (3.0 to 28.7)113 per arm
Maintenance Phase: Percentage of Participants With Durable Clinical RemissionBinary EndpointRisk difference+7.0 pts (-1.5 to 15.6)464 per arm

Maintenance Phase: Percentage of Participants With Enhanced Clinical Response at Week 52

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Vedolizumab Q8WVedolizumab Q4W-2.093.9710162228risk difference (percentage points) vs control (95% CI)

Maintenance Phase: Percentage of Participants in Corticosteroid-free Clinical Remission at Week 52

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Vedolizumab Q8WVedolizumab Q4W-2.294.3611182431risk difference (percentage points) vs control (95% CI)

Maintenance Phase: Percentage of Participants With Durable Clinical Remission

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Vedolizumab Q8WVedolizumab Q4W-7.94-2.892.177.221217risk difference (percentage points) vs control (95% CI)

The secondary outcomes add information about different aspects of maintenance treatment: enhanced clinical response, corticosteroid-free clinical remission, and durable clinical remission. Their overall pattern is not uniform. The response and corticosteroid-free remission comparisons generally show higher observed percentages in the vedolizumab maintenance groups than in placebo. For durable remission, the observed percentages are also higher for the every-8-weeks group than placebo, while the every-4-weeks estimate is closer to placebo. These results do not all carry the same degree of statistical support or precision.

These outcomes complement, but do not duplicate, the primary Week 6 remission result. The primary endpoint concerns induction and a specific CDAI remission threshold. Maintenance endpoints concern later outcomes, different definitions, and participants selected for maintenance randomization after demonstrating a Week 6 response. Consequently, secondary results address a later stage of the study and a different analysis population; they should not be read as a direct extension of the primary comparison in the original induction population.

There are multiple reported secondary comparisons. When several outcomes and treatment contrasts are examined, the chance of observing at least one nominally small p-value can increase. The registry does not report a multiplicity adjustment or a hierarchy for interpreting the secondary tests. Their reported p-values should therefore be treated as exploratory evidence unless the planned inferential status is otherwise established; that status is not reported in the registry record.

Viewed together, the secondary results suggest a broadly favorable direction for some maintenance measures, but they do not establish a single consistent pattern across all outcomes. Interpretation should weigh the endpoint definitions, confidence intervals, response-based eligibility, and multiplicity rather than count nominally significant results. The registry record does not report enough of the statistical plan to establish which secondary comparisons, if any, were intended as confirmatory.

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

9. Statistical Interpretation

Clinical Biostats interpretation

At Week 6, clinical remission was recorded for 6.8% of participants in the placebo group and 14.5% in the vedolizumab group. The respective 95% confidence intervals were 2.7 to 10.8 and 9.9 to 19.2. These arm-specific percentages describe the observed proportions in the primary analysis population; they are not estimates of the probability that an individual participant will experience remission.

The sponsor-reported comparison used the Cochran-Mantel-Haenszel method. It reported a risk difference of 7.8 percentage points, with a 95% confidence interval from 1.2 to 14.3 and p = 0.021. A separate unadjusted recalculation from the posted summary counts gives p = 0.021. The recalculation is close to the reported p-value, but it is not the same analysis: the reported result uses the sponsor's stated method, whereas the recalculation is unadjusted. The registry does not explain the strata or other details used in the sponsor's analysis.

The reported confidence interval for the risk difference lies on the positive side of the null value, and the reported p-value is below 0.05. In statistical terms, the posted primary analysis is evidence of a difference between groups under the reported analysis. This describes the statistical result, not the clinical importance of the difference. The study's endpoint is a threshold outcome at one assessment time, and the observed percentages do not describe the full course of symptoms or disease activity.

The maintenance outcomes provide additional observations, but they answer different questions and use populations selected by induction response for maintenance randomization. The posted estimates for enhanced clinical response and corticosteroid-free clinical remission generally favor the vedolizumab maintenance groups over placebo, while durable remission estimates show a less consistent pattern. These are secondary results, and the registry's record of 11 analyses means they should be interpreted in the context of multiple comparisons. The record does not report a multiplicity adjustment, so isolated nominal p-values among secondary outcomes warrant more caution than a prespecified primary result.

The results are limited to the outcomes, populations, and analysis descriptions in the registry record. Details about the original power calculation, interim monitoring, handling of missing maintenance outcomes, and broader analysis plan are not reported in the registry record. Those omissions constrain how fully the statistical evidence can be reconstructed from the posted summaries.

10. Statistical Methods Explained

The primary outcome is binary: each participant is classified as having achieved clinical remission or not achieved it by Week 6. A percentage is the natural summary for such an outcome because it reports the share of participants meeting the definition. The arm percentages are accompanied by 95% confidence intervals, which express uncertainty about the population percentages compatible with the observed data under the method used to construct the intervals.

What does a risk difference express?

A risk difference compares the proportions with an outcome in two groups by subtracting one group proportion from the other. Its units are percentage points when the proportions are reported as percentages. A positive risk difference for the vedolizumab group indicates a higher observed remission proportion in that group than in placebo. Unlike a relative measure, a risk difference keeps the comparison on the absolute percentage scale. It can therefore be read alongside each group's observed percentage, while still reflecting uncertainty in the estimated contrast.

The registry reports a sponsor analysis using the Cochran-Mantel-Haenszel method for the primary risk difference. This method can combine group comparisons across strata. The registry does not report the strata used or enough detail to reconstruct that analysis. The simple recalculation uses the posted group counts and is unadjusted; it should not be mistaken for the sponsor's analysis. Because the discrepancy flag is false, no discrepancy requiring the sponsor result to take precedence is identified, but the method distinction remains important.

How should the p-value be read?

A p-value describes how compatible the observed data are with a null hypothesis of no group difference, under the assumptions of the chosen analysis. It is not the probability that the null hypothesis is true, nor does it measure the size or clinical importance of an effect. The sponsor's p-value and the unadjusted recalculated p-value are close, but they arise from analyses that are not identical. Statistical interpretation should center on the reported sponsor analysis and consider its confidence interval as well as its p-value.

Why are confidence intervals useful?

A confidence interval communicates the range of effect estimates reasonably compatible with the data and analysis assumptions. Its width reflects precision: a narrower interval indicates more precise estimation, while a wider interval allows a broader range of plausible effects. Whether an interval includes the null value is relevant to conventional tests of a difference, but the interval also conveys the possible magnitude and direction of the effect. It does not imply that every value in the interval is equally likely.

The registry lists several maintenance comparisons, each with its own estimate, interval, and p-value. Those comparisons should not automatically be treated as independent confirmation of the primary result. The outcomes differ, and maintenance eligibility depended on Week 6 response. Further, the record does not report whether the analysis plan adjusted for testing multiple endpoints and comparisons.

What does the outcome definition contribute?

The CDAI threshold converts a multidimensional score into a remission classification. That makes the primary result straightforward to state as a percentage, but a threshold discards information about how close participants were to the cut point and how much scores changed. A participant just above the remission threshold and one with a substantially higher score both count as not achieving remission under the stated definition. The registry also classifies every premature discontinuation as not achieving remission, a rule that affects how the outcome is assigned.

General statistical interpretation should distinguish the observed endpoint from broader claims. The analysis estimates the proportion meeting a defined remission criterion at Week 6; it does not estimate every aspect of disease activity, durability, or individual response. Those limits apply even when a group comparison is statistically distinguishable from the null value.

11. Confidence Intervals and Precision

The primary arm percentages are 6.8% for placebo and 14.5% for vedolizumab. Their 95% confidence intervals are 2.7 to 10.8 and 9.9 to 19.2, respectively. These intervals indicate uncertainty around each group's remission percentage. They should not be confused with the confidence interval for the difference between groups, which addresses a different quantity.

For the primary comparison, the sponsor-reported risk difference is 7.8 percentage points, with a 95% confidence interval from 1.2 to 14.3. The interval is entirely above the null value, so it supports a positive group contrast under the reported method. Its span also shows that the precise size of the contrast remains uncertain: the data are compatible with a range of positive differences rather than a single exact effect.

Confidence intervals are not guarantees that the true effect lies within the particular interval, and they do not include uncertainty about the endpoint definition, analysis choices, or generalizability. They describe sampling uncertainty under the method and assumptions used. The registry does not report all details needed to assess every assumption behind the sponsor's interval.

For the maintenance outcomes, interval widths vary across comparisons. Some reported intervals include the null value, while others do not. This variation is relevant when judging how precisely each effect is estimated, but the secondary comparisons also require caution about multiple testing and the response-selected maintenance population. Precision is not the same as importance: a precise estimate can still be modest in size, and a less precise estimate can leave substantial uncertainty about magnitude and direction.

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 effect246328
75% of the observed effect401537
50% of the observed effect8221,100
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. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: DB Vedolizumab.

The planning figures are illustrations based on the observed effect, not the trial's original sample-size design. For these binary outcomes, the figures are participants per arm, not total participants. The distinction matters: each displayed planning number describes the size of one group in a hypothetical equal-allocation comparison. The event-total convention applies to time-to-event calculations; the posted outcomes are percentages, so that convention does not turn these figures into total event counts.

The stated planning 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 set as a stated fraction of the observed effect. The rows for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect illustrate how planning changes when the target difference is smaller than the observed difference.

The 80% power column describes the number of participants per arm in a hypothetical design intended to have an 80% chance of detecting the specified effect under the stated assumptions, if that effect is the true effect. The 90% power column uses a higher target chance of detection. These are planning concepts, not guarantees that a future study will detect an effect. Smaller effects need more participants to achieve the same target power, which is why the figures increase as the assumed fraction of the observed effect decreases.

This is not observed power. It is a planning illustration calculated from the observed effect, and it does not establish what power the completed trial had under its original design. The trial's own sample-size justification and original design assumptions are not reported in the registry record.

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 = 0.068; treatment proportion p1 = 0.145; average p̄ = 0.107.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.4363 = 0.8551.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.4328 = 0.3642.
  4. n = (0.8551 + 0.3642)2 / (0.0779)2 = 245.1, rounded up to 246 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 <- 0.0675675675675676                          # control proportion
p1 <- 0.145454545454545                          # 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(783692)
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 = 246 (80% power), 328 (90% power)
 75% of observed effect: n per arm = 401 (80% power), 537 (90% power)
 50% of observed effect: n per arm = 822 (80% power), 1,100 (90% power)
power.prop.test: 245.1 
Simulated power at n = 246 per arm: 0.813 (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-HaenszelRisk Difference (RD) 7.81.2 to 14.30.021

The sponsor's primary analysis reports a Cochran-Mantel-Haenszel risk difference of 7.8 percentage points, with a 95% confidence interval from 1.2 to 14.3 and p = 0.021. The unadjusted recalculation from the posted summary statistics gives p = 0.021. The close p-values are consistent with a similar overall signal, but they should not be presented as if they came from the same method.

The recalculation is a simple comparison of the posted group summaries. It does not reproduce any stratification or other features of the Cochran-Mantel-Haenszel analysis. Since the registry does not identify the analysis strata or provide further computational details, the sponsor's reported estimate and interval are the direct record of the sponsor's own analysis. The recalculated value is a supplementary, unadjusted check rather than a replacement.

The registry does not flag a discrepancy between the posted summary and the reported analysis. The primary interpretation should therefore retain the sponsor's reported result and clearly identify the recalculation as unadjusted. Neither p-value alone conveys the precision or clinical meaning of the comparison; the sponsor's confidence interval and the endpoint definition remain central to interpretation.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists 7 outcome measures and 11 analyses, including a primary induction endpoint and several maintenance comparisons. Testing multiple endpoints or treatment contrasts can increase the chance that at least one result appears statistically significant by chance, even when each individual test uses a conventional significance threshold. General statistical practice addresses this concern by prespecifying a primary outcome, defining the role of secondary outcomes, and sometimes adjusting inference for multiple comparisons.

The primary outcome is identified in the registry, but the registry record does not report a multiplicity procedure, a testing hierarchy for secondary outcomes, or whether the secondary comparisons were intended to be confirmatory. It also does not report interim analyses or a statistical monitoring plan. These elements should not be inferred from the number or pattern of posted p-values. As a result, the primary comparison has a clearer stated role than the set of secondary results, while the secondary p-values should be interpreted cautiously.

The primary analysis population is described as randomized patients in Cohort 1 who received any amount of blinded study drug. The registry says participants who prematurely discontinued for any reason were considered not to have achieved clinical remission for the primary endpoint. That is a specific outcome-assignment rule and should be kept in view when interpreting the Week 6 percentage.

For maintenance, eligibility for randomization depended on clinical response at Week 6. The resulting maintenance comparisons therefore concern the response-selected population described in the record, rather than all participants originally enrolled. The registry does not report detailed missing-data procedures for the maintenance outcomes, sensitivity analyses, or the handling of missing Week 52 assessments. Those details are not reported in the registry record, so the robustness of the maintenance estimates to missingness cannot be assessed from the posted summary alone.

The original sample-size justification and the trial's planned analysis assumptions are also not reported in the registry record. The separate planning illustrations based on observed effects are not a substitute for those design details. In particular, they cannot establish the intended power or confirmatory scope of the completed 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
Placebo2314815.5%
VDZ/PBO2315315.0%
VDZ/VDZ19981424.4%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo15.5%VDZ/PBO15.0%VDZ/VDZ24.4%% 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
Placebo96 of 148
VDZ/PBO96 of 153
VDZ/VDZ476 of 814

Most frequent serious adverse event terms

Event termOrgan systemPlaceboVDZ/PBOVDZ/VDZ
Crohn's diseaseGastrointestinal disorders13 of 1488 of 15399 of 814
Anal abscessInfections and infestations1 of 1480 of 15316 of 814
Small intestinal obstructionGastrointestinal disorders1 of 1481 of 1536 of 814
Abdominal abscessInfections and infestations0 of 1482 of 1535 of 814
Abdominal painGastrointestinal disorders1 of 1482 of 1533 of 814
Intestinal obstructionGastrointestinal disorders1 of 1480 of 1534 of 814
Ileal stenosisGastrointestinal disorders0 of 1482 of 1532 of 814
NephrolithiasisRenal and urinary disorders0 of 1480 of 1534 of 814
AnaemiaBlood and lymphatic system disorders0 of 1480 of 1534 of 814
NauseaGastrointestinal disorders0 of 1480 of 1533 of 814

Most frequent non-serious adverse event terms

Event termOrgan systemPlaceboVDZ/PBOVDZ/VDZ
ArthralgiaMusculoskeletal and connective tissue disorders19 of 14821 of 153110 of 814
HeadacheNervous system disorders19 of 14828 of 15397 of 814
PyrexiaGeneral disorders17 of 14822 of 153102 of 814
Crohn's diseaseGastrointestinal disorders28 of 14823 of 15384 of 814
NasopharyngitisInfections and infestations10 of 14814 of 153100 of 814
NauseaGastrointestinal disorders12 of 14818 of 15388 of 814
Abdominal painGastrointestinal disorders21 of 14818 of 15379 of 814
VomitingGastrointestinal disorders10 of 14813 of 15348 of 814
Upper respiratory tract infectionInfections and infestations11 of 1485 of 15354 of 814
FatigueGeneral disorders5 of 1489 of 15353 of 814

Serious events with the highest arm-level rate: crohn's disease (12.2%), anal abscess (2.0%), abdominal pain (1.3%), ileal stenosis (1.3%), abdominal abscess (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 safety summary reports serious adverse events by group as counts of participants affected and participants at risk. The placebo group lists 23 affected among 148 at risk; VDZ/PBO lists 23 among 153; and VDZ/VDZ lists 199 among 814. Other adverse events are reported as 96 among 148 for placebo, 96 among 153 for VDZ/PBO, and 476 among 814 for VDZ/VDZ. These are counts, not calculated rates or adjusted comparisons.

The registry also lists serious adverse event terms with percentages: Crohn's disease, 12.2%; anal abscess, 2.0%; abdominal pain, 1.3%; ileal stenosis, 1.3%; abdominal abscess, 1.3%; and small intestinal obstruction, 0.7%. These entries identify the most frequently listed serious terms in the posted record, but the record does not provide the term-specific group breakdown in the registry record.

Deaths are not reported in the registry record. The safety figures do not by themselves establish a causal relationship or permit a fully adjusted safety comparison. The group labels, denominators, follow-up details, and the limitations of the available summary should be considered when reading these counts.

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

The posted primary result describes the proportion of participants meeting a defined clinical remission threshold at Week 6. The sponsor analysis estimates a positive difference between the vedolizumab and placebo groups, with a confidence interval that remains above the null value. This is evidence of a group difference under the reported analysis, not proof that every participant had the same response or that the observed difference applies to every clinical setting.

The endpoint represents one time point and a classification based on CDAI. It does not show the amount of symptom change for each participant, the distribution of scores, or whether remission persisted. Maintenance outcomes address later response and remission measures, but they are distinct endpoints in a response-selected population. They should not be collapsed into a single conclusion about the entire treatment course.

A statistically supported difference is not automatically a clinically important difference. The registry reports the remission percentages and estimated risk difference, but it does not state a threshold for clinical importance. The results also do not, by themselves, establish how the outcomes compare with other treatments or with care outside the study.

The safety summary gives counts of participants with serious and other adverse events, along with selected serious event terms. It is descriptive and does not provide enough detail to assess every possible safety comparison, causal relationship, or difference in risk. Deaths are not reported in the registry record.

Overall, the record supports a careful statement about the measured Week 6 outcome and the sponsor-reported comparison. Broader claims about individual benefit, long-term outcomes, clinical importance, or comparative safety go beyond what these posted summaries establish. The interpretation is bounded by the definitions, populations, analysis details, and missing information in the registry record.

18. Why This Trial Matters Statistically

This trial illustrates why a clinical result should be read at several levels. The arm percentages describe the observed outcome; the risk difference expresses the absolute group contrast; the confidence interval communicates uncertainty about that contrast; and the p-value summarizes compatibility with a null hypothesis under a specified analysis. These quantities are related, but none replaces the others.

It also demonstrates the importance of distinguishing a sponsor-reported adjusted method from a simple recalculation using summary counts. Close numerical results do not make different methods interchangeable. The registry's reported Cochran-Mantel-Haenszel result is the sponsor analysis, while an unadjusted recalculation is a supplementary check with less information about the original analytic structure.

The study's two-stage design matters statistically. The primary induction endpoint concerns randomized groups at Week 6, while maintenance comparisons depend on response at Week 6 and address later outcomes. The populations, timing, and endpoint definitions differ, so later results should not be interpreted as though they estimate the same contrast as the primary analysis.

Finally, the record shows why multiplicity and missing-data information matter. A set of secondary analyses can generate useful evidence, but the interpretation depends on prespecified roles, adjustment plans, and missing-data methods. Those details are not reported in the registry record. Clear separation of primary findings, secondary patterns, and unresolved analytic details helps prevent a collection of p-values from being mistaken for a complete account of evidence.

19. Limitations

The primary endpoint is a thresholded CDAI outcome at Week 6. It does not retain the full information in the underlying scores, and it cannot describe remission durability. The registry's rule that premature discontinuations count as not achieving remission is explicit, but the record does not provide sensitivity analyses that would show how alternative missing-outcome assumptions might affect the estimate.

The primary analysis population is defined as randomized Cohort 1 patients who received any amount of blinded study drug. This is the population stated in the registry and should not be silently broadened to all enrolled participants. The record does not report further detail on exclusions, protocol deviations, or the flow of participants through the primary analysis.

Maintenance comparisons are response-selected: Week 6 clinical response determined eligibility for maintenance randomization. They therefore address a different population from the overall induction comparison. The registry does not report detailed missing-data handling for these later endpoints, nor does it provide enough information to reconstruct the full maintenance analysis plan.

The sponsor reports a Cochran-Mantel-Haenszel analysis, but the registry does not identify the strata or other details needed to reproduce it. The unadjusted recalculation is not a substitute for those details. Multiplicity procedures, interim monitoring, the original sample-size justification, and a full statistical analysis plan are not reported in the registry record. These omissions limit independent assessment of the planned inferential framework and the weight intended for secondary findings.

The safety results are summarized as counts and selected event terms. The registry record does not provide a detailed causal assessment or enough information to compare event patterns across all relevant exposure periods. The listed results should be read as descriptive summaries rather than as a complete safety analysis.

20. Related Tutorials

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23. Record Summary

NCT00783692 is a completed phase 3, randomized, placebo-controlled, triple-masked, multicenter study of vedolizumab in moderate to severe Crohn's disease. The listed enrollment is 1116, with study start in 2008-12 and primary completion in 2012-03. Induction treatment was administered at Week 0 and Week 2, and the primary endpoint was clinical remission at Week 6, defined as a CDAI score at or below 150 points.

The sponsor-reported primary analysis found a risk difference of 7.8 percentage points, with a 95% confidence interval from 1.2 to 14.3 and p = 0.021. The record also includes maintenance outcomes at Week 52 and descriptive safety summaries. Important details—including the original sample-size justification, multiplicity approach, and maintenance missing-data methods—are not reported in the registry record.

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