Natalizumab in the Treatment of Rheumatoid Arthritis in Subjects Receiving Methotrexate: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Natalizumab in the Treatment of Rheumatoid Arthritis in Subjects Receiving Methotrexate (NCT00083759), a randomized phase 2 study. The primary outcome is American College of Rheumatology (ACR)20..

2. Clinical Question

3. Trial Design

The registry describes NCT00083759 as a randomized, double-blind, parallel-group, placebo-controlled Phase II study. Its official title identifies intravenous natalizumab at 300 mg in people with moderate to severe rheumatoid arthritis receiving methotrexate. The named sponsor is Biogen. The condition listed is rheumatoid arthritis.

The registry lists enrollment as 299. In the posted primary outcome, the natalizumab group has 137 participants and the placebo group has 136 participants. These are the denominators associated with that outcome; the registry record does not explain how they relate to the overall enrollment figure or describe the analysis population in further detail. The arm descriptions are not populated in the record.

The study began in 2004-05, had a primary completion date of 2005-02, and is listed as terminated. The reason for termination, the timing of termination, and whether it affected the conduct or reporting of outcomes are not reported in the registry record. The record does not report the planned sample-size justification, the original design assumptions, interim analyses, or a detailed statistical analysis plan.

The primary outcome was the number of participants meeting the ACR20 response definition at Month 6. The record also lists ACR50 and ACR70 as secondary outcomes, both assessed at Month 6. The outcome results therefore concern response thresholds at one stated time point; they do not describe change over time or outcomes beyond that visit. The record does not provide details of treatment duration, adherence, withdrawals, or follow-up beyond the listed endpoint timeframe.

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: Patients who met these criteria were randomized to natalizumab or placebo: aged 18-75 with a diagnosis of rheumatoid arthritis (RA) Functional Class 1-3 for ≥ 6 months, on a stable dose of methotrexate (MTX), having ≥ 10 painful/tender joints, and with elevated C-reactive protein. Stratification based on baseline number of painful/tender joints.

Overall Study

Reasons for not completing this period:

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.

6. Primary Endpoint

The registry lists the primary outcome as American College of Rheumatology (ACR)20., measured over Month 6.

The primary endpoint counts participants meeting the ACR20 response definition at Month 6. ACR20 requires at least a 20% reduction from baseline in both painful or tender joint count and swollen joint count, together with at least a 20% improvement in at least three of five secondary clinical parameters. The listed examples include subject global assessment, physician global assessment, pain scale, disability score, and an acute phase reactant.

This is a composite response measure: a participant must meet the joint-count criteria and the required number of other improvement criteria. A binary response outcome reduces each participant’s status at the specified assessment to whether the definition was met. Comparing the counts between randomized groups can therefore describe the difference in the proportion meeting that response definition, although the posted primary result is reported as participant counts and a recalculated risk difference.

As general statistical context, a composite endpoint can capture improvement across more than one clinical dimension, rather than relying on a single measurement. Its interpretation depends on the stated components and threshold. ACR20 is the primary measure named in the registry record; ACR50 and ACR70 are the listed secondary response thresholds. The registry record does not report a rationale for choosing ACR20 as the primary endpoint, or additional information about endpoint assessment procedures.

7. Results Posted in the Registry

• Natalizumab: 43.1% (59/137) versus 33.1% (45/136) on control; risk difference 10.0 percentage points (95% CI -1.5 to 21.4), risk ratio 1.30 (0.96–1.77); unadjusted two-proportion z-test p = 0.090.

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.

American College of Rheumatology (ACR)50

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Natalizumab: 16.8% (23/137) versus 11.0% (15/136) on control; risk difference 5.8 percentage points (95% CI -2.4 to 13.9), risk ratio 1.52 (0.83–2.79); unadjusted two-proportion z-test p = 0.169.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Natalizumab and the control. The interval gives the range of effects that remain compatible with the data.

American College of Rheumatology (ACR)70

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Natalizumab: 9.5% (13/137) versus 7.4% (10/136) on control; risk difference 2.1 percentage points (95% CI -4.4 to 8.7), risk ratio 1.29 (0.59–2.84); unadjusted two-proportion z-test p = 0.525.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Natalizumab and the control. The interval gives the range of effects that remain compatible with the data.

ACR50 and ACR70 are the two secondary outcomes listed in the registry record, and both are assessed at Month 6. Across these thresholds, the recalculated point estimates follow the same general direction as the primary comparison, while the intervals include no difference. The secondary outcomes therefore do not provide a clear, precise contrast that changes the overall reading of the primary result.

As general statistical context, more stringent response definitions identify participants meeting a higher threshold of improvement. Results across related thresholds can add context about the pattern of responses, but they are not independent replications: the measures are related and may involve many of the same participants. The registry record does not describe a hierarchy or a prespecified testing sequence for the outcomes.

Unadjusted secondary p-values carry less weight when several outcomes are examined because the chance of at least one apparently notable result can rise with repeated testing. A multiplicity adjustment or a prespecified strategy can address that issue, but neither is reported in the registry record. The secondary results are best treated as supportive descriptive evidence rather than as separate confirmatory tests. Their direction and uncertainty should be read alongside, not in place of, the primary endpoint and its sponsor-reported analysis.

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

• American College of Rheumatology (ACR)50
• American College of Rheumatology (ACR)70

9. Statistical Interpretation

10. Statistical Methods Explained

What is the risk difference?

The risk difference compares the proportion of participants meeting the endpoint in one group with the proportion in the other. Here, the comparison is natalizumab relative to placebo. The recalculated estimate is 0.100. A positive value indicates that the response proportion was higher in the natalizumab group in these posted counts; the estimate is not an adjusted effect estimate. The associated interval, -0.015 to 0.214, expresses uncertainty around that unadjusted comparison.

Risk differences are expressed on an absolute scale. In general, this scale can help readers understand how far apart the observed group response proportions are, while ratios describe a relative contrast. The posted comparison also includes risk-ratio and odds-ratio estimates, but the primary interpretation emphasizes the risk difference and the sponsor’s reported analysis. No adjusted effect estimate is reported in the registry record.

What does the interval communicate?

A confidence interval gives a range of values compatible with the data and the assumptions of the method, at the stated confidence level. In general, a wider interval indicates less precision than a narrower one. For the recalculated primary risk difference, the interval extends from -0.015 to 0.214 and crosses zero. Thus the data do not sharply distinguish no difference from a range of possible differences. An interval is not a guarantee that the true effect lies within its bounds, nor does it assign a probability to any single effect value.

What does the p-value mean?

The registry reports a Cochran-Mantel-Haenszel analysis for the primary comparison, with p = 0.089. The recalculated unadjusted comparison has p = 0.09. A p-value is calculated under a null hypothesis and the assumptions of the analysis; it describes how unusual the observed result, or a result more extreme, would be if that null model held. It is not the probability that a treatment is effective, and it does not describe the magnitude or clinical importance of a difference.

The registry record names the Cochran-Mantel-Haenszel method but does not report the stratification variables or further implementation details. In general, this method can combine comparisons across strata while accounting for the strata in the analysis. Without the relevant details, the exact adjustment represented by the sponsor analysis cannot be reconstructed from the registry record. The posted summary-count re-calculation is unadjusted and should not be treated as a substitute for the sponsor’s stated method.

Why distinguish the two analyses?

The recalculated result uses the posted group counts to make a simple, unadjusted comparison. The sponsor’s analysis is reported as Cochran-Mantel-Haenszel and gives a p-value, but no effect estimate or interval bounds are reported for that analysis. These approaches can produce slightly different p-values because they do not necessarily use the same information or assumptions. In this case, the two reported p-values are close, and the record does not flag a discrepancy.

When interpreting a clinical trial, the distinction matters because an unadjusted comparison may not reproduce an analysis that accounts for design features or stratification. General statistical practice gives priority to the analysis specified for the trial, but the registry record does not report the complete original analysis plan. The posted sponsor result can be identified as the registry analysis, while the recalculation remains a transparent comparison of the available summary counts.

How should the response counts be understood?

The endpoint is binary: each participant either met the response criteria or did not, at the listed assessment. The values in the outcome arms are counts, and the associated denominators are the participants represented in those results. In general, binary outcomes can be compared through absolute differences or relative measures, but each measure answers a different question. The risk difference describes an absolute contrast, while a risk ratio or odds ratio expresses a relative contrast.

The record does not provide participant-level data, so further checks of endpoint classification, covariate adjustment, missing outcomes, or alternative models cannot be made from the posted summary. It also does not report whether the analysis was intention-to-treat, per-protocol, or another population definition. These omissions limit the ability to assess the robustness of the result beyond the posted counts and reported analysis.

11. Confidence Intervals and Precision

The recalculated primary risk difference is 0.100, and its interval runs from -0.015 to 0.214. This interval is broad enough to include no difference and effects in either direction. It also includes positive differences larger than the point estimate. That span signals uncertainty about the size and direction of the underlying difference, rather than a precise estimate.

For general interpretation, an interval describes a range of effect values reasonably compatible with the data and the method used. Its width reflects sampling uncertainty, alongside the assumptions of the calculation. The interval does not show that every value inside it is equally plausible, and the point estimate does not have special certainty simply because it is centered within the reported range.

The registry record identifies 95 as the confidence level for the sponsor analysis, but does not report its confidence limits. The interval accompanying the recalculated risk difference is available, while the sponsor’s reported result is a p-value from the Cochran-Mantel-Haenszel method. Because the effect estimates and inferential methods differ in what is reported, readers should keep the recalculated interval distinct from the sponsor analysis.

More generally, a confidence interval that includes zero does not prove that the groups are equivalent. It indicates that the posted data do not rule out zero difference under the method used. Establishing equivalence or noninferiority requires a specified margin and a corresponding analysis; such a margin is not reported in the registry record.

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.

The sample-size figures are planning illustrations for participants per arm, not total event counts. The stated calculation assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each planning scenario uses a stated fraction of the observed effect as the effect to detect. The registry record does not report the trial’s original sample-size justification or original design assumptions.

The 80% power column indicates the number of participants per arm estimated to provide an 80% chance of detecting the specified effect under those planning assumptions, if that effect were present. The 90% power column gives the corresponding planning target for a 90% chance. These are design calculations, not guarantees that a future study will detect an effect; actual results depend on the true effect, variability, conduct, and analysis.

The rows describe planning for 100%, 75%, and 50% of the observed effect. As the target effect becomes smaller, more participants are needed to detect it at the same stated power. For example, the primary-outcome illustration lists 371 participants per arm for 80% power when planning for 100% of the observed effect, and 1,445 participants per arm when planning for 50% of it. These calculations are derived from the observed effect and are not the trial’s own original design calculations.

This is not observed power. Observed power is not a useful substitute for interpreting the uncertainty in the result; the effect estimate and its interval are more informative about the range of effects compatible with the data. The planning figures illustrate how sample-size requirements change with the effect targeted, under the stated calculation assumptions.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−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

1. Control proportion p₀ = 0.331; treatment proportion p₁ = 0.431; average p̄ = 0.381.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6867 = 1.3459.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6831 = 0.5749.
4. n = (1.3459 + 0.5749)² / (0.0998)² = 370.6, rounded up to 371 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 <- 0.330882352941176                          # control proportion
p1 <- 0.430656934306569                          # 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(83759)
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 = 371 (80% power), 496 (90% power)
 75% of observed effect: n per arm = 652 (80% power), 872 (90% power)
 50% of observed effect: n per arm = 1,445 (80% power), 1,934 (90% power)
power.prop.test: 370.6 
Simulated power at n = 371 per arm: 0.797 (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

The registry reports the sponsor’s primary comparison as a Cochran-Mantel-Haenszel analysis with p = 0.089. The registry record gives a 95% confidence level for that analysis but does not report an effect estimate or confidence limits. The sponsor’s reported method and p-value should therefore be distinguished from the unadjusted calculations based on the posted summary counts.

The recalculated unadjusted risk difference is 0.100, with an interval from -0.015 to 0.214, and the recalculated unadjusted p-value is 0.09. These results are close to the sponsor’s p-value, but they do not reproduce the named Cochran-Mantel-Haenszel analysis. The registry record does not flag a discrepancy between the analyses.

The recalculation is useful as a straightforward reading of the group counts, while the sponsor result is the analysis reported in the registry. The record does not provide enough methodological detail to determine the stratification or other implementation choices behind the sponsor analysis. Neither result alone resolves uncertainty about the magnitude or clinical importance of a difference.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists one primary outcome, ACR20, and two secondary outcomes, ACR50 and ACR70. The record does not report a multiplicity adjustment, a hierarchical testing strategy, or a plan for interpreting several outcomes together. Without such information, the role of the secondary p-values in confirmatory inference is unclear. In general, testing multiple outcomes without adjustment can increase the chance of a nominally unusual result arising by chance.

The record does not report how missing Month 6 outcomes were handled, whether participants who discontinued treatment were included in the outcome analysis, or whether any imputation was used. It also does not specify an intention-to-treat, per-protocol, or other analysis population. The posted denominators describe the results, but they do not establish why those denominators apply or how participants without an observed assessment were treated.

These gaps matter because the interpretation of a binary response outcome can depend on how missing assessments are classified or handled. General statistical methods can use different assumptions for missing data, and those choices may affect estimates and uncertainty. Participant-level data and a complete analysis plan would be needed to examine those choices; they are not reported in the registry record.

The registry does not report interim analyses, stopping criteria, or the statistical plan in enough detail to assess whether analyses or outcome definitions were changed. The study is listed as terminated, but the reason and implications for analysis are not reported in the registry record. These omissions do not establish that a particular bias occurred; they limit how fully the reported estimates can be evaluated.

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

The posted results describe the number of participants meeting the ACR20 response definition at Month 6 in the natalizumab and placebo groups. The recalculated point estimate favors natalizumab, but the interval includes no difference and is compatible with a range of possible effects. The sponsor’s reported p-value is close to the recalculated unadjusted p-value. Together, these statistics describe a result with meaningful uncertainty rather than a precise estimate.

In general, failure to distinguish a difference from zero is not proof that there is no difference. Likewise, a point estimate in one direction does not establish that a treatment caused the difference. Statistical uncertainty, the design and conduct of the study, analysis choices, and clinical interpretation all matter. The registry record does not report enough information about missing data, analysis populations, or multiplicity to resolve those considerations fully.

The primary endpoint is a composite clinical response threshold, not a direct measure of every aspect of rheumatoid arthritis or a complete account of a participant’s experience. The posted endpoint results do not provide information about outcomes beyond Month 6, treatment adherence, safety events, or longer-term follow-up. Although safety and tolerability are included in the study’s stated purpose, detailed safety results are not part of the registry entries reported for these outcome comparisons.

These results should therefore be read narrowly: they describe the registered outcome counts and statistical comparisons, with uncertainty around the estimated group contrast. They do not establish that natalizumab works or does not work, nor do they establish the clinical importance of the estimated difference. The registry record also does not provide the reason the study was terminated.

17. Why This Trial Matters Statistically

This trial illustrates why a point estimate and a test result should not be read in isolation. The primary risk difference is positive, but its interval spans zero and extends over a broad range. That combination conveys both the direction of the observed contrast and the limits on how precisely its size is known. A p-value alone would not communicate that range.

It also illustrates the value of distinguishing an analysis reported by the sponsor from a simple recalculation using summary counts. The registry names a Cochran-Mantel-Haenszel method, while the recalculation is unadjusted. Their p-values are close, but the available record does not provide enough detail to reconstruct the sponsor method or its effect estimate. Clear separation of these analyses avoids presenting an unadjusted calculation as if it were the original trial analysis.

The related ACR response thresholds add descriptive context, while raising the general issue of multiplicity. Several related outcomes can be informative, but their results do not have the same confirmatory force when an adjustment or testing hierarchy is not reported. Finally, planning illustrations based on the observed effect show how the sample-size target depends on the effect a study is designed to detect. They are not a substitute for the trial’s unreported original design rationale, and they are not observed power.

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.

The registry record gives limited information about the analysis behind the outcome results. It does not report the original sample-size justification, a full statistical analysis plan, the analysis population, or how missing assessments were handled. The sponsor analysis is named as Cochran-Mantel-Haenszel, but the record does not state the strata or provide its effect estimate and confidence limits.

The record lists the study as terminated, but the reason, timing, and consequences of termination are not reported in the registry record. No inference about why it ended or whether termination affected the analysis can be made from that status alone. The record also does not describe treatment adherence, withdrawals, or endpoint assessment procedures.

The primary and secondary outcomes are reported at Month 6. The registry entries do not include longer-term outcomes, detailed safety results, or participant-level data. The posted response counts therefore cannot support assessments of missing-data sensitivity, subgroup effects, adjusted comparisons, or robustness to alternative analysis choices. The outcome denominators are reported, but the registry record does not explain their relationship to the overall enrollment figure.

These limitations concern what can be evaluated from the registry record; they do not establish that any specific problem occurred. They constrain how confidently readers can assess the analysis and generalize beyond the posted Month 6 comparisons.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Natalizumab in the Treatment of Rheumatoid Arthritis in Subjects Receiving Methotrexate — NCT00083759.
• Registry record last updated 2016-07-18; status last verified 2009-04.
• Results first posted 2009-06-02.
• 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.

22. Record Summary

NCT00083759 is a randomized, double-blind, parallel-group, placebo-controlled Phase II study sponsored by Biogen. It assessed intravenous natalizumab at 300 mg alongside methotrexate in people with moderate to severe rheumatoid arthritis. The registry lists enrollment as 299, a start date of 2004-05, a primary completion date of 2005-02, and status as terminated.

The primary outcome was the number meeting the ACR20 response definition at Month 6. The sponsor-reported analysis used the Cochran-Mantel-Haenszel method and reported p = 0.089. A recalculated unadjusted risk difference was 0.100, with an interval from -0.015 to 0.214. ACR50 and ACR70 were listed as secondary outcomes at Month 6.

The registry record does not report the reason for termination, the original sample-size justification, missing-data handling, analysis population, or a full multiplicity plan.