← Clinical Trials
Rheumatoid Arthritis Phase 3 Binary Endpoint NCT00673920

A Study to Evaluate Ocrelizumab Compared With Placebo in Patients With Rheumatoid Arthritis Who Have an Inadequate Response to Methotrexate Therapy: Complete Statistical Analysis

This page examines a randomized, double-blind, phase 3 trial of ocrelizumab and placebo in people with active rheumatoid arthritis who had an inadequate response to methotrexate. It focuses on the Week 24 ACR20 endpoint, the posted secondary results, and the limits of the registry record.

Trial start: 2008-04-24  ·  Enrollment: 314  ·  Sponsor: Genentech, 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 to Evaluate Ocrelizumab Compared With Placebo in Patients With Rheumatoid Arthritis Who Have an Inadequate Response to Methotrexate Therapy (NCT00673920), a randomized phase 3 study. The primary outcome is Percentage of Participants With American College of Rheumatology (ACR) 20 Response.

314
Enrollment
Phase 3
8
Arms
In the primary outcome
+9.5 pts
Risk difference
Ocrelizumab 400mg
-4.6 to 23.6 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00673920
PhasePhase 3
ConditionRheumatoid Arthritis
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment314
Arms in the primary outcome8
Lead sponsorGenentech, Inc.
Results postedYes

2. Clinical Question

Population

Participants had active rheumatoid arthritis and an inadequate response to methotrexate therapy. The primary endpoint population is described as the ITT population based on original randomization.

Intervention

Ocrelizumab was given with stable-dose methotrexate. In Cycle 1, one group received 200 mg on Days 1 and 15; another received 400 mg on Day 1.

Comparator

The comparator was matching placebo with methotrexate. Participants in the placebo group received placebo on Days 1 and 15 of Cycle 1.

Primary question

At Week 24, what percentage of participants in each original randomized group achieved an ACR20 response? The registry also posts unadjusted comparisons of each ocrelizumab group with placebo.

The clinical question is about the proportion reaching a prespecified response threshold, rather than the average change in a continuous measure. ACR20 requires at least 20% improvement in tender or swollen joint counts, together with 20% improvement in 3 of 5 additional criteria: physician's global assessment of disease activity, participant assessment of disease activity, patient assessment of pain on a visual analog scale, participant assessment of functional disability via a Health Assessment Questionnaire, and erythrocyte sedimentation rate. The endpoint is assessed at Week 24, during the placebo-controlled treatment period.

The study compared two Cycle 1 ocrelizumab regimens with placebo, all alongside methotrexate. The brief study summary describes subsequent treatment and re-randomization after the placebo-controlled period. Those later assignments do not form part of this Week 24 comparison; the endpoint uses the original randomization groups.

3. Trial Design

This was a phase 3, randomized, double-blind, parallel-group study. The registry describes it as international. It enrolled 314 participants and is listed as terminated. The reason for termination is not reported in the registry record, so the status alone does not establish why the study ended or whether the planned follow-up was completed.

The brief summary describes a planned 2:2:1 allocation across three Cycle 1 groups: ocrelizumab 200 mg intravenously on Days 1 and 15, ocrelizumab 400 mg intravenously on Day 1 with placebo on Day 15, or placebo on both days. All participants were to continue a stable dose of concomitant methotrexate, described as 7.5-25 mg per week. The primary endpoint results are reported for 64 participants in the placebo group, 117 in the ocrelizumab 400 mg group, and 131 in the ocrelizumab 200 mg Cycle 1 group.

The primary outcome is measured at Week 24, at the end of the placebo-controlled treatment period. The brief summary says that participants would then enter further treatment assignments: some groups would be re-randomized between ocrelizumab schedules, while the 400 mg group would receive a further 400 mg infusion. The registry lists later arm descriptions, but the primary endpoint table has no Week 24 results for those later treatment labels. They should not be treated as additional independent Week 24 comparison groups.

The primary endpoint population is the ITT population based on original randomization. The registry record does not report the detailed randomization procedure, concealment process, or full visit and follow-up schedule. It also does not report the reason for termination or a complete account of how many participants discontinued before endpoint assessment. These omissions limit what can be concluded about implementation and the flow of participants through the study.

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 8 groups are shown.

Baseline up to Week 48

StagePlaceboOcrelizumab 400mgOcrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 400mgOcrelizumab 400mg/ Ocrelizumab 400mg
STARTED64117133000
COMPLETED60114126000
NOT COMPLETED437000

Reasons for not completing this period:

ReasonPlaceboOcrelizumab 400mgOcrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 400mgOcrelizumab 400mg/ Ocrelizumab 400mg
Withdrew consent102000
Refused treatment100000
Insufficient therapeutic response210000
Protocol Violation001000
Violation of selection criteria at entry001000
Administrative/Other012000
Adverse event/intercurrent illness011000

Week 24 to Week 48

StagePlaceboOcrelizumab 400mgOcrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 400mgOcrelizumab 400mg/ Ocrelizumab 400mg
STARTED0006161109
COMPLETED0006061106
NOT COMPLETED000103

Reasons for not completing this period:

ReasonPlaceboOcrelizumab 400mgOcrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 400mgOcrelizumab 400mg/ Ocrelizumab 400mg
Adverse event/intercurrent illness000000
Failure to return000001
Insufficient therapeutic response000001
Death000001
Adminstrative/Other000100

Analysis population for the primary outcome, as defined in the registry: ITT Population (original randomization)

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 not provided for Participants who were re-randomized at Week 24 (Cycle 2)

Only the first 6 of 9 groups are shown.

CharacteristicUnitPlaceboOcrelizumab 400mgOcrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 400mgOcrelizumab 400mg/ Ocrelizumab 400mg
Participants analysed64117131000
Age, ContinuousYears53.1 (SD 11.45)52.3 (SD 11.14)53.0 (SD 11.15)———
Sex: Female, Male: FemaleParticipants5693105———
Sex: Female, Male: MaleParticipants82426———
Ethnicity (NIH/OMB): Hispanic or LatinoParticipants102224———
Ethnicity (NIH/OMB): Not Hispanic or LatinoParticipants5495107———
Ethnicity (NIH/OMB): Unknown or Not ReportedParticipants000———
Race (NIH/OMB): American Indian or Alaska NativeParticipants332———
Race (NIH/OMB): AsianParticipants41310———
Race (NIH/OMB): Native Hawaiian or Other Pacific IslanderParticipants000———
Race (NIH/OMB): Black or African AmericanParticipants999———
Race (NIH/OMB): WhiteParticipants448599———
Race (NIH/OMB): More than one raceParticipants000———
Race (NIH/OMB): Unknown or Not ReportedParticipants4711———

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants With American College of Rheumatology (ACR) 20 Response, measured over Week 24.

ElementRegistry entry
Result typeNumber
Measure of spread95% Confidence Interval
UnitPercentage of Participants
Endpoint classificationBinary Endpoint

The primary endpoint is the percentage of participants with an American College of Rheumatology 20 response at Week 24. ACR20 is a categorical measure: a participant either meets the response definition or does not. The definition requires at least 20% improvement in tender or swollen joint counts and 20% improvement in 3 of 5 additional measures covering clinician and participant assessments, pain, function, and erythrocyte sedimentation rate.

A composite response measure brings several aspects of rheumatoid arthritis assessment into one outcome. It can be easier to interpret as the proportion of participants who cross a defined threshold than as separate changes in each component. At the same time, a threshold does not show the size or pattern of change for every participant. Two people may both meet ACR20 while having different changes across joint counts, pain, function, or other criteria.

The endpoint is assessed at Week 24, during the placebo-controlled phase, and is reported for the ITT population based on original randomization. This aligns the comparison with the groups assigned at the start of treatment. It does not, by itself, describe later outcomes after re-randomization or establish how missing Week 24 assessments were handled. The detailed missing-data procedure is not reported in the registry record.

7. Results Posted in the Registry

Risk difference: Ocrelizumab 400mg

+9.5

95% CI: -4.6 to 23.6 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals14.424.534.744.955.165.3Placebo (n=64)Ocrelizumab 400mg (n=117)Ocrelizumab 200mg - Cycle 1 (n=131)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ocrelizumab 400mgOcrelizumab 200mg - Cycle 1-8.051.9512223242risk difference (percentage points) vs control (95% CI)

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Percentage of Participants Achieving Disease Activity Score 28 (DAS28) Remission (DAS28 < 2.6)Binary EndpointRisk difference+1.1 pts (-4.5 to 6.8)4,239 per arm
Change in DAS28 From BaselineContinuous EndpointMean difference-0.81 (-1.26 to -0.36)44 per arm
Percentage of Participants Achieving an ACR50 ResponseBinary EndpointRisk difference+11.0 pts (1.3 to 20.7)149 per arm

Percentage of Participants Achieving Disease Activity Score 28 (DAS28) Remission (DAS28 < 2.6)

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ocrelizumab 400mgOcrelizumab 200mg - Cycle 1-5.47-2.580.303.196.078.96risk difference (percentage points) vs control (95% CI)

Change in DAS28 From Baseline

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Ocrelizumab 400mgOcrelizumab 200mg - Cycle 1-1.42-1.11-0.81-0.50-0.200.11mean difference vs control (95% CI)

Percentage of Participants Achieving an ACR50 Response

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Ocrelizumab 400mgOcrelizumab 200mg - Cycle 1-2.645.0113202836risk difference (percentage points) vs control (95% CI)

The secondary outcomes give additional views of response and disease activity at Week 24. The posted numerical results include DAS28 remission, change in DAS28 from baseline, and ACR50 response. In broad terms, the response percentages and mean DAS28 changes show a pattern in which the ocrelizumab groups have higher response proportions or more negative mean change estimates than placebo. These measures complement the primary ACR20 endpoint because they use different thresholds or summarize change on a scale.

They do not independently confirm the primary result. DAS28 remission is a stricter categorical threshold than a change score, while ACR50 requires a greater response threshold than ACR20. Change in DAS28 preserves more information about the magnitude of score change but represents a different outcome. Differences among these measures are not inherently contradictory; each captures a distinct feature of the observed results.

The registry also lists outcomes including EULAR response rates, ACR70 response, and changes in individual ACR core-set parameters, including C-reactive protein concentration and erythrocyte sedimentation rate. Detailed numerical results for outcomes beyond those summarized in the posted results are not reported in the registry record. The listed outcome names alone do not establish their direction or size.

The secondary comparisons are unadjusted. When multiple outcomes and treatment comparisons are examined, the chance of seeing an apparently notable result by chance can increase. Without a reported multiplicity procedure, these p values and intervals should be treated as exploratory rather than as a collection of confirmatory tests. The endpoint hierarchy and analysis plan are not reported in the registry record. The secondary results can help describe consistency and context, but they carry less evidential weight than a prespecified primary analysis interpreted under a known analysis plan.

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

9. Statistical Interpretation

Clinical Biostats interpretation

At Week 24, the posted ACR20 response was 28.1% in the placebo group, 37.6% in the ocrelizumab 400 mg group, and 52.7% in the ocrelizumab 200 mg Cycle 1 group. The group-specific 95% confidence intervals are 17.1 to 39.1, 28.8 to 46.4, and 44.1 to 61.2, respectively. These are descriptive estimates for the original randomized groups, not results from the later treatment assignments.

For ocrelizumab 400 mg compared with placebo, the posted unadjusted risk difference is 0.095, with a 95% confidence interval from -0.046 to 0.236 and an unadjusted p value of 0.199. The interval includes zero, so this estimate is compatible with a range that includes no difference as well as differences in either direction. Its width also shows that the registry estimate is not precise enough to pin down a narrow range of possible group differences.

For ocrelizumab 200 mg in Cycle 1 compared with placebo, the unadjusted risk difference is 0.245, with a 95% confidence interval from 0.106 to 0.385 and an unadjusted p value of 0.001. This interval lies above zero. It indicates that the posted estimate is more consistent with a positive difference than with no difference under this unadjusted comparison. The interval remains broad, so the size of the difference is not estimated with high precision.

These numerical comparisons do not establish a definitive treatment effect. The registry record does not report the sponsor's detailed statistical analysis, a multiplicity adjustment, or a full analysis plan. The p values shown are unadjusted comparisons derived from posted summary statistics, and the two ocrelizumab comparisons are not presented as a single adjusted testing procedure. The trial's status is terminated, but the reason is not reported in the registry record. Readers should therefore distinguish the posted endpoint estimates from unreported protocol decisions and analyses.

The posted results describe response proportions at one endpoint and time point. They do not, on their own, summarize response durability, the full pattern of individual symptoms, or outcomes after the later treatment assignments. They should be read alongside the confidence intervals, the secondary outcomes, and the limitations in the registry record rather than as a complete account of the trial.

10. Statistical Methods Explained

The registry describes a randomized, double-blind, parallel-group study. Randomization assigns participants to treatment groups by chance, which is intended to make the groups comparable at the start on average. Double blinding means that participants and investigators were masked, as stated in the record; details of who else was masked and how masking was maintained are not reported in the registry record. A parallel-group design compares groups assigned to different regimens over the same study period.

What does the primary response measure?

ACR20 is a binary endpoint. Each participant is classified according to whether the response criteria are met at Week 24. The posted percentages summarize the share of participants classified as responders in each original randomization group. A percentage is a group summary: it does not reveal the response profile of each participant, nor which individual components of the composite were most responsible for meeting the threshold.

The endpoint is defined using joint counts and a set of additional disease activity, pain, function, and inflammation measures. Its threshold helps make the outcome clinically interpretable as a response category. However, any threshold discards information about the degree of improvement above or below that cut point. Other outcomes, such as changes in DAS28 and ACR50, provide complementary perspectives but do not replace the primary endpoint.

How should the risk difference be read?

The risk difference compares the response proportion in an ocrelizumab group with the response proportion in placebo. A value above zero represents a higher observed response proportion in the ocrelizumab group; a value below zero represents a lower observed response proportion. The posted estimates are expressed as proportions rather than percentage points. The confidence interval describes uncertainty around the estimated difference. If it includes zero, the interval includes no difference under this measure; if it lies entirely to one side, it excludes zero for that unadjusted interval.

The registry also includes unadjusted p values for these comparisons. A p value assesses how compatible the observed data are with a specified null model, given the calculation's assumptions. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. The detailed statistical plan and any sponsor-adjusted analyses are not reported in the registry record. The comparisons are unadjusted calculations from the posted summary statistics.

What do the confidence intervals add?

A confidence interval gives a range of values compatible with the data under the method used to calculate it. It communicates estimation uncertainty, which a point estimate alone cannot show. Wider intervals indicate less precision than narrower intervals. For binary endpoints, the group percentages and the confidence interval for a group difference answer related but distinct questions: the first describes each group's response estimate, while the latter estimates the contrast between groups.

Confidence intervals do not incorporate every source of uncertainty. In particular, they do not automatically account for multiple endpoints or comparisons, missing outcome data, or departures from the model used to calculate them. Those issues require details from the analysis plan and the underlying data. The record does not describe a multiplicity procedure or the missing-data approach.

What is the role of the reported analysis population?

The primary population is identified as ITT based on original randomization. An intention-to-treat approach generally retains participants in the groups to which they were initially assigned, preserving the randomized comparison. The registry's population label does not explain exactly how participants without a Week 24 assessment were handled, whether imputation was used, or whether all randomized participants contributed to each posted estimate. Those details are not reported in the registry record.

The Week 24 primary results are attached to the original Cycle 1 groups. After the placebo-controlled period, the study summary describes re-randomization for some participants and further ocrelizumab dosing. Later arm labels therefore refer to subsequent treatment sequences, not independent original randomized groups for the primary endpoint. This distinction matters when reading safety and follow-up summaries, where the listed groups include those later sequences.

How should the planning illustrations be interpreted?

The sample-size illustrations use the observed effect as a starting point and show planning scenarios for detecting the full observed effect or a stated fraction of it. They assume a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The figures are participants per arm for these non-time-to-event outcomes. The trial's original sample-size justification and design assumptions are not reported in the registry record.

These illustrations are distinct from the trial's actual analysis. They do not establish the trial's power after completion, and the trial should not be described as having observed power calculated from its results. The planning values change with the assumed effect size and are intended to show how design requirements depend on the effect researchers want to detect. A smaller target effect generally requires more participants to distinguish it from random variation under the stated assumptions.

The registry record lists no reported analyses in the secondary outcome entries. That absence should not be filled in by assuming a model, adjustment, or analysis population beyond what is explicitly stated. The statistical method for the trial's original sponsor analyses is not reported in the registry record.

11. Confidence Intervals and Precision

The primary endpoint table presents both group-specific estimates and comparisons with placebo. The 95% confidence intervals around the group response percentages show uncertainty in each response estimate. The intervals for placebo, ocrelizumab 400 mg, and ocrelizumab 200 mg Cycle 1 are 17.1 to 39.1, 28.8 to 46.4, and 44.1 to 61.2. They give a sense of the range of values compatible with the observed data under the interval method.

For the risk difference, the ocrelizumab 400 mg comparison has a 95% confidence interval from -0.046 to 0.236. This crosses zero and spans values on both sides of no difference. The ocrelizumab 200 mg Cycle 1 comparison has an interval from 0.106 to 0.385, which does not include zero. Both intervals have meaningful width, so the point estimates should not be read as exact values for the underlying group contrast.

A confidence interval is not a guarantee that the true value lies within the displayed bounds, nor is it a probability statement about a particular treatment effect. Its interpretation depends on the statistical procedure and assumptions. In repeated use under those assumptions, intervals constructed in this way have their stated coverage property. The registry does not report full details of the sponsor's interval calculation.

The posted estimates also have limitations that intervals cannot repair. The record does not report the handling of missing Week 24 data, adjustments for multiple comparisons, or a complete sponsor analysis plan. The intervals describe statistical uncertainty from the posted calculations, not these broader design and analysis uncertainties. Precision should therefore be considered together with the registry's reporting gaps.

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 effect385514
75% of the observed effect671898
50% of the observed effect1,4801,980
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect5001,0002,0005,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, pooled-variance normal approximation for two proportions. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: Ocrelizumab 400mg.

The sample-size table and curve are planning illustrations based on the observed effect, not a report of the trial's original design calculation. For these outcomes, the figures are participants per arm. The registry's planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation; each scenario uses the stated fraction of the observed effect as the effect to detect. The original trial sample-size justification and assumptions are not reported in the registry record.

The 80% power column describes the number of participants per arm that the illustration estimates would be needed to have an 80% chance of detecting the assumed effect under those planning conditions, if the effect and assumptions were correct. The 90% column expresses the analogous planning target with a higher chance of detection. These are prospective design concepts: they describe how a future study might be planned, not what the completed trial achieved.

Rows showing 100%, 75%, or 50% of the observed effect represent different assumed effect sizes for planning. The smaller the effect researchers want to detect, the more participants the illustration generally requires. The sample sizes are not a claim that these effects are true, and the calculations are not observed power. The curve should be read as a visual representation of the same planning relationship, not as additional evidence about the trial outcome.

These calculations use equal allocation even though the brief study summary describes a planned 2:2:1 allocation. They are therefore illustrative rather than a reconstruction of the original design. No justification for the actual allocation or original enrollment target is 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 = 0.281; treatment proportion p1 = 0.376; average p̄ = 0.329.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6643 = 1.3020.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6609 = 0.5562.
  4. n = (1.3020 + 0.5562)2 / (0.0948)2 = 384.1, rounded up to 385 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 <- 0.28125                          # control proportion
p1 <- 0.376068376068376                          # 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(673920)
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 = 385 (80% power), 514 (90% power)
 75% of observed effect: n per arm = 671 (80% power), 898 (90% power)
 50% of observed effect: n per arm = 1,480 (80% power), 1,980 (90% power)
power.prop.test: 384.1 
Simulated power at n = 385 per arm: 0.802 (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. Multiplicity, Missing Data and Analysis Populations

The registry record lists one primary endpoint and multiple secondary outcomes. It does not report how the statistical plan controlled the risk of false-positive findings from examining multiple endpoints, treatment comparisons, or analyses. No multiplicity adjustment is shown in the posted comparisons. The unadjusted p values should therefore not be interpreted as though they were part of a reported family-wise testing procedure, and the nominal results do not by themselves establish confirmatory evidence across outcomes.

The record also does not report whether there were interim analyses, stopping rules, or planned adaptations. The study status is terminated, but the reason and the decision process behind termination are not reported. It would be inappropriate to infer that termination followed a particular efficacy, safety, or operational rule from the status alone.

The primary population is labeled ITT based on original randomization, but the registry does not explain how missing Week 24 outcomes were handled. It does not state whether missing values were imputed, whether a particular nonresponder rule was used, or how many participants lacked an endpoint assessment. The group denominators in the primary outcome table are visible, but they do not supply a complete account of missingness or participant flow.

The record does not provide a detailed statistical analysis plan, including model specifications, covariate adjustment, sensitivity analyses, or the sponsor's full inferential procedure. The comparisons are unadjusted calculations from posted summary statistics. The registry reports no analysis entries for the listed secondary outcomes. These gaps constrain interpretation: the estimates can be described as posted, but their relation to any planned confirmatory analysis cannot be established from the registry record.

15. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Placebo5647.8%
Ocrelizumab 400mg31172.6%
Ocrelizumab 200mg21311.5%
Ocrelizumab 200mg/ Ocrelizumab 200mg5618.2%
Ocrelizumab 200mg/ Ocrelizumab 400mg5618.2%
Ocrelizumab 400mg/ Ocrelizumab 400mg101099.2%
Placebo/ Ocrelizumab 200mg32910.3%
Placebo/ Ocrelizumab 400mg0280.0%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo7.8%Ocrelizumab 400mg2.6%Ocrelizumab 200mg1.5%Ocrelizumab 200mg/ Ocrelizuma…8.2%Ocrelizumab 200mg/ Ocrelizuma…8.2%Ocrelizumab 400mg/ Ocrelizuma…9.2%Placebo/ Ocrelizumab 200mg10.3%Placebo/ Ocrelizumab 400mg0.0%% of participants with at least one serious adverse event

Deaths

ArmDeaths (participants affected of at risk)
Placebo0 of 64
Ocrelizumab 400mg0 of 117
Ocrelizumab 200mg0 of 131
Ocrelizumab 200mg/ Ocrelizumab 200mg0 of 61
Ocrelizumab 200mg/ Ocrelizumab 400mg0 of 61
Ocrelizumab 400mg/ Ocrelizumab 400mg1 of 109

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0.05% reporting threshold.

ArmParticipants affected of at risk
Placebo32 of 64
Ocrelizumab 400mg59 of 117
Ocrelizumab 200mg80 of 131
Ocrelizumab 200mg/ Ocrelizumab 200mg46 of 61
Ocrelizumab 200mg/ Ocrelizumab 400mg49 of 61
Ocrelizumab 400mg/ Ocrelizumab 400mg86 of 109

Most frequent serious adverse event terms

Event termOrgan systemPlaceboOcrelizumab 400mgOcrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 400mgOcrelizumab 400mg/ Ocrelizumab 400mg
BRONCHIECTASISInfections and infestations2 of 643 of 1171 of 1315 of 615 of 619 of 109
URINARY TRACT INFECTIONInfections and infestations0 of 640 of 1171 of 1311 of 610 of 610 of 109
PROSTATE INFECTIONInfections and infestations0 of 641 of 1170 of 1310 of 610 of 611 of 109
INFLUENZA LIKE ILLNESSGeneral disorders0 of 640 of 1171 of 1310 of 611 of 610 of 109
DEPRESSIONPsychiatric disorders0 of 640 of 1171 of 1311 of 610 of 610 of 109
MYCOBACTERIUM ABSCESSUS INFECTIONInfections and infestations0 of 641 of 1170 of 1310 of 610 of 610 of 109
COLITIS ULCERATIVEGastrointestinal disorders1 of 640 of 1170 of 1310 of 610 of 610 of 109
DYSPNOEARespiratory, thoracic and mediastinal disorders1 of 640 of 1170 of 1310 of 610 of 610 of 109
CELLULITISInfections and infestations1 of 640 of 1170 of 1310 of 610 of 610 of 109
PNEUMONIAInfections and infestations0 of 641 of 1170 of 1310 of 610 of 610 of 109

Most frequent non-serious adverse event terms

Event termOrgan systemPlaceboOcrelizumab 400mgOcrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 200mgOcrelizumab 200mg/ Ocrelizumab 400mgOcrelizumab 400mg/ Ocrelizumab 400mg
INFUSION RELATED REACTIONGeneral disorders7 of 6425 of 11728 of 13119 of 6117 of 6128 of 109
UPPER RESPIRATORY TRACT INFECTIONInfections and infestations5 of 6412 of 11716 of 1315 of 6114 of 6114 of 109
HEADACHENervous system disorders4 of 645 of 1177 of 1315 of 615 of 616 of 109
DIARRHOEAGastrointestinal disorders3 of 644 of 11710 of 1316 of 612 of 616 of 109
URINARY TRACT INFECTIONInfections and infestations5 of 643 of 1177 of 1316 of 611 of 614 of 109
NAUSEAGastrointestinal disorders4 of 646 of 1173 of 1313 of 612 of 617 of 109
HYPERTENSIONVascular disorders0 of 640 of 1177 of 1314 of 615 of 613 of 109
BRONCHITISInfections and infestations0 of 640 of 1170 of 1314 of 617 of 617 of 109
FATIGUEGeneral disorders4 of 644 of 1172 of 1311 of 612 of 615 of 109
NASOPHARYNGITISInfections and infestations0 of 640 of 1170 of 1312 of 612 of 615 of 109

Serious events with the highest arm-level rate: bronchiectasis (10.3%), mycobacterium abscessus infection (3.4%), dyspnoea (3.4%), uterine leiomyoma (3.4%), urinary tract infection (1.6%).

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 summary lists the number at risk and the number affected by serious adverse events and other adverse events for each treatment sequence, along with deaths. These are counts, not adjusted comparisons. For the original Cycle 1 groups, the serious adverse event counts are 5 of 64 for placebo, 3 of 117 for ocrelizumab 400 mg, and 2 of 131 for ocrelizumab 200 mg. The corresponding counts for other adverse events are 32 of 64, 59 of 117, and 80 of 131. The registry also lists later sequence groups, which should be distinguished from the original Week 24 endpoint groups.

The safety table reports one death in the ocrelizumab 400 mg/ocrelizumab 400 mg sequence and zero in the other listed groups. It also lists serious adverse event terms and associated percentages, including bronchiectasis, Mycobacterium abscessus infection, dyspnoea, uterine leiomyoma, urinary tract infection, and influenza-like illness. The registry summary does not establish that a treatment caused an event. It also does not provide a detailed exposure-adjusted analysis or a complete account of event timing and duration in the information.

Counts should be read in relation to their group denominators and the treatment sequence labels. They do not provide, by themselves, a basis for comparing risk across groups when exposure and follow-up details are not available. The posted figures are descriptive and should not be interpreted as a safety conclusion.

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

The posted Week 24 results show different observed ACR20 response proportions across the original randomized groups. The unadjusted comparison for ocrelizumab 200 mg Cycle 1 has a risk-difference interval above zero, while the interval for ocrelizumab 400 mg includes zero. The confidence intervals communicate the uncertainty around these estimates; neither the percentages nor the p values alone describe the full evidential picture.

These results do not mean that every participant in a group had the same experience. ACR20 is a threshold-based composite: it records whether the response definition was met, not the detailed improvement in each component. The secondary results offer related but distinct summaries, and the registry record does not report numerical results for every listed outcome.

The findings also do not settle questions about long-term outcomes or later treatment schedules. The primary endpoint is at Week 24, before the subsequent assignments described in the study summary. The registry status is terminated, but the reason for termination is not reported. The record does not give enough information to infer why the study ended or how termination affected follow-up.

The posted comparisons are unadjusted calculations, and the registry record does not report a multiplicity procedure, detailed missing-data handling, or the sponsor's complete statistical plan. Those omissions matter when assessing how much weight to place on multiple endpoint results and how representative the analyzed participants are of all randomized participants. The results should therefore be understood as estimates from the posted registry information, not as a complete substitute for a full analysis report.

Nothing in these statistical summaries alone establishes a clinical recommendation, a definitive causal conclusion, or an individual outcome. They show the reported group-level response and safety counts, together with uncertainty and reporting limitations. Interpretation requires attention to the endpoint definition, the original randomization groups, the confidence intervals, and the unreported analysis details.

17. Why This Trial Matters Statistically

This trial illustrates why the contrast between an endpoint estimate and its uncertainty matters. A response percentage gives a concise summary, but the risk difference and its confidence interval address the comparison directly. For one ocrelizumab regimen, the posted interval includes zero; for the other, it lies above zero. The distinction is visible in the interval, not merely in the ordering of the group percentages.

It also demonstrates the role of endpoint choice. ACR20, ACR50, DAS28 remission, and change in DAS28 capture related but nonidentical aspects of response. A threshold endpoint is easy to express as a proportion, while a continuous change score describes average movement on a scale. Agreement in broad direction can be informative, but multiple endpoints do not become independent confirmation simply because they point in a similar direction.

The trial's later re-randomization makes it important to keep treatment sequence and original allocation separate. Week 24 efficacy comparisons use the original groups; later safety groups include subsequent treatment sequences. Reading all labels as though they represented interchangeable arms would blur the study phases and the populations being summarized.

Finally, the registry shows how reporting gaps shape statistical interpretation. The primary population is named, and several estimates are posted, but detailed analysis methods, multiplicity handling, missing-data procedures, and the termination reason are not reported. Statistical literacy includes recognizing both what the numerical results show and what a registry summary cannot establish.

18. Limitations

The trial is listed as terminated, but the reason for termination is not reported in the registry record. The record does not explain whether termination affected planned recruitment, treatment, or follow-up, so its implications for the results cannot be determined from the status alone.

The primary endpoint is reported at Week 24, while the brief summary describes later treatment and re-randomization. The primary results are tied to original randomization and do not describe outcomes for all later treatment sequences. The safety summary includes those later sequence groups, but the details needed to compare exposure periods and follow-up are not reported.

The record gives an ITT population label but does not describe missing Week 24 data, participant flow by outcome, or the procedure used for incomplete assessments. The analysis method and any covariate adjustments are also not reported. This makes it difficult to assess how closely the posted estimates follow the intended analysis plan.

The listed secondary outcomes are numerous, yet multiplicity control is not reported. The displayed p values are unadjusted, and secondary results should not be treated as independent confirmation of the primary comparison. Numerical results are not available in the registry record for every secondary outcome listed.

Finally, the safety counts are descriptive. The registry summary does not provide detailed timing, duration, exposure-adjusted rates, or causal attribution for events. The trial's sample-size justification is not reported; planning illustrations based on observed effects do not resolve that gap or reconstruct the original design rationale.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

Continue through the Clinical Biostats statistical pathway

Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.

22. Record Summary

This phase 3 study randomized 314 participants with active rheumatoid arthritis and an inadequate response to methotrexate. It compared Cycle 1 ocrelizumab regimens with placebo, alongside stable-dose methotrexate, in a double-blind, parallel-group design. The primary endpoint was Week 24 ACR20 response in the ITT population based on original randomization.

The registry posts response estimates and unadjusted comparisons for the two ocrelizumab groups versus placebo. The 200 mg Cycle 1 comparison has a risk-difference confidence interval above zero; the 400 mg comparison's interval includes zero. Secondary outcomes provide additional, nonidentical measures, and the record includes descriptive adverse-event counts.

The study is listed as terminated. The reason, detailed statistical plan, multiplicity procedure, and missing-data handling are not reported in the registry record. The posted results should be interpreted with those limitations in view.

Clinical Biostats