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 Rituximab on Immune Responses in Subjects With Active Rheumatoid Arthritis Receiving Background Methotrexate (NCT00282308), a randomized phase 2 study. The primary outcome is Percentage of Patients With a Positive Immune Response to Tetanus Toxoid Adsorbed Booster Vaccine.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00282308 |
| Phase | Phase 2 |
| Condition | Rheumatoid Arthritis |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 103 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Genentech, Inc. |
| Results posted | Yes |
2. Clinical Question
Population
People with active rheumatoid arthritis who were receiving background methotrexate. The primary outcome used an immune-response per-protocol population, with eligibility based on treatment, vaccination and availability of blood samples; the full population description is not reported in the registry record.
Intervention
Rituximab added to methotrexate. Group A received 2 intravenous rituximab infusions of 1000 mg, 14 days apart, with methotrexate 10-25 mg per week by mouth or subcutaneously during the Treatment Period.
Comparator
Methotrexate alone. Group B received methotrexate 10-25 mg per week by mouth or subcutaneously during the Treatment Period.
Primary question
What percentage of patients in each group had a positive immune response to a tetanus toxoid adsorbed booster vaccine? The primary outcome was assessed from blood samples taken immediately before vaccination and 4 weeks afterward, at Week 24 to Week 28 for Group A and Day 1 to Week 4 for Group B.
The trial focused on vaccine-related immune responses in people with active rheumatoid arthritis receiving methotrexate, rather than on a measure of rheumatoid arthritis symptoms or disease control. It compared rituximab plus methotrexate with methotrexate alone. Random allocation supports a between-group comparison, while the open-label design means participants and study personnel were not masked to group assignment. The registry describes the study as multicenter, but the number and locations of centers are not reported in the registry record.
3. Trial Design
The registry describes NCT00282308 as a completed, randomized, parallel-group, open-label Phase II study sponsored by Genentech, Inc. It lists rheumatoid arthritis as the condition and enrollment of 103. The study started on 2006-01-23, and primary completion was recorded as 2008-01-31. The registry does not report the original sample-size justification or the assumptions used to select enrollment.
Group A received rituximab with background methotrexate; Group B received methotrexate alone during the Treatment Period. Both groups received methotrexate 10-25 mg per week orally or subcutaneously. The rituximab group received 2 intravenous infusions of 1000 mg, 14 days apart. The study description says it evaluated immune responses after rituximab administration in people receiving background methotrexate.
The primary outcome was a positive immune response to a tetanus toxoid adsorbed booster vaccine, assessed using pre-vaccination and 4-week post-vaccination serum samples. The schedule differed by group: Week 24 to Week 28 for Group A and Day 1 to Week 4 for Group B. The registry also lists secondary measures related to tetanus, pneumococcal vaccine serotypes, keyhole limpet hemocyanin antibody levels and maintenance of a positive C. albicans skin-test response.
Although enrollment was 103, the primary outcome lists 64 patients for Group A and 26 for Group B. These are the outcome-specific analysis counts in the registry, not a statement that every enrolled participant contributed to that outcome. The record describes a per-protocol population requiring treatment or vaccination and pre- and post-vaccination blood samples, with some group-specific criteria. The complete criteria are not reported in the registry record. Details about allocation concealment, protocol deviations, and the statistical plan are also not reported in the registry record.
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.
Treatment Period
| Stage | Rituximab + Methotrexate (Group A) | Methotrexate (Group B) | All Patients (Combined Groups A and B) |
|---|---|---|---|
| STARTED | 69 | 34 | 0 |
| COMPLETED | 65 | 28 | 0 |
| NOT COMPLETED | 4 | 6 | 0 |
Reasons for not completing this period:
| Reason | Rituximab + Methotrexate (Group A) | Methotrexate (Group B) | All Patients (Combined Groups A and B) |
|---|---|---|---|
| Lost to Follow-up | 1 | 0 | 0 |
| Subject/Guardian Decision to Withdraw | 2 | 4 | 0 |
| Adverse Event | 0 | 2 | 0 |
| Not Treated with Study Drug | 1 | 0 | 0 |
Optional Extension Re-treatment Period
| Stage | Rituximab + Methotrexate (Group A) | Methotrexate (Group B) | All Patients (Combined Groups A and B) |
|---|---|---|---|
| STARTED | 0 | 0 | 78 |
| COMPLETED | 0 | 0 | 72 |
| NOT COMPLETED | 0 | 0 | 6 |
Reasons for not completing this period:
| Reason | Rituximab + Methotrexate (Group A) | Methotrexate (Group B) | All Patients (Combined Groups A and B) |
|---|---|---|---|
| Adverse Event | 0 | 0 | 4 |
| Physician's Decision to Withdraw | 0 | 0 | 1 |
| Subject/Guardian Decision to Withdraw | 0 | 0 | 1 |
Safety Follow-up Period
| Stage | Rituximab + Methotrexate (Group A) | Methotrexate (Group B) | All Patients (Combined Groups A and B) |
|---|---|---|---|
| STARTED | 0 | 0 | 100 |
| COMPLETED | 0 | 0 | 81 |
| NOT COMPLETED | 0 | 0 | 19 |
Reasons for not completing this period:
| Reason | Rituximab + Methotrexate (Group A) | Methotrexate (Group B) | All Patients (Combined Groups A and B) |
|---|---|---|---|
| Adverse Event | 0 | 0 | 1 |
| Lost to Follow-up | 0 | 0 | 5 |
| Physician Decision to Withdraw | 0 | 0 | 1 |
| Subject/Guardian Decision to Withdraw | 0 | 0 | 12 |
Analysis population for the primary outcome, as defined in the registry: Immune response per-protocol population: Group A - All patients randomized to Group A who received any rituximab infusion and any vaccine and had pre-vaccination and 4-week post-vaccination blood samples. Group B - All patients randomized to Group B who received any vaccine and had pre-vaccination and 4-week post-vaccination blood samples.
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: Safety population: All patients who received any amount of rituximab or any vaccine.
| Characteristic | Unit | Rituximab + Methotrexate (Group A) | Methotrexate (Group B) | Total |
|---|---|---|---|---|
| Participants analysed | 68 | 32 | 100 | |
| Age, Continuous | years | 49.7 (SD 9.60) | 49.7 (SD 10.51) | 49.7 (SD 9.85) |
| Sex: Female, Male: Female | Participants | 51 | 25 | 76 |
| Sex: Female, Male: Male | Participants | 17 | 7 | 24 |
6. Primary Endpoint
The registry lists the primary outcome as Percentage of Patients With a Positive Immune Response to Tetanus Toxoid Adsorbed Booster Vaccine, measured over Week 24 to Week 28 for Group A and Day 1 to Week 4 for Group B.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | Percentage of patients |
| Endpoint classification | Binary Endpoint |
The primary endpoint is the percentage of patients with a positive immune response to a tetanus toxoid adsorbed booster vaccine. Serum samples were collected immediately before vaccination and 4 weeks afterward. The registry describes an ELISA using tetanus toxoid as the capturing reagent and alkaline phosphatase-conjugated anti-human IgG for detection.
The definition of a positive response depended on the pre-vaccination antibody titer. For patients whose pre-vaccination titer was below 0.1 IU/mL, a positive response required a post-vaccination titer of at least 0.2 IU/mL. For patients whose pre-vaccination titer was at least 0.1 IU/mL, a positive response required a 4-fold increase in antibody titer. This threshold-based definition combines an absolute post-vaccination level for one baseline category with a relative increase for the other.
Vaccine antibody response was used because the study’s stated purpose was to evaluate immune responses to vaccines after rituximab administration in people receiving methotrexate. In general, a binary endpoint such as this makes the outcome easy to describe as the proportion meeting a prespecified response definition. It also reduces information: patients just below and just above a cutoff are classified differently, while variation in antibody levels within either category is not conveyed by the positive-response percentage. The registry does not report a rationale for choosing the specific thresholds or describe how the endpoint definition was selected.
7. Results Posted in the Registry
- Methotrexate (Group B): 42.3% (11/26) versus 39.1% (25/64) on control; risk difference 3.2 percentage points (95% CI -19.2 to 25.7), risk ratio 1.08 (0.63–1.86); unadjusted two-proportion z-test p = 0.776.
Risk difference: Methotrexate (Group B)
95% CI: -19.2 to 25.7 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 Patients With a 2-fold Increase in Tetanus Antibody Titers or With Tetanus Antibody Titers ≥ 0.2 IU/mL in Response to Tetanus Toxoid Adsorbed Booster Vaccine | Binary Endpoint | Risk difference | +6.9 pts (-15.5 to 29.2) | 813 per arm |
| Percentage of Patients With a Positive Immune Response to at Least 50% (≥ 6 of 12) of the 12 Anti-pneumococcal Antibody Serotypes in Response to the 23-valent Pneumococcal Polysaccharide Vaccine | Binary Endpoint | Risk difference | +41.7 pts (21.1 to 62.2) | 21 per arm |
| Percentage of Patients Who Maintained a Positive Response to the C. Albicans Skin Test From Day 1 to Week 24 for Group A or From Day 1 to Week 12 for Group B | Binary Endpoint | Risk difference | -6.7 pts (-26.3 to 12.9) | 660 per arm |
Percentage of Patients With a 2-fold Increase in Tetanus Antibody Titers or With Tetanus Antibody Titers ≥ 0.2 IU/mL in Response to Tetanus Toxoid Adsorbed Booster 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:
- Methotrexate (Group B): 61.5% (16/26) versus 54.7% (35/64) on control; risk difference 6.9 percentage points (95% CI -15.5 to 29.2), risk ratio 1.13 (0.77–1.64); unadjusted two-proportion z-test p = 0.552.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Methotrexate (Group B) and the control. The interval gives the range of effects that remain compatible with the data.
Percentage of Patients With a Positive Immune Response to at Least 50% (≥ 6 of 12) of the 12 Anti-pneumococcal Antibody Serotypes in Response to the 23-valent Pneumococcal Polysaccharide 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:
- Methotrexate (Group B): 60.7% (17/28) versus 19.0% (12/63) on control; risk difference 41.7 percentage points (95% CI 21.1 to 62.2), risk ratio 3.19 (1.77–5.75); 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 Methotrexate (Group B) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Percentage of Patients Who Maintained a Positive Response to the C. Albicans Skin Test From Day 1 to Week 24 for Group A or From Day 1 to Week 12 for Group B
- 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:
- Methotrexate (Group B): 71.4% (20/28) versus 78.1% (50/64) on control; risk difference -6.7 percentage points (95% CI -26.3 to 12.9), risk ratio 0.91 (0.70–1.19); unadjusted two-proportion z-test p = 0.488.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Methotrexate (Group B) and the control. The interval gives the range of effects that remain compatible with the data.
The registry lists a broad set of secondary outcomes related to immune responses to tetanus, pneumococcal vaccination, keyhole limpet hemocyanin and maintenance of a positive C. albicans skin-test response. The overall pattern is not uniform across these measures. Some posted comparisons favor one group numerically, while others are closer or point in the other direction. That variation is compatible with the fact that the outcomes measure different immune responses, use different definitions, and are assessed at different times.
The secondary measures add context to the primary tetanus result, but they do not replace it. They address related aspects of immune response rather than repeating the same primary endpoint. Their findings should not be condensed into a single general conclusion about immune function: each outcome has its own assessment method, analysis population and timing. The registry record does not report a single prespecified summary measure that combines the secondary outcomes.
Unadjusted secondary results carry less weight when many outcomes are examined. In general, examining multiple endpoints increases the chance that at least one result will appear notable by chance, even when there is no underlying effect. The registry lists 10 outcome measures, and it does not report a multiplicity strategy or adjusted analyses. This makes individual secondary comparisons more exploratory than a result supported by a prespecified analysis that accounts for the full set of comparisons.
The secondary results should therefore be interpreted as descriptive evidence about the specific immune measures recorded, with attention to their uncertainty and assessment schedules. The registry does not report a formal hierarchy for the secondary outcomes, nor does it report confirmatory analysis details for them. A scattered pattern across endpoints should not be treated as independent confirmation of the primary finding, and an isolated difference should not be elevated without considering the number of outcomes and the missing analysis-plan details.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Percentage of Patients With a 2-fold Increase in Tetanus Antibody Titers or With Tetanus Antibody Titers ≥ 0.2 IU/mL in Response to Tetanus Toxoid Adsorbed Booster Vaccine
- Percentage of Patients With a Positive Immune Response to Each of the 12 Anti-pneumococcal Antibody Serotypes in Response to the 23-valent Pneumococcal Polysaccharide Vaccine
- Percentage of Patients With a Positive Immune Response to at Least 50% (≥ 6 of 12) of the 12 Anti-pneumococcal Antibody Serotypes in Response to the 23-valent Pneumococcal Polysaccharide Vaccine
- Percentage of Patients With a Positive Immune Response to at Least k (for k = 1, 2, 3, 4, 5) of the 12 Anti-pneumococcal Antibody Serotypes in Response to the 23-valent Pneumococcal Polysaccharide Vaccine
- Serum Level of Anti-tetanus Antibody Measured Immediately Prior to and 4 Weeks After Administration of a Tetanus Toxoid Adsorbed Booster Vaccine
- Serum Level of Anti-pneumococcal Antibody Measured Immediately Prior to and 4 Weeks After Administration of a 23-valent Pneumococcal Polysaccharide Vaccine
- Serum Level of Anti-keyhole Limpet Hemocyanin Antibody Measured Immediately Prior to and 4 Weeks After the First Administration of Keyhole Limpet Hemocyanin
- Percentage of Patients Who Maintained a Positive Response to the C. Albicans Skin Test From Day 1 to Week 24 for Group A or From Day 1 to Week 12 for Group B
9. Statistical Interpretation
For the primary endpoint, the registry reports a positive response in 39.1% of Group A and 42.3% of Group B. The reported risk difference is 0.032, with an interval from -0.192 to 0.257, and the unadjusted p-value is 0.776. The percentage was numerically higher in the methotrexate-only group, but the interval includes values on either side of no difference. The results therefore do not establish a clear between-group difference in this endpoint. They also do not show that the groups are equivalent: the interval allows for a range of possible differences, including effects in either direction.
The outcome-specific counts were 64 for Group A and 26 for Group B. These counts are smaller than the enrollment recorded for the trial and reflect the primary outcome population, which required relevant treatment or vaccination and blood samples. They should not be interpreted as the overall enrollment or as evidence that all enrolled participants had complete outcome data.
The p-value is an unadjusted comparison. In general, it describes how compatible the observed data are with a specified no-difference model under the assumptions of the test; it is not the probability that the no-difference hypothesis is true. The registry record does not report a multiplicity strategy, a detailed analysis plan, or a sponsor-reported statistical analysis for this outcome. The comparison should consequently be read as the posted unadjusted result, not as a fully documented confirmatory analysis.
The endpoint is an antibody response to a booster vaccine, not a direct measure of rheumatoid arthritis activity, clinical protection from infection, or a patient-centered health outcome. A difference in this laboratory-defined response would not by itself establish a difference in clinical outcomes. Likewise, the lack of a clear separation in the posted primary comparison does not establish that the treatments have identical effects on this immune measure.
Interpretation also needs to account for the study design. Randomization is a strength for comparing groups, but the study was open-label, and the registry describes a per-protocol analysis population rather than an analysis of everyone randomized. The timing of vaccination and measurement differed between groups. The registry record does not explain whether or how those design features were addressed in the analysis. The posted result is therefore best understood as a comparison of the recorded outcome percentages in the stated outcome populations, with substantial uncertainty around the estimated difference.
10. Statistical Methods Explained
The primary outcome is binary at the patient level: each patient is classified as having a positive or non-positive immune response under the registry’s tetanus antibody definition. The reported group percentages describe the proportion classified as positive. In general, a binary endpoint compresses a measurement into categories, which can aid interpretation but discards information about the magnitude of antibody levels within each category.
What does a risk difference describe?
The comparison is reported as a risk difference. In general, a risk difference subtracts one group’s event proportion from the other group’s event proportion, with the sign depending on which group is placed first. It expresses the absolute separation between the proportions on the probability scale. The registry lists a risk difference of 0.032 for the primary outcome, with an interval from -0.192 to 0.257. The comparison is labelled as Group B relative to Group A. Because the interval extends across zero, it includes no difference as well as possible differences in either direction. The record does not state the confidence level for this interval, so the interval should not be assigned a confidence percentage based on the registry information alone.
How should the p-value be read?
The primary comparison has an unadjusted p-value of 0.776. In general, a p-value assesses how unusual data at least as far from a null value would be if the null model and test assumptions held. It is not a measure of the size or importance of an effect, and it does not give the probability that the null hypothesis is true. The label “unadjusted” matters because the registry does not report correction for multiple comparisons. The p-value should not be treated as evidence that the groups are equivalent, especially when the interval remains compatible with a range of effects.
What does the per-protocol population imply?
The primary outcome uses an immune-response per-protocol population. The description specifies that Group A participants had to be randomized to Group A, receive any rituximab infusion and any vaccine, and have pre-vaccination and 4-week post-vaccination blood samples. Group B participants had to be randomized to Group B, receive any vaccine and have the corresponding samples; the available registry wording for that description is incomplete. The full population criteria are not reported in the registry record. In general, restricting analysis to participants with specified treatment and outcome data can make an endpoint measurable, but it can also mean that the comparison is not based on every randomized participant. If inclusion depends on events after randomization, the groups being compared may no longer retain all the advantages of random assignment. Whether that affected this study cannot be determined from the registry record.
What does open-label mean for interpretation?
The study had no masking. In general, open-label assignment can influence behavior, care, reporting, or decisions about participation in assessments. The primary outcome is based on an antibody assay, which is more objective than a patient-reported outcome, but that does not remove every possible influence on who contributes a sample or how the study is conducted. The registry does not report details about laboratory blinding or safeguards against bias, so those procedures should not be assumed.
Why does the timing matter?
The primary endpoint was assessed at Week 24 to Week 28 for Group A and Day 1 to Week 4 for Group B. This means the groups were not assessed on the same study-time schedule relative to treatment. In general, timing can matter when an immune response changes over time or when treatment exposure differs before vaccination. The registry gives the assessment windows but does not report an analysis of timing effects or a rationale for the differing schedules. Thus, the comparison should be read within the stated schedules rather than as proof that timing had no influence.
What statistical details are absent?
The registry lists no reported analyses, and the primary outcome is presented without a detailed account of the test procedure, missing-data handling, covariate adjustment, or multiplicity control. The original statistical analysis plan, including the intended primary comparison and any interim analyses, is not reported in the registry record. General statistical explanations can clarify what the posted percentages, interval and p-value represent, but they cannot fill in those study-specific omissions. The registry also does not report a confidence level for the interval. These gaps limit the ability to assess whether every analytic choice followed a prespecified plan.
11. Confidence Intervals and Precision
The primary comparison has an interval from -0.192 to 0.257 for the reported risk difference of 0.032. In general, an interval estimates a range of values reasonably compatible with the data and the method used to construct it. A narrower interval indicates greater precision, while a wider interval indicates more uncertainty. The interval for this comparison spans zero and extends in both directions, so the posted estimate does not pinpoint the direction or size of the difference precisely. The registry does not report the confidence level attached to the interval; it is therefore not appropriate to label it with a specific confidence percentage.
The outcome counts are 64 for Group A and 26 for Group B. In general, estimates based on fewer observations tend to be less precise, although precision also depends on the observed proportions and the analysis method. The difference in group counts is relevant context when interpreting an interval, but it does not by itself determine the interval’s width. The outcome-specific counts also reflect the per-protocol population described for the endpoint rather than the trial’s enrollment figure.
Precision and statistical significance are related but not interchangeable concepts. A p-value gives a test-based summary under a null model, whereas an interval displays uncertainty across a range of effect values. Here, the interval includes both negative and positive values, and the unadjusted p-value is 0.776. Taken together, the results do not tightly distinguish between no difference and a range of possible group differences. They do not establish equivalence or rule out meaningful differences. The registry record does not report a prespecified equivalence margin or a precision target for the primary endpoint.
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 | 3,596 | 4,814 |
| 75% of the observed effect | 6,374 | 8,532 |
| 50% of the observed effect | 14,294 | 19,135 |
The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design assumptions. The registry does not report the original sample-size justification, so these calculations should not be read as evidence about how enrollment was chosen. The figures are participants per arm for 80% power and participants per arm for 90% power. They are not total enrollment figures or total event counts.
The 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 at the stated fraction of the observed effect. The row for 100% of the observed effect uses the observed effect as the target; the rows for 75% and 50% use progressively smaller target effects. The planning figures show that smaller effects need more participants to detect, because a smaller separation between group proportions is harder to distinguish from sampling variation.
The 80% power column represents a planning scenario in which a study using those assumptions would have an 80% chance of detecting the specified effect at the stated significance level, if that effect were the true one and the assumptions held. The 90% power column describes the corresponding planning target with a higher chance of detection, which requires more participants under the same assumptions. These are theoretical design calculations, not a description of the chance that the completed study detected an effect. This is not observed power.
Because the calculations use the observed effect, they are illustrative and depend on an estimate from the trial itself. They do not show what effect size was considered important before enrollment, nor do they establish that the study was adequately designed for its primary endpoint. The assumptions used in the trial’s original design 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 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 = 0.391; treatment proportion p1 = 0.423; average p̄ = 0.407.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6947 = 1.3616.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6943 = 0.5844.
- n = (1.3616 + 0.5844)2 / (0.0325)2 = 3,595.9, rounded up to 3,596 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 <- 0.390625 # control proportion
p1 <- 0.423076923076923 # 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(282308)
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 = 3,596 (80% power), 4,814 (90% power)
75% of observed effect: n per arm = 6,374 (80% power), 8,532 (90% power)
50% of observed effect: n per arm = 14,294 (80% power), 19,135 (90% power)
power.prop.test: 3595.9
Simulated power at n = 3,596 per arm: 0.799 (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 lists 10 outcome measures, including the primary tetanus response and secondary measures spanning several vaccines and immune assays. The record reports no analyses in its analysis listing and does not describe a prespecified hierarchy for testing the outcomes. It also does not report whether multiplicity was handled through a correction, gatekeeping procedure, or another strategy. Without that information, the posted unadjusted comparisons should be viewed as separate exploratory results rather than as a set of error-controlled confirmatory tests.
In general, multiplicity matters because the chance of observing at least one apparently unusual result rises as more hypotheses are tested. This does not mean a secondary result is false; it means the evidence from an unadjusted p-value is less compelling when it comes from a wider family of comparisons. The record does not specify whether any outcomes were designated as key secondary endpoints or whether any analysis was planned to follow a successful primary test.
Missing-data handling is also not reported in detail. For the primary endpoint, the registry describes an immune-response per-protocol population requiring vaccination and blood samples before and after vaccination. The reported outcome counts differ from the overall enrollment, but the record does not provide a complete accounting of missing samples, reasons for exclusion, or how missing outcomes were treated. It does not report a sensitivity analysis assessing the influence of missing data.
The per-protocol definition makes the analysis population important to interpretation. In general, a per-protocol comparison can differ from an analysis that includes all randomized participants, especially if exclusions occur after randomization. The record does not report an intention-to-treat analysis for the primary outcome or details of the allocation process beyond randomized assignment. It also does not report the statistical analysis plan, interim analyses, or the original sample-size rationale. These omissions limit assessment of prespecification, selection effects and the robustness of the reported comparisons.
15. 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 |
|---|---|---|---|
| Rituximab + Methotrexate (Group A) - Treatment Period | 3 | 68 | 4.4% |
| Methotrexate (Group B) - Treatment Period | 2 | 32 | 6.2% |
| Group A - Optional Extension Re-treatment Period | 2 | 52 | 3.8% |
| Group B - Optional Extension Re-treatment Period | 2 | 26 | 7.7% |
| Group A - Safety Follow-up Period | 3 | 68 | 4.4% |
| Group B - Safety Follow-up Period | 1 | 32 | 3.1% |
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 |
|---|---|
| Rituximab + Methotrexate (Group A) - Treatment Period | 51 of 68 |
| Methotrexate (Group B) - Treatment Period | 19 of 32 |
| Group A - Optional Extension Re-treatment Period | 7 of 52 |
| Group B - Optional Extension Re-treatment Period | 13 of 26 |
| Group A - Safety Follow-up Period | 19 of 68 |
| Group B - Safety Follow-up Period | 11 of 32 |
Most frequent serious adverse event terms
| Event term | Organ system | Rituximab + Methotrexate (Group A) - Treatment Period | Methotrexate (Group B) - Treatment Period | Group A - Optional Extension Re-treatment Period | Group B - Optional Extension Re-treatment Period | Group A - Safety Follow-up Period | Group B - Safety Follow-up Period |
|---|---|---|---|---|---|---|---|
| Pyelonephritis | Infections and infestations | 0 of 68 | 0 of 32 | 1 of 52 | 0 of 26 | 1 of 68 | 0 of 32 |
| Thyroid cancer | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 0 of 68 | 0 of 32 | 0 of 52 | 1 of 26 | 0 of 68 | 1 of 32 |
| Coronary artery disease | Cardiac disorders | 1 of 68 | 0 of 32 | 0 of 52 | 0 of 26 | 0 of 68 | 0 of 32 |
| Chest pain | General disorders | 1 of 68 | 0 of 32 | 0 of 52 | 0 of 26 | 0 of 68 | 0 of 32 |
| Hip fracture | Infections and infestations | 1 of 68 | 0 of 32 | 0 of 52 | 0 of 26 | 0 of 68 | 0 of 32 |
| Rheumatoid arthritis | Musculoskeletal and connective tissue disorders | 0 of 68 | 1 of 32 | 0 of 52 | 0 of 26 | 0 of 68 | 0 of 32 |
| Ovarian cyst | Reproductive system and breast disorders | 0 of 68 | 1 of 32 | 0 of 52 | 0 of 26 | 0 of 68 | 0 of 32 |
| Amaurosis fugax | Eye disorders | 0 of 68 | 0 of 32 | 1 of 52 | 0 of 26 | 0 of 68 | 0 of 32 |
| Ovarian cancer | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 0 of 68 | 0 of 32 | 0 of 52 | 1 of 26 | 0 of 68 | 0 of 32 |
| Basal cell carcinoma | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 0 of 68 | 0 of 32 | 0 of 52 | 0 of 26 | 1 of 68 | 0 of 32 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Rituximab + Methotrexate (Group A) - Treatment Period | Methotrexate (Group B) - Treatment Period | Group A - Optional Extension Re-treatment Period | Group B - Optional Extension Re-treatment Period | Group A - Safety Follow-up Period | Group B - Safety Follow-up Period |
|---|---|---|---|---|---|---|---|
| Upper respiratory tract infection | Infections and infestations | 7 of 68 | 2 of 32 | 1 of 52 | 4 of 26 | 8 of 68 | 6 of 32 |
| Sinusitis | Infections and infestations | 5 of 68 | 0 of 32 | 2 of 52 | 3 of 26 | 7 of 68 | 2 of 32 |
| Rheumatoid arthritis | Musculoskeletal and connective tissue disorders | 12 of 68 | 0 of 32 | 0 of 52 | 2 of 26 | 2 of 68 | 3 of 32 |
| Arthralgia | Musculoskeletal and connective tissue disorders | 8 of 68 | 1 of 32 | 2 of 52 | 2 of 26 | 0 of 68 | 0 of 32 |
| Headache | Nervous system disorders | 9 of 68 | 3 of 32 | 0 of 52 | 0 of 26 | 0 of 68 | 0 of 32 |
| Pruritus | Skin and subcutaneous tissue disorders | 9 of 68 | 3 of 32 | 0 of 52 | 0 of 26 | 0 of 68 | 0 of 32 |
| Cough | Respiratory, thoracic and mediastinal disorders | 7 of 68 | 1 of 32 | 0 of 52 | 3 of 26 | 0 of 68 | 0 of 32 |
| Nausea | Gastrointestinal disorders | 7 of 68 | 1 of 32 | 0 of 52 | 0 of 26 | 0 of 68 | 0 of 32 |
| Throat irritation | Respiratory, thoracic and mediastinal disorders | 5 of 68 | 2 of 32 | 0 of 52 | 0 of 26 | 0 of 68 | 0 of 32 |
| Diarrhoea | Gastrointestinal disorders | 5 of 68 | 1 of 32 | 0 of 52 | 0 of 26 | 0 of 68 | 0 of 32 |
Serious events with the highest arm-level rate: ovarian cancer (3.8%), thyroid cancer (3.8%), rheumatoid arthritis (3.1%), ovarian cyst (3.1%), amaurosis fugax (1.9%).
The registry reports serious adverse events by study period and group. During the Treatment Period, serious adverse events affected 3 of 68 participants in Group A and 2 of 32 in Group B. During the Optional Extension Re-treatment Period, the corresponding counts were 2 of 52 for Group A and 2 of 26 for Group B. During the Safety Follow-up Period, the counts were 3 of 68 for Group A and 1 of 32 for Group B. These are period-specific counts and denominators; they should not be combined into a single overall count because the record does not explain participant overlap across periods.
The registry also lists serious-event terms and percentages, including ovarian cancer, thyroid cancer, rheumatoid arthritis, ovarian cyst, amaurosis fugax and pyelonephritis. The record does not provide enough context in this summary to determine whether individual events were considered related to a study treatment. A serious adverse event listing is not, by itself, evidence of causation or a comparative safety effect.
Deaths are not reported in the registry record. The record does not provide a detailed definition of serious adverse events, exposure-adjusted event rates, or a formal statistical comparison of safety between groups. These figures describe the reported counts and should be interpreted with those limits in mind.
16. What the Result Does, and Does Not, Mean
The primary result describes the percentage of patients meeting the study’s tetanus antibody response definition in each treatment group. In the posted outcome population, the percentages are 39.1% for rituximab plus methotrexate and 42.3% for methotrexate alone. The comparison’s interval spans zero, and its unadjusted p-value is 0.776. The record therefore does not establish a clear difference in this particular immune response, but it also does not demonstrate that the groups are equivalent.
The endpoint concerns a laboratory-defined antibody response to a tetanus booster. It is not a direct measure of rheumatoid arthritis activity, overall immune competence, clinical protection from tetanus, or the risk of infection. A positive antibody response under the study definition should not be interpreted as proof of protection, and a non-positive response should not be taken as proof of susceptibility. The registry record does not report clinical infection outcomes tied to this endpoint.
The study’s broader aim was to evaluate vaccine immune responses after rituximab administration in participants receiving background methotrexate. The posted outcomes cover multiple immune measures, but they do not establish a general effect across all vaccine responses. Each endpoint has its own criteria and timing, and secondary comparisons are unadjusted with no reported multiplicity strategy.
Interpretation is also limited by the open-label design and by use of a per-protocol population for the primary outcome. Randomization is a useful design feature, but the outcome counts represent participants meeting specified treatment and sample requirements, not necessarily everyone randomized. The registry record does not report a detailed missing-data analysis, a complete statistical analysis plan, or the original sample-size assumptions. These limits mean the posted results are best read as the recorded group-specific immune-response data and their uncertainty, not as a definitive statement about treatment effects beyond this measured endpoint.
17. Why This Trial Matters Statistically
This trial illustrates how a clinical study can focus on a biological response rather than a direct clinical outcome. The primary endpoint converts antibody measurements into a positive-response classification, with different criteria depending on the baseline titer. That makes the result easy to communicate as a percentage, while also highlighting how endpoint definitions determine what counts as a response.
It also shows why an effect estimate and its uncertainty should be read together. The primary comparison has a small numerical separation in the posted percentages, but its interval spans values on both sides of zero. The unadjusted p-value alone cannot communicate the range of effects compatible with the data, nor does it prove that there is no difference. This is a useful example of distinguishing absence of clear evidence from evidence of equivalence.
The design raises practical statistical questions about outcome timing and analysis populations. The primary measurement windows differ between groups, and the analysis is based on a per-protocol population requiring treatment or vaccination and blood samples. The registry does not report whether timing or exclusions were addressed in the statistical plan. These details matter because a randomized design does not automatically resolve concerns introduced after randomization or by different assessment schedules.
Finally, the record lists multiple immune endpoints but no reported analyses or multiplicity strategy. That makes it important to avoid over-interpreting an isolated secondary comparison. The trial is a useful case for reading percentages, risk differences, intervals and unadjusted p-values in context, while keeping the measured laboratory outcome distinct from broader claims about clinical benefit or harm.
18. 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 for a fuller assessment are not reported in the registry record. The primary outcome population description is incomplete, and the record does not give a full account of who was excluded from each outcome analysis or why. Although the primary endpoint lists 64 participants for Group A and 26 for Group B, the registry does not provide a complete flow of randomized participants through vaccination, sample collection and analysis.
The primary endpoint was measured at different study times in the two groups: Week 24 to Week 28 for Group A and Day 1 to Week 4 for Group B. The record does not explain the rationale for this difference or report an analysis of its potential effect. It also does not report the confidence level for the interval, the full statistical test specification, covariate adjustment, or a sensitivity analysis.
The study was open-label. The registry does not report whether laboratory personnel were masked or what other procedures were used to reduce bias. It does not provide the original sample-size justification, so the planning illustrations based on the observed effect cannot establish what power or precision the investigators intended. A protocol, full analysis plan and interim-analysis details are not reported in the registry record.
Multiple secondary immune outcomes are listed, but the record does not report a testing hierarchy or a multiplicity adjustment. The safety summary provides period-specific serious adverse event counts but does not supply a detailed account of event relatedness, exposure-adjusted rates, or formal comparative safety analyses. These omissions do not invalidate the posted data, but they limit the strength and breadth of conclusions that can be drawn from them.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: A Study to Evaluate the Effects of Rituximab on Immune Responses in Subjects With Active Rheumatoid Arthritis Receiving Background Methotrexate — NCT00282308.
- Registry record last updated 2017-08-10; status last verified 2017-07.
- Results first posted 2013-10-21.
- 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.
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
NCT00282308 was a completed, randomized, open-label, parallel-group Phase II study in people with active rheumatoid arthritis receiving background methotrexate. The registry records enrollment of 103 and compares rituximab plus methotrexate with methotrexate alone. The primary outcome was the percentage of patients with a positive immune response to a tetanus booster, assessed using serum samples before vaccination and 4 weeks afterward.
The posted primary outcome percentages were 39.1% for Group A and 42.3% for Group B. The reported risk difference was 0.032, with an interval from -0.192 to 0.257 and an unadjusted p-value of 0.776. These results do not establish a clear difference in the measured endpoint or demonstrate equivalence. Interpretation is limited by the per-protocol outcome population, different assessment schedules, open-label design, multiple listed outcomes, and statistical details not reported in the registry record.