This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for A Study to Evaluate the Effects of Ocrelizumab on Immune Responses In Participants With Relapsing Forms of Multiple Sclerosis (NCT02545868), a randomized phase 3 study. The primary outcome is Percentage of Participants With Positive Response to TT Vaccine Measured 8 Weeks After TT Vaccine.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02545868 |
| Phase | Phase 3 |
| Condition | Multiple Sclerosis, Relapsing-Remitting |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 102 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Hoffmann-La Roche |
| Results posted | Yes |
2. Clinical Question
Population
Participants with relapsing forms of multiple sclerosis were eligible for this study. The primary analysis population was the OC population, defined in the registry as randomized participants who completed the ISP. The registry record does not report the meaning of ISP in the outcome description.
Intervention
Group A received ocrelizumab, abbreviated OCR, as dual infusions of 300 mg on Day 1 and Day 15, followed by an immunization course. The listed vaccines and immunogens included a tetanus toxoid-containing adsorbed vaccine, pneumococcal vaccines, influenza vaccine, and repeated keyhole limpet hemocyanin administration. The registry description of the immunization course is incomplete.
Comparator
Group B received immunizations from Day 1 until Week 12 of the immunization period, with optional OCR in an extension. The registry lists tetanus toxoid-containing vaccine, 23-valent pneumococcal polysaccharide vaccine, influenza vaccine, and repeated keyhole limpet hemocyanin administration for this group.
Primary question
What proportion of participants had a positive tetanus vaccine response at 8 weeks, comparing Group A, which received OCR with vaccines, with Group B, which received vaccines during the immunization period? The outcome used different response definitions depending on participants’ pre-vaccination tetanus antibody titers.
The study addresses an immune-response question, not a clinical disease outcome. A positive response was defined using antibody measurements after vaccination: for participants with low pre-vaccination tetanus antibody titers, the criterion was a specified post-vaccination titer; for participants starting at or above the stated threshold, the criterion was a specified increase relative to baseline. The outcome therefore represents the proportion meeting the registry’s antibody-based definition, rather than a direct measure of protection from infection or of a clinical benefit.
3. Trial Design
The registry describes a Phase IIIB, multicenter, randomized, parallel-group, open-label study. It lists 102 participants enrolled and identifies the study as completed. The listed condition is relapsing-remitting multiple sclerosis, while the official title and study description refer more broadly to relapsing forms of multiple sclerosis.
Participants were assigned to Group A, receiving OCR with vaccines, or Group B, receiving vaccines during the immunization period. Group A was described as receiving OCR infusions of 300 mg on Day 1 and Day 15, then an immunization course. Group B was described as receiving immunizations from Day 1 until Week 12, with optional OCR in an extension. The registry’s Group A description ends mid-sentence, so the remainder of the course and its timing are not reported in the registry record.
Random allocation can help balance participant characteristics between groups on average, but the record does not report the allocation ratio or sequence-generation and concealment details. Open-label means masking was listed as none. The record does not report whether outcome laboratory personnel or other assessors were masked. The groups also differ in their OCR exposure during the stated study period, so the comparison is between the recorded treatment strategies, not a vaccine-versus-no-vaccine comparison.
The study ran from 2015-10-27 to the listed primary completion date of 2017-02-14. The record lists Hoffmann-La Roche as sponsor. It does not report the trial’s original sample-size justification, the planned enrollment rationale, or the full analysis protocol. The primary outcome was assessed at 8 weeks after TT vaccine, and several secondary outcomes were assessed at other stated time points, including 4 weeks after vaccination.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Before assignment: A total of 122 participants were screened of which 102 participants were randomized.
Overall Study
| Stage | Group A1 | Group A2 | Group B |
|---|---|---|---|
| STARTED | 33 | 35 | 34 |
| COMPLETED | 2 | 1 | 0 |
| NOT COMPLETED | 31 | 34 | 34 |
Reasons for not completing this period:
| Reason | Group A1 | Group A2 | Group B |
|---|---|---|---|
| Lack of Efficacy | 1 | 1 | 0 |
| Lost to Follow-up | 1 | 5 | 1 |
| Non-compliance | 1 | 1 | 1 |
| Treatment change | 21 | 19 | 22 |
| Physician Decision | 1 | 1 | 1 |
| Withdrawal by Subject | 6 | 7 | 9 |
Analysis population for the primary outcome, as defined in the registry: OC population included all randomized participants who completed the ISP.
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: Observed Cases (OC) Population was defined as all randomized participants who completed the ISP.
| Characteristic | Unit | Group A1 | Group A2 | Group B | Total |
|---|---|---|---|---|---|
| Participants analysed | 33 | 35 | 34 | 102 | |
| Age, Continuous | years | 40.1 (SD 8.0) | 39.3 (SD 9.7) | 41.4 (SD 7.9) | 40.3 (SD 8.6) |
| Sex: Female, Male: Female | Participants | 21 | 24 | 27 | 72 |
| Sex: Female, Male: Male | Participants | 12 | 11 | 7 | 30 |
| Race/Ethnicity, Customized: Ethnicity – Hispanic or Latino | Participants | 2 | 2 | 2 | 6 |
| Race/Ethnicity, Customized: Ethnicity – Not Hispanic or Latino | Participants | 29 | 30 | 32 | 91 |
| Race/Ethnicity, Customized: Ethnicity – Not reported | Participants | 1 | 1 | 0 | 2 |
| Race/Ethnicity, Customized: Ethnicity – Unknown | Participants | 1 | 2 | 0 | 3 |
| Race/Ethnicity, Customized: Race – Asian | Participants | 1 | 0 | 2 | 3 |
| Race/Ethnicity, Customized: Race – Black or African American | Participants | 0 | 3 | 2 | 5 |
| Race/Ethnicity, Customized: Race – White | Participants | 32 | 32 | 30 | 94 |
6. Primary Endpoint
The registry lists the primary outcome as Percentage of Participants With Positive Response to TT Vaccine Measured 8 Weeks After TT Vaccine, measured over 8 weeks after TT vaccine.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | percentage of participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint is the percentage of participants with a positive response to TT vaccine measured 8 weeks after vaccination. TT refers to tetanus toxoid. The registry defines response using participants’ pre-vaccination tetanus antibody titers: for those with a pre-vaccination titer < 0.1 IU/mL, a post-vaccination titer >= 0.2 IU/mL met the criterion; for those with a pre-vaccination titer >= 0.1 IU/mL, the criterion was at least a 4-fold increase from pre-vaccination levels.
This binary endpoint reduces each participant’s antibody measurements to whether the specified response criterion was met. The reported percentage is the share of the analysis population classified as responders under that definition. The endpoint is used to characterize immune response to vaccination, and the threshold-based definition makes the response rule explicit for different starting antibody levels.
That design also limits what the endpoint can establish. It does not describe the size or persistence of antibody changes for each participant, and a positive antibody response is not itself a clinical event such as infection. The registry does not report the scientific rationale for selecting the thresholds, further details on laboratory measurement, or the handling of participants whose measurements were unavailable. Those details are not reported in the registry record.
7. Results Posted in the Registry
- Group B: 55.9% (19/34) versus 23.5% (16/68) on control; risk difference 32.4 percentage points (95% CI 12.9 to 51.9), risk ratio 2.38 (1.41–4.00); unadjusted two-proportion z-test p = 0.001.
Risk difference: Group B
95% CI: 12.9 to 51.9 percentage points
Recalculated from the posted summary statistics
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 outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Percentage of Participants With Positive Response to TT Vaccine Measured 4 Weeks After TT Vaccine | Binary Endpoint | Risk difference | +38.2 pts (19.0 to 57.4) | 26 per arm |
| Percentage of Participants With Tetanus Antibody Titer >/=0.2 IU/mL or 2-Fold Increase in Tetanus Antibody Titers | Binary Endpoint | Risk difference | +47.1 pts (31.1 to 63.0) | 15 per arm |
| Percentage of Participants With Positive Response Against >/=2 Pneumococcal Serotypes | Binary Endpoint | Risk difference | +13.2 pts (5.2 to 21.3) | n/a |
Percentage of Participants With Positive Response to TT Vaccine Measured 4 Weeks After TT Vaccine
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Group B: 61.8% (21/34) versus 23.5% (16/68) on control; risk difference 38.2 percentage points (95% CI 19.0 to 57.4), risk ratio 2.62 (1.59–4.34); unadjusted two-proportion z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Group B than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Percentage of Participants With Tetanus Antibody Titer >/=0.2 IU/mL or 2-Fold Increase in Tetanus Antibody Titers
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Group B: 88.2% (30/34) versus 41.2% (28/68) on control; risk difference 47.1 percentage points (95% CI 31.1 to 63.0), risk ratio 2.14 (1.57–2.92); unadjusted two-proportion z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Group B than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Percentage of Participants With Positive Response Against >/=2 Pneumococcal Serotypes
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Group B: 100.0% (34/34) versus 86.8% (59/68) on control; risk difference 13.2 percentage points (95% CI 5.2 to 21.3), risk ratio 1.15 (1.05–1.26); unadjusted two-proportion z-test p = 0.026.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Group B than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary outcomes cover additional measures of tetanus antibody response, keyhole limpet hemocyanin antibody levels, and responses to pneumococcal serotypes. The posted results include both binary response outcomes and antibody-level measures, assessed at specified post-vaccination times. This wider set of outcomes provides context about immune responses beyond the primary TT response at 8 weeks.
Across the posted binary secondary comparisons, the listed response outcomes generally show a higher observed response proportion in Group B than Group A. The registry also reports an outcome for response against at least two pneumococcal serotypes; that result follows the same broad direction. These outcomes are related to the primary result because they concern immune responses after vaccination, but they are not interchangeable endpoints. They involve different vaccines or response definitions, and some use a different assessment time.
The secondary findings can add descriptive context, but they do not independently establish a single overall conclusion about all immune responses. The registry lists 31 secondary outcomes posted and 32 outcome measures, with numerous analyses. When many outcomes are tested, interpreting each unadjusted result as if it were the only analysis can overstate the strength of evidence. The record does not report a multiplicity strategy, a testing hierarchy, or which secondary outcomes were intended as confirmatory.
For that reason, secondary p-values should be read as unadjusted unless the registry says otherwise; the posted comparisons identify them as unadjusted. Their weight is lower than a prespecified primary result when multiplicity control and analysis priorities are not documented. The secondary results can be considered alongside the primary estimate and its uncertainty, but should not be treated as independent replications of the primary comparison. Further details of the analysis populations and missing-data handling for each secondary endpoint are not reported in the registry record.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Percentage of Participants With Positive Response to TT Vaccine Measured 4 Weeks After TT Vaccine
- Percentage of Participants With Tetanus Antibody Titer >/=0.2 IU/mL or 2-Fold Increase in Tetanus Antibody Titers
- Mean Levels of Anti-Tetanus Antibody
- Mean Levels of Anti-KLH Antibody: Immunoglobulin (Ig) G
- Mean Levels of Anti-KLH Antibody: Ig M
- Percentage of Participants With Positive Response Against Individual Pneumococcal Serotypes in 23-PPV
- Percentage of Participants With Positive Response Against >/=2 Pneumococcal Serotypes
- Percentage of Participants With Positive Response Against >/=12 Pneumococcal Serotypes
9. Statistical Interpretation
For the primary outcome, the registry reports positive responses in 23.9% of Group A and 54.5% of Group B. The posted group sizes are 68 for Group A and 34 for Group B. The registry’s own reported analysis gives a difference of -30.7, with a 95% confidence interval from -50.5 to -10.8. The signed result is consistent with the order of groups in that analysis, Group A followed by Group B: the reported value is negative when the first group’s percentage is lower.
The simple unadjusted re-calculation is expressed in the opposite direction, Group B compared with Group A. It gives a risk difference of 0.324, with a 95% confidence interval from 0.129 to 0.518, and an unadjusted p-value of 0.001. These two presentations use opposite group order, so their signs differ; they describe the same direction of contrast. The sponsor’s own analysis takes precedence over the simple re-calculation. The registry does not report the method behind the sponsor’s analysis beyond describing a normal distribution approximation for the reported estimate and interval.
In plain terms, the posted percentages show a higher observed proportion meeting the TT response definition in Group B than in Group A. The interval for the unadjusted re-calculation is entirely on the positive side of zero in the Group B minus Group A direction. A confidence interval describes a range of values compatible with the data and the statistical method, not a guarantee that the true value lies in that range. The p-value is an unadjusted statistical measure of how inconsistent the observed data are with a no-difference model under its assumptions; it does not measure the size or practical importance of the difference.
The comparison should be interpreted as an immune-response result in the registry’s OC population, not as evidence about clinical outcomes. The analysis population included randomized participants who completed the ISP, which may not be the same as all randomized participants. The registry does not report the number excluded from this analysis, reasons for exclusion, or how missing antibody measurements were handled. That limits assessment of whether the analysis population remained comparable after randomization.
The open-label design is relevant to the conduct of the study, although the primary outcome is based on antibody titers. The registry does not report masking of laboratory personnel or further details about measurement procedures. The posted result is one outcome among many analyses, and the record does not report a multiplicity-adjustment plan. Accordingly, the result is best read alongside the endpoint definition, population, uncertainty interval, and the study’s other reported outcomes, rather than as a stand-alone conclusion about vaccine performance or patient health.
10. Statistical Methods Explained
The primary outcome is binary: each participant either met the registry’s positive-response definition or did not. For a binary outcome, the observed percentage is the number classified as responders relative to the analysis group. The clinical interpretation depends on the response definition, which uses baseline antibody level and the subsequent antibody result. It is not a continuous summary of the full antibody distribution.
What does a risk difference express?
A risk difference subtracts the proportion with the outcome in one group from the proportion in the other. The re-calculation uses Group B compared with Group A, so a positive estimate means the observed responder proportion is higher in Group B. The registry’s reported analysis is ordered Group A then Group B and reports a negative value. A reversal in group order reverses the sign; it does not mean the two estimates point in different directions.
The risk difference is an absolute contrast in proportions, while a relative measure such as a risk ratio expresses one group’s proportion relative to the other. These measures answer different descriptive questions. Neither alone resolves whether an observed contrast is clinically meaningful. In this case, the registry posts a risk difference for the simple re-calculation and also includes relative measures in its comparison data, but the sponsor’s result is the registry’s reported analysis.
How should the p-value be read?
The re-calculated p-value is unadjusted. In general, a p-value measures how unusual data at least as discrepant as those observed would be under a specified null model, assuming the analysis conditions hold. It is not the probability that the null hypothesis is true, and it does not express the probability that the result arose by chance. A small p-value does not establish causation, rule out bias, or quantify the size of an effect. Interpretation also depends on the study design, outcome definition, analysis population, and the number of outcomes examined.
The registry’s reported analysis lists a normal distribution approximation and a 95% confidence interval, but no p-value. The re-calculated p-value comes from a simple unadjusted comparison based on posted summary statistics. It should not be mistaken for the sponsor’s own inferential result or for an adjusted analysis.
What does randomization contribute?
Randomization is intended to make assignment independent of participant characteristics, reducing systematic differences between groups at baseline on average. It does not ensure that groups are identical in a particular trial, and it cannot by itself address exclusions after randomization, missing outcome data, or deviations from assigned treatment. The record does not report enough detail to assess the allocation process or all post-randomization handling.
The analysis population is described as randomized participants who completed the ISP. This is narrower than a statement that every randomized participant was analyzed, and the record does not explain how this completion requirement was applied. If inclusion depends on events after assignment, the analyzed groups can differ from the randomized groups in ways that randomization alone may not protect against. The registry record does not report an intention-to-treat analysis or a comparison with another analysis population.
What can the confidence interval tell readers?
A confidence interval communicates uncertainty around an estimate under the chosen method. Its width reflects both the data and the method’s assumptions. It is not a range containing a known fixed percentage of individual participant outcomes, nor is it a forecast of results in a future trial. A narrower interval generally indicates greater statistical precision for the estimated contrast, while still allowing for sources of bias and measurement limitations that an interval does not capture.
The sponsor-reported interval and the recalculated interval are based on different reported presentations. The sponsor’s analysis is the primary registry result; the recalculation is a simple unadjusted check using posted summary statistics. Because the two results differ in sign convention and may use different procedures, they should not be treated as interchangeable estimates from an identical analysis.
Why does multiplicity matter?
When a study examines multiple endpoints, time points, groups, or response definitions, the chance of finding one apparently unusual result can increase if each is judged separately without adjustment. This is the general statistical issue of multiplicity. The registry lists many outcome measures and analyses, but it does not report a plan for controlling multiplicity, identifying a prespecified hierarchy, or distinguishing confirmatory analyses from exploratory ones. The unadjusted p-values therefore have to be interpreted with that uncertainty in mind.
All statistical methods beyond the information noted in the registry record, including model covariates, missing-data procedures, and any sensitivity analyses, are not reported in the registry record. General statistical explanations do not fill in those details. They describe how these types of estimates are usually interpreted, not what analysis choices were made for this trial.
11. Confidence Intervals and Precision
The sponsor-reported primary estimate is -30.7, with a 95% confidence interval from -50.5 to -10.8, for the registry’s listed group order. The simple unadjusted re-calculation, expressed as Group B compared with Group A, is a risk difference of 0.324 with a 95% confidence interval from 0.129 to 0.518. The opposite signs reflect opposite ordering of the groups. Both intervals exclude zero in their stated direction, but the sponsor-reported analysis remains the registry’s own analysis and takes precedence over the simple re-calculation.
A confidence interval gives a range of estimates compatible with the observed data and the statistical method at the stated confidence level. Its endpoints show uncertainty in the estimated contrast; they do not show the range of individual responses. The width also does not account for all possible uncertainty, such as bias from missing data, outcome measurement, or analysis choices. Those issues are not resolved by a confidence interval.
The posted percentages are 23.9% for Group A and 54.5% for Group B, but the registry does not provide confidence intervals for each group’s percentage in the primary result. The comparison interval addresses the contrast, not the precision of each percentage separately. The analysis population is defined by ISP completion, and details on exclusions and missing measurements are not reported. Consequently, statistical precision in the analyzed sample should be distinguished from certainty about all randomized participants or broader populations.
The re-calculated estimate is unadjusted and based on posted summary statistics. The reported sponsor interval uses a normal distribution approximation; additional details of the sponsor’s analysis are not reported. Intervals calculated under different approaches may differ, so the method and group order matter when reading the values.
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 detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 35 | 46 |
| 75% of the observed effect | 60 | 80 |
| 50% of the observed effect | 129 | 172 |
The planning figures are participants per arm, not total event counts. They are illustrations based on the observed effect, not the trial’s original design calculation. The registry record does not report the original sample-size justification or its design assumptions.
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 to a stated fraction of the observed effect. The entries for 100% of the observed effect use the full observed contrast; the entries for 75% and 50% of the observed effect ask what planning counts would correspond to smaller contrasts. The displayed 80% power column means the planning illustration targets an 80% chance of detecting the specified effect under the assumptions if that effect were the true one. The 90% power column targets a higher chance under the same kind of assumptions.
Smaller effects are harder to distinguish from random variation, so the planning illustrations require more participants per arm as the target effect becomes smaller. The values are not a reconstruction of the study’s enrollment rationale, and they do not establish what the trial was designed to detect. They are not observed power: they are planning illustrations conditional on specified effects and assumptions, rather than a measure of power after seeing the trial results.
The assumptions are simplified. They do not incorporate any unreported design features, adjustments, attrition assumptions, or analysis plans. The registry’s primary analysis population is based on completing the ISP, and the record does not report how the planning illustrations account for exclusions or unavailable outcome measurements. These figures should therefore be read as hypothetical planning aids, not as a description of the trial’s actual design process.
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 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
- Control proportion p0 = 0.235; treatment proportion p1 = 0.559; average p̄ = 0.397.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6920 = 1.3562.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6530 = 0.5496.
- n = (1.3562 + 0.5496)2 / (0.3235)2 = 34.7, rounded up to 35 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 <- 0.235294117647059 # control proportion
p1 <- 0.558823529411765 # 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(2545868)
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 = 35 (80% power), 46 (90% power)
75% of observed effect: n per arm = 60 (80% power), 80 (90% power)
50% of observed effect: n per arm = 129 (80% power), 172 (90% power)
power.prop.test: 34.7
Simulated power at n = 35 per arm: 0.801 (20000 replicates)
The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| not stated | normal distribution approximation -30.7 | -50.5 to -10.8 | not reported |
The registry reports the sponsor’s primary comparison as -30.7, with a 95% confidence interval from -50.5 to -10.8, using a normal distribution approximation. The reported group order is Group A followed by Group B. The negative estimate corresponds to a lower observed positive-response percentage in Group A than in Group B under that ordering.
The simple recalculation uses posted summary statistics and expresses the contrast as Group B compared with Group A. It gives a risk difference of 0.324, with a 95% confidence interval from 0.129 to 0.518 and an unadjusted p-value of 0.001. The sign changes because the group order is reversed. The directions of the two comparisons are consistent once that ordering is taken into account.
The recalculation is not a replacement for the sponsor’s analysis. It is an unadjusted calculation from the posted results, while the record’s sponsor analysis is the official reported result. The registry indicates no discrepancy between them. The details needed to reproduce the sponsor’s analysis fully, including any further model or variance specifications, are not reported in the registry record. The sponsor’s own analysis takes precedence; the recalculation is a transparent secondary check, not an alternative trial conclusion.
15. Multiplicity, Missing Data and Analysis Populations
The registry includes a primary endpoint and a substantial set of secondary outcomes, with multiple analyses. Testing several outcomes or response definitions can increase the chance that at least one result appears statistically notable when each test is considered separately. Statistical approaches such as a prespecified hierarchy or adjustment for multiple comparisons can address that issue, but the registry record does not report whether such an approach was planned or used. The secondary comparison p-values are unadjusted.
The record does not report whether interim analyses were planned or conducted, whether any stopping rules applied, or how the primary outcome was designated in the analysis plan beyond its registry listing. These details should not be inferred from the number of posted outcomes. Nor does the record report a statistical analysis plan that would establish which analyses were prespecified.
The primary analysis population is described as randomized participants who completed the ISP. The registry does not report the number of randomized participants who did not meet this population definition, reasons for non-completion, or whether these participants differed between groups. It also does not report how missing antibody titers were handled, whether any imputation was used, or whether sensitivity analyses assessed the impact of missing data. Missingness could affect the estimated response proportions if availability of measurements is related to response or group assignment; the record does not provide information to assess that possibility.
The registry labels the study randomized, but the outcome population is defined by completion rather than simply by random assignment. It does not report an intention-to-treat analysis, a per-protocol definition, or results comparing alternative populations. Further information on protocol deviations, adherence, and post-randomization exclusions is not reported in the registry record. These omissions limit assessment of how closely the analyzed groups preserve the advantages of randomization.
Consequently, the primary and secondary estimates describe the recorded analysis populations and methods. The available record does not support assumptions about multiplicity control, interim monitoring, missing-data procedures, or a broader analysis strategy beyond what it states explicitly.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Group A1 | 5 | 33 | 15.2% |
| Group A2 | 5 | 35 | 14.3% |
| Group B | 6 | 34 | 17.6% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Group A1 | 0 of 33 |
| Group A2 | 0 of 35 |
| Group B | 0 of 34 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Group A1 | 31 of 33 |
| Group A2 | 34 of 35 |
| Group B | 32 of 34 |
Most frequent serious adverse event terms
| Event term | Organ system | Group A1 | Group A2 | Group B |
|---|---|---|---|---|
| SEPSIS | Infections and infestations | 0 of 33 | 1 of 35 | 2 of 34 |
| PNEUMONIA | Infections and infestations | 0 of 33 | 2 of 35 | 0 of 34 |
| VENTRICULAR TACHYCARDIA | Cardiac disorders | 0 of 33 | 0 of 35 | 1 of 34 |
| ANAPHYLACTIC REACTION | Immune system disorders | 1 of 33 | 0 of 35 | 0 of 34 |
| APPENDICITIS | Infections and infestations | 1 of 33 | 0 of 35 | 0 of 34 |
| GASTROENTERITIS | Infections and infestations | 0 of 33 | 0 of 35 | 1 of 34 |
| HERPES ZOSTER DISSEMINATED | Infections and infestations | 0 of 33 | 1 of 35 | 0 of 34 |
| FALL | Injury, poisoning and procedural complications | 0 of 33 | 0 of 35 | 1 of 34 |
| HEAD INJURY | Injury, poisoning and procedural complications | 0 of 33 | 0 of 35 | 1 of 34 |
| OVERDOSE | Injury, poisoning and procedural complications | 0 of 33 | 1 of 35 | 0 of 34 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Group A1 | Group A2 | Group B |
|---|---|---|---|---|
| INFUSION RELATED REACTION | Injury, poisoning and procedural complications | 21 of 33 | 19 of 35 | 16 of 34 |
| UPPER RESPIRATORY TRACT INFECTION | Infections and infestations | 18 of 33 | 11 of 35 | 11 of 34 |
| FATIGUE | General disorders | 16 of 33 | 10 of 35 | 7 of 34 |
| URINARY TRACT INFECTION | Infections and infestations | 13 of 33 | 9 of 35 | 9 of 34 |
| HEADACHE | Nervous system disorders | 9 of 33 | 12 of 35 | 6 of 34 |
| NASOPHARYNGITIS | Infections and infestations | 8 of 33 | 11 of 35 | 7 of 34 |
| ARTHRALGIA | Musculoskeletal and connective tissue disorders | 8 of 33 | 7 of 35 | 9 of 34 |
| MULTIPLE SCLEROSIS RELAPSE | Nervous system disorders | 10 of 33 | 5 of 35 | 7 of 34 |
| NAUSEA | Gastrointestinal disorders | 6 of 33 | 8 of 35 | 5 of 34 |
| SINUSITIS | Infections and infestations | 2 of 33 | 8 of 35 | 9 of 34 |
Serious events with the highest arm-level rate: sepsis (5.9%), pneumonia (5.7%), anaphylactic reaction (3.0%), appendicitis (3.0%), carotid artery aneurysm (3.0%).
The registry reports serious adverse events by group. The counts shown are 5 of 33 at risk in Group A1, 5 of 35 in Group A2, and 6 of 34 in Group B. Deaths are reported as 0 in each group. The record also lists other adverse events affecting 31 of 33 in Group A1, 34 of 35 in Group A2, and 32 of 34 in Group B.
These figures describe event counts within the listed at-risk groups. They are not a comparison adjusted for differences in follow-up, baseline characteristics, or exposure time; such details are not reported in the registry record. Group A is divided into A1 and A2 for the safety reporting, while the primary efficacy comparison uses Group A (A1 + A2) as a combined group. The record does not explain the safety subgroup definitions in the details given.
The registry lists sepsis, pneumonia, anaphylactic reaction, appendicitis, carotid artery aneurysm, and syncope among the serious adverse event terms, with percentages attached to the terms. The safety figures should be read as descriptive reports from the registry, not as proof that a particular event was caused by a study intervention or as a complete assessment of comparative risk. The record does not provide the event narratives or further causality assessment in the available information.
17. What the Result Does, and Does Not, Mean
The posted primary results describe a difference in the proportion of participants meeting a defined tetanus antibody response criterion: the reported proportion was 23.9% in Group A and 54.5% in Group B. The sponsor’s analysis reports a negative contrast in Group A-to-Group B order, while the simple recalculation gives a positive contrast in Group B-to-Group A order. Both presentations point in the same direction when the group order is recognized.
This is an immune-response finding in the registry’s stated analysis population. It does not show whether participants were protected from tetanus or any other infection, whether vaccine responses persisted, or whether clinical outcomes differed. An antibody-based endpoint is a measure of immune response as defined by the study; the record does not establish that meeting the criterion guarantees a particular health outcome.
The comparison also does not isolate the effect of OCR from every other feature of the treatment strategies. Group A received OCR with vaccines, whereas Group B received vaccines during the immunization period and could receive OCR in an extension. The registry description of Group A’s vaccine course is incomplete. The posted result should therefore be understood within the specific groups and procedures described, rather than generalized to unlisted regimens or settings.
Randomization supports a comparison between assigned groups, but interpretation is limited by the open-label design and the outcome population defined by completion of the ISP. The record does not report exclusions, missing outcome handling, the full analysis plan, or multiplicity procedures. The confidence interval conveys statistical uncertainty around the contrast under the analysis method; it cannot account for every source of uncertainty or bias.
No treatment recommendation follows from these registry data. The result concerns one primary antibody-response endpoint in one trial population and should not be converted into a claim about clinical effectiveness, safety in other populations, or individual care. Those questions are not answered by the posted endpoint alone.
18. Why This Trial Matters Statistically
This study illustrates how a clinical trial can use a laboratory-defined immune response as its primary outcome. The endpoint converts antibody measurements into a binary response according to baseline-dependent criteria. That makes the comparison interpretable as proportions meeting a rule, while also making the exact rule essential to understanding what the percentages mean.
It also illustrates why direction and group order matter. The sponsor’s reported contrast is negative in Group A-to-Group B order; the unadjusted recalculation is positive in Group B-to-Group A order. A sign by itself does not indicate whether an outcome favored one group until the order and definition of the contrast are clear. Reporting the groups and endpoint alongside the estimate prevents a common misreading.
The trial also provides a useful example of the difference between the reported analysis and a simple recalculation from summary statistics. The latter can make a basic comparison transparent, but it does not reproduce undocumented elements of a sponsor analysis. The registry’s own result remains the primary reported estimate, while recalculation adds a check that should be labeled and interpreted with its assumptions.
Finally, the study’s many secondary outcomes make multiplicity and analysis-population transparency important. A pattern across related immune outcomes may be informative descriptively, but unadjusted tests do not have the same evidential standing as an isolated, prespecified primary comparison. Clear reporting of outcome priorities, missing-data handling, and analysis populations would help readers judge how robustly results reflect the randomized groups. Those details are not reported in the registry record.
19. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
- Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.
Several trial-specific details needed to assess generalizability and reproducibility are not reported in the registry record. The full Group A immunization description is truncated, and the schedule details for the vaccine course cannot be reconstructed from the available description. The registry also does not explain the meaning of ISP in the primary population definition.
The primary outcome uses different criteria according to pre-vaccination antibody titers. The rationale for the thresholds and the laboratory procedures are not reported. That makes the response definition clear at a high level but leaves uncertainty about measurement quality, assay handling, and the interpretation of borderline results.
The primary analysis population includes randomized participants who completed the ISP, rather than explicitly naming all randomized participants as analyzed. The record does not report how many participants were excluded from that population, why they were excluded, or how unavailable antibody results were treated. Without those details, it is difficult to evaluate selection after randomization or the potential impact of missing measurements.
The study is open-label, with no masking listed. Whether outcome assessors or laboratory staff were masked is not reported. The record also does not report allocation concealment, the original sample-size justification, interim analyses, a full statistical analysis plan, multiplicity control, or sensitivity analyses. These absences restrict assessment of prespecification and robustness.
Finally, the endpoint is an antibody-response measure rather than a clinical outcome, and the registry does not report how long responses persisted. The safety data are descriptive and do not include further details about exposure time or event causality. These limitations define what can be concluded from the posted record; they do not establish that any unreported procedure was absent.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: A Study to Evaluate the Effects of Ocrelizumab on Immune Responses In Participants With Relapsing Forms of Multiple Sclerosis — NCT02545868.
- Registry record last updated 2024-03-26; status last verified 2024-02.
- Results first posted 2018-06-06.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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23. Record Summary
NCT02545868 is a completed, multicenter, randomized, parallel-group, open-label Phase IIIB study sponsored by Hoffmann-La Roche. It enrolled 102 participants with relapsing forms of multiple sclerosis and evaluated immune responses to vaccines after OCR administration in one group, compared with vaccines during the immunization period in the other group.
The primary endpoint was positive response to TT vaccine 8 weeks after vaccination, using antibody criteria dependent on pre-vaccination titers. The posted response percentages were 23.9% for Group A and 54.5% for Group B. The sponsor-reported contrast was -30.7 with a 95% confidence interval from -50.5 to -10.8; the simple unadjusted recalculation, in the reverse group order, was a risk difference of 0.324 with a 95% confidence interval from 0.129 to 0.518.
The record lists a broad set of secondary immune-response outcomes and descriptive safety counts. Multiplicity handling, missing-data procedures, the original sample-size justification, and several analysis details are not reported in the registry record.