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 of Tocilizumab and Methotrexate in Combination or as Monotherapy in Treatment-Naïve Patients With Early Rheumatoid Arthritis (NCT01034137), a randomized phase 3 study. The primary outcome is Percentage of Participants Achieving Sustained Remission Rate At Week 104.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01034137 |
| Phase | Phase 3 |
| Condition | Rheumatoid Arthritis |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 317 |
| Arms in the primary outcome | 3 |
| Lead sponsor | Hoffmann-La Roche |
| Results posted | Yes |
2. Clinical Question
Population
The study concerned treatment-naïve participants with early rheumatoid arthritis. The primary outcome population was the intent-to-treat population, defined in the registry record as randomized participants who received at least one dose of an infusion or capsules and completed at least one post-baseline efficacy measurement. The record reports enrollment of 317 participants.
Intervention
One group received intravenous tocilizumab at 8 mg/kg every four weeks, for a maximum of 26 infusions, together with weekly oral methotrexate. Methotrexate began at 10 mg/week and could increase in 5 mg steps to a maximum of 30 mg/week. The dose was taken on one designated day of the week.
Comparator
The other groups received tocilizumab with matching placebo methotrexate, or methotrexate with matching placebo tocilizumab. Thus, the comparisons address combination treatment versus each monotherapy, as well as tocilizumab versus methotrexate monotherapy. The study used matching placebos to support blinding.
Primary question
At Week 104, what proportion met the registry’s definition of sustained remission in each group, and how did the groups compare? Sustained remission required DAS28 below 2.6 during at least 23 weeks, no more than 4 swollen joints at the specified assessment, and allowed a limited number of in-between DAS28 values from 2.6 to 3.2.
The central statistical distinction is between a remission status measured at one visit and a sustained outcome requiring remission over time. The record also lists secondary measures of remission timing, duration, and disease activity. Those outcomes broaden the description of response but do not replace the primary comparison at Week 104.
3. Trial Design
This was a completed, randomized, double-blind, parallel-group, phase 3 study with a placebo-controlled design. It enrolled 317 participants with early rheumatoid arthritis who were naïve to disease-modifying antirheumatic drugs and biological treatment. The registry record identifies Hoffmann-La Roche as the sponsor. The recorded start was 2010-01, and primary completion was 2014-09.
Participants were assigned to tocilizumab plus methotrexate, tocilizumab plus placebo methotrexate, or methotrexate plus placebo tocilizumab. Tocilizumab was administered intravenously at 8 mg/kg every four weeks, for a maximum of 26 infusions. Methotrexate was given orally each week, beginning at 10 mg and increasing in 5 mg steps up to 30 mg. Matching placebo was used for the treatment not assigned in the monotherapy groups. The registry summary describes anticipated time on study treatment as 2 years and states a target sample size of 300; the actual recorded enrollment was 317.
Randomization is intended to make treatment groups comparable on average, while double blinding and matching placebos can reduce the influence of treatment knowledge on participant experience and outcome assessment. These are general design purposes, not guarantees that every source of bias is eliminated. Details such as the randomization procedure, allocation concealment, stratification factors, and the practical implementation of blinding are not reported in the registry record.
The primary endpoint was the percentage achieving sustained remission at Week 104. The sponsor’s reported analyses compare each treatment group with another using a Cochran-Mantel-Haenszel method and risk ratios. The registry also includes secondary outcomes, including measures of remission duration and DAS28 remission. Detailed protocol information about the planned analysis hierarchy, handling of missing observations, and sample-size justification is 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.
Before assignment: Of 360 participants, 43 failed screening.
Overall Study
| Stage | Tocilizumab + Methotrexate | Tocilizumab + Placebo Methotrexate | Methotrexate + Placebo Tocilizumab |
|---|---|---|---|
| STARTED | 106 | 103 | 108 |
| COMPLETED | 78 | 81 | 78 |
| NOT COMPLETED | 28 | 22 | 30 |
Reasons for not completing this period:
| Reason | Tocilizumab + Methotrexate | Tocilizumab + Placebo Methotrexate | Methotrexate + Placebo Tocilizumab |
|---|---|---|---|
| Adverse Event | 9 | 10 | 8 |
| Withdrawal by Subject | 4 | 3 | 3 |
| Lack of Efficacy | 9 | 4 | 13 |
| Protocol Violation | 2 | 2 | 1 |
| Refused treatment or did not cooperate | 2 | 0 | 1 |
| Administrative or other | 2 | 3 | 4 |
Analysis population for the primary outcome, as defined in the registry: The intent to treat (ITT) population consisted of all participants who were randomized and received at least one dose of TCZ/placebo infusion or MTX/placebo capsules and performed at least one post-baseline efficacy measurement.
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.
| Characteristic | Unit | Tocilizumab + Methotrexate | Tocilizumab + Placebo Methotrexate | Methotrexate + Placebo Tocilizumab | Total |
|---|---|---|---|---|---|
| Participants analysed | 106 | 103 | 108 | 317 | |
| Age, Categorical: <=18 years | Participants | 0 | 0 | 0 | 0 |
| Age, Categorical: Between 18 and 65 years | Participants | 85 | 79 | 87 | 251 |
| Age, Categorical: >=65 years | Participants | 21 | 24 | 21 | 66 |
| Age, Continuous | years | 53.1 (SD 11.8) | 55.0 (SD 12.9) | 52.2 (SD 13.7) | 53.4 (SD 12.8) |
| Sex: Female, Male: Female | Participants | 65 | 78 | 69 | 212 |
| Sex: Female, Male: Male | Participants | 41 | 25 | 39 | 105 |
6. Primary Endpoint
The registry lists the primary outcome as Percentage of Participants Achieving Sustained Remission Rate At Week 104, measured over Week 104.
| 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 achieving sustained remission at Week 104. The registry defines sustained remission using DAS28 below 2.6 during at least 23 weeks, together with no more than 4 swollen joints at the Week 24 assessment of remission. The definition allows up to 2 in-between DAS28 values between 2.6 and 3.2. DAS28 combines joint counts, an acute-phase response measure, and the participant’s global assessment of disease activity. Its scale ranges from 0 to 10, with higher scores indicating worsening; the registry identifies a score below 2.6 as remission.
A sustained endpoint is designed to capture persistence of a defined state rather than a single favorable measurement. That can make the outcome clinically and statistically different from a remission measure at one visit: a participant must satisfy a pattern over time, subject to the endpoint’s stated exceptions. The percentage is a binary-outcome summary: each participant either meets the definition or does not, and the group result is the proportion meeting it.
The primary analysis population is defined in the registry record as randomized participants who received at least one dose of study infusion or capsules and had at least one post-baseline efficacy measurement. This definition is important when interpreting the denominators. It is not simply a statement that every randomized participant contributed a primary outcome. The registry does not report the detailed method used to handle missing Week 104 or intervening measurements.
7. Results Posted in the Registry
- Tocilizumab + Methotrexate: 85.8% (91/106) versus 83.5% (86/103) on control; risk difference 2.4 percentage points (95% CI -7.4 to 12.1), risk ratio 1.03 (0.92–1.15); unadjusted two-proportion z-test p = 0.637.
- Methotrexate + Placebo Tocilizumab: 44.4% (48/108) versus 83.5% (86/103) on control; risk difference -39.1 percentage points (95% CI -50.8 to -27.3), risk ratio 0.53 (0.42–0.67); unadjusted two-proportion z-test p = <0.001.
Risk difference: Tocilizumab + Methotrexate
95% CI: -7.4 to 12.1 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 |
|---|---|---|---|---|
| Mean Duration of First Sustained Remission | Continuous Endpoint | Mean difference | 0.85 (-6.73 to 8.43) | 14,431 per arm |
| Mean Duration of First Disease Activity Score 28 Remission | Continuous Endpoint | Mean difference | 5.98 (-2.52 to 14.48) | 432 per arm |
Mean Duration of First Sustained Remission
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Tocilizumab + Methotrexate: mean 65.85 versus 65.00 on control; difference 0.85 (95% CI -6.73 to 8.43), standardized effect d = 0.03; z-test p = 0.826.
- Methotrexate + Placebo Tocilizumab: mean 52.90 versus 65.00 on control; difference -12.10 (95% CI -20.92 to -3.28), standardized effect d = -0.49; z-test p = 0.007.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Tocilizumab + Methotrexate and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Methotrexate + Placebo Tocilizumab than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Mean Duration of First Disease Activity Score 28 Remission
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Tocilizumab + Methotrexate: mean 42.99 versus 37.01 on control; difference 5.98 (95% CI -2.52 to 14.48), standardized effect d = 0.19; z-test p = 0.168.
- Methotrexate + Placebo Tocilizumab: mean 20.49 versus 37.01 on control; difference -16.52 (95% CI -24.00 to -9.04), standardized effect d = -0.60; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Tocilizumab + Methotrexate and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Methotrexate + Placebo Tocilizumab than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The registry lists a broad set of secondary outcomes, including remission timing, remission duration, DAS28 remission at multiple visits, cumulative remission, changes in DAS28, and changes in Clinical Disease Activity Index. Forty-one secondary outcomes are posted, but the registry record does not include a reported inferential analysis for the two duration comparisons discussed in the posted numerical results.
Across those duration measures, the descriptive pattern places the tocilizumab-containing groups above the methotrexate-alone group, while the two tocilizumab-containing groups are closer to one another. This general pattern is directionally consistent with the primary endpoint’s sponsor-reported comparisons against methotrexate alone and with the more limited contrast between the combination and tocilizumab-alone groups. It is contextual support, not an independent confirmation of the primary result: the secondary endpoints measure different features, may involve different analysis populations, and have their own uncertainty.
Secondary outcomes are often numerous and can be exploratory. When many outcomes or comparisons are examined, some apparently notable results can arise by chance even if there is no underlying difference. Adjustment procedures or a prespecified hierarchy can control aspects of that problem, but whether they were used is not reported in the registry record. The posted unadjusted secondary comparisons therefore carry less weight than a clearly prespecified primary analysis with a documented multiplicity strategy.
The record’s list of secondary measures also does not establish that every listed result was measured or analyzed in the same way. Timing, duration, and visit-specific remission are related but not interchangeable outcomes. The registry does not report sufficient detail about the planned testing hierarchy, missing-data handling, or which secondary hypotheses were confirmatory. The secondary findings are best read as additional descriptive context rather than as a collection of separate definitive conclusions.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Median Time to First Sustained Remission
- Mean Duration of First Sustained Remission
- Number of Participants Achieving Disease Activity Score 28 Remission at Weeks 12, 24, 52, and 104
- Median Time to First Disease Activity Score 28 Remission
- Percentage of Participants With Cumulative Remission Rate at Weeks 12, 24, 52, and 104
- Mean Duration of First Disease Activity Score 28 Remission
- Absolute Change From Baseline in Disease Activity Score 28 at Weeks 12, 24, 52, and 104
- Median Change From Baseline in Clinical Disease Activity Index Score at Weeks 24, 52, and 104
9. Statistical Interpretation
At Week 104, the posted sustained remission percentages were 85.8% for tocilizumab plus methotrexate, 83.5% for tocilizumab plus placebo methotrexate, and 44.4% for methotrexate plus placebo tocilizumab. The corresponding group sizes reported for this endpoint were 106, 103, and 108. These are descriptive group results; interpretation of the comparisons also depends on the analysis method and uncertainty.
The sponsor’s reported Cochran-Mantel-Haenszel analysis gave a risk ratio of 1.030 for tocilizumab plus methotrexate versus tocilizumab alone, with a 95% confidence interval from 0.915 to 1.160 and p = 0.616. For tocilizumab alone versus methotrexate alone, the reported risk ratio was 1.855, with a 95% confidence interval from 1.481 to 2.323 and p < 0.001. For combination treatment versus methotrexate alone, the reported risk ratio was 1.996, with a 95% confidence interval from 1.589 to 2.506 and p < 0.001.
These analyses show different patterns across the comparisons. The reported comparison between the two groups receiving tocilizumab has a confidence interval that includes a risk ratio of 1, and its p-value is not small by conventional thresholds. The reported comparisons of either tocilizumab-containing group with methotrexate alone have confidence intervals above 1 and p-values below 0.001. A risk ratio above 1 means the endpoint occurred more often in the numerator group than in the denominator group, given the analysis’s stated ordering. These statistical results describe the posted endpoint and do not, by themselves, establish why the groups differed or what the result means for any individual.
Simple unadjusted recalculations from the posted group summaries are not identical to the sponsor’s reported analyses in all respects. The registry record flags a discrepancy, so the sponsor’s own analysis takes precedence. The recalculations are best treated as a check based on the displayed summaries, not as a replacement for the reported analysis. They cannot reproduce details of the sponsor’s analysis that are not documented in the registry record.
The endpoint’s sustained definition adds useful information beyond a snapshot, but it also depends on repeated observations and the rule for handling intervening values. The registry does not report enough detail to assess the impact of missing observations, protocol deviations, or any analysis choices beyond the population definition and methods named in the reported comparisons. Accordingly, the most defensible reading is a description of the recorded proportions and sponsor-reported relative comparisons, with those documentation limits kept in view.
10. Statistical Methods Explained
Different statistical summaries answer different questions. The endpoint is binary at the participant level: the participant either satisfied the sustained-remission definition or did not. Group percentages describe the observed frequency. Risk ratios compare those frequencies on a relative scale, while risk differences compare them on an absolute scale. Confidence intervals describe the range of values reasonably compatible with the data and the stated calculation method. A p-value describes how compatible the observed data are with a specified null hypothesis under the analysis assumptions; it is not the probability that the null hypothesis is true.
What does the sponsor’s risk ratio represent?
The sponsor reported risk ratios using the Cochran-Mantel-Haenszel method. In general, a risk ratio divides the event frequency in one group by that in the comparison group. A value of 1 corresponds to equal frequencies on this relative scale; a value above 1 indicates a higher frequency in the numerator group, and a value below 1 indicates a lower frequency. The analysis method named in the registry is commonly used to combine comparisons across strata. The registry record does not identify the strata or provide enough detail to reconstruct the exact analysis.
The sponsor’s reported ratio for combination treatment versus methotrexate alone was 1.996, with a 95% confidence interval from 1.589 to 2.506. For tocilizumab alone versus methotrexate alone, the reported ratio was 1.855, with a 95% confidence interval from 1.481 to 2.323. For combination treatment versus tocilizumab alone, it was 1.030, with a 95% confidence interval from 0.915 to 1.160. These are relative comparisons, not percentage-point differences. Their interpretation depends on the group ordering used in the reported analysis.
How do the recalculations differ?
The recalculated comparisons use unadjusted summaries of the posted group results. An unadjusted comparison does not incorporate stratification or other model features unless those are explicitly part of the method. The recalculated output includes risk differences and unadjusted p-values. The sponsor instead reported Cochran-Mantel-Haenszel risk ratios. Because the registry record flags a discrepancy, the sponsor’s own analysis takes precedence; a recalculation from summary values should not be represented as a correction to that analysis.
In general, absolute and relative effects can present the same data in different ways. A risk difference is the event frequency in one group minus the frequency in another. A risk ratio expresses one frequency relative to the other. Neither scale is universally sufficient: the absolute scale describes the gap in event frequencies, and the relative scale describes their proportional relation. The registry’s sponsor analyses are on the relative scale. The simple recalculations are not the sponsor’s reported inferential analysis.
What do the confidence intervals and p-values add?
A confidence interval conveys uncertainty around an estimate. A narrow interval indicates greater precision than a wide interval, under the method used; it does not remove possible bias or limitations in outcome measurement. For the reported risk ratios, intervals that include 1 are compatible with equal event frequencies on the relative scale at the corresponding confidence level. Intervals entirely above 1 are compatible with a higher event frequency in the numerator group under that analysis. These statements concern compatibility with a statistical value, not proof of a causal mechanism.
The reported p-values are 0.616 for combination treatment versus tocilizumab alone, and < 0.001 for each comparison with methotrexate alone. A small p-value indicates that data at least as incompatible with the null hypothesis would be unusual under that null and the model assumptions. It does not measure the size or importance of an effect, and it does not account automatically for multiple comparisons. The registry record does not report whether the p-values were adjusted for multiplicity.
How should continuous secondary outcomes be read?
Two posted secondary outcomes report mean durations in weeks, with standard deviations. A mean describes the arithmetic average among the participants included for that outcome; the standard deviation describes variability among individual observations around that average. For mean duration of first sustained remission, the reported means were 65.85 weeks for combination treatment, 65.0 weeks for tocilizumab alone, and 52.9 weeks for methotrexate alone. For mean duration of first DAS28 remission, the means were 42.99 weeks, 37.01 weeks, and 20.49 weeks, respectively. These outcomes have their own denominators and should not be assumed to include the same participants as the primary endpoint.
A mean difference compares group averages. Its confidence interval indicates uncertainty in that difference under the calculation, and a value of zero represents no mean difference. The posted recalculations are unadjusted. Their p-values are not a substitute for a prespecified sponsor analysis, and the registry record contains no reported analyses for these secondary comparisons. Standard deviations also matter: similar means can coexist with substantial variation among participants.
What are the planning illustrations?
The planning calculations use the observed effect as a reference and show hypothetical sample sizes for detecting specified fractions of that effect. General statistical planning uses assumptions about the target effect, allocation, variability, significance level, and analysis method. The listed illustration assumes a two-sided significance level of 0.05, equal allocation between the two groups, and a normal approximation. It considers 100%, 75%, and 50% of the observed effect. These are planning illustrations, not the original trial’s design justification; the trial’s own design assumptions are not reported in the registry record.
11. Confidence Intervals and Precision
Precision concerns how much uncertainty surrounds an estimate. For the primary endpoint, the sponsor’s 95% confidence interval for combination treatment versus methotrexate alone runs from 1.589 to 2.506 on the risk-ratio scale. For tocilizumab alone versus methotrexate alone, it runs from 1.481 to 2.323. Both intervals lie above 1, which is consistent with the reported p-values below 0.001. The interval for combination treatment versus tocilizumab alone runs from 0.915 to 1.160 and includes 1; the sponsor-reported p-value is 0.616.
An interval is more informative than a single point estimate because it shows a range of values compatible with the observed data under the analysis. It does not say that every value in the interval is equally likely, nor does it account for systematic error, missing data, or unreported analytic decisions. Confidence intervals are conditional on the method and its assumptions. The registry record names the Cochran-Mantel-Haenszel method but does not describe the strata or all implementation details.
The observed group percentages also have sampling uncertainty. The registry record gives the group sizes, but the sponsor’s displayed risk-ratio intervals are the inferential intervals to prioritize for the reported analysis. Unadjusted recalculations from summary statistics can yield different estimates or p-values because they do not necessarily reproduce the sponsor’s method. The record flags a discrepancy, so those recalculations should not be treated as a competing sponsor result.
Precision is not the same as importance. A precise estimate may describe a small difference, and a less precise estimate may still be compatible with a range of effects. Nor does an interval that excludes a null value establish that the endpoint captures every aspect of disease activity. The primary result is specific to the recorded sustained-remission definition at Week 104 and the population included in the analysis. Broader claims require evidence beyond this endpoint and its confidence intervals.
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 | 3,676 | 4,921 |
| 75% of the observed effect | 6,638 | 8,886 |
| 50% of the observed effect | 15,165 | 20,301 |
The sample-size illustrations are planning scenarios based on the observed effect, not a record of how the trial was originally designed. For these binary and continuous comparisons, the displayed figures are participants per arm. The record’s planning note also describes a different convention for time-to-event calculations: those figures would be total events. The outcomes discussed in these comparisons are not presented as time-to-event planning calculations.
The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each scenario uses a stated fraction of the observed effect: 100%, 75%, or 50%. The 80% power column means the hypothetical per-arm enrollment that, under those assumptions and effect size, would give an 80% chance of rejecting the null hypothesis if that effect were the true one. The 90% power column expresses the corresponding planning target for a 90% chance. These are design concepts, not measures of what happened in the completed study.
Smaller effects require more participants to detect with the same planned power and significance level, all else equal. This is why the rows using a smaller fraction of the observed effect generally call for larger planned groups. The illustration can help readers understand how sensitive a future study’s size would be to its target effect, but the observed effect is an uncertain estimate and may not be a reliable target for a new trial.
The trial’s own sample-size justification and original design assumptions are not reported in the registry record. The registry summary gives a target sample size of 300, while recorded enrollment was 317; those details do not establish the assumptions used to set the target. These figures are not observed power. Observed outcomes and confidence intervals describe the data; the planning display describes hypothetical future study sizes under stated 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 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 = 0.835; treatment proportion p1 = 0.858; average p̄ = 0.847.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5095 = 0.9986.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5092 = 0.4286.
- n = (0.9986 + 0.4286)2 / (0.0235)2 = 3,675.7, rounded up to 3,676 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 <- 0.83495145631068 # control proportion
p1 <- 0.858490566037736 # 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(1034137)
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 = 3,676 (80% power), 4,921 (90% power)
75% of observed effect: n per arm = 6,638 (80% power), 8,886 (90% power)
50% of observed effect: n per arm = 15,165 (80% power), 20,301 (90% power)
power.prop.test: 3675.7
Simulated power at n = 3,676 per arm: 0.803 (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 |
|---|---|---|---|
| Cochran-Mantel-Haenszel | Risk Ratio (RR) 1.996 | 1.589 to 2.506 | < 0.001 |
| Cochran-Mantel-Haenszel | Risk Ratio (RR) 1.855 | 1.481 to 2.323 | < 0.001 |
| Cochran-Mantel-Haenszel | Risk Ratio (RR) 1.030 | 0.915 to 1.160 | 0.616 |
The sponsor’s reported primary comparisons use the Cochran-Mantel-Haenszel method and present risk ratios with 95% confidence intervals and p-values. Those are the analyses to use when describing the sponsor’s inferential results. The registry reports a ratio of 1.030 for combination treatment versus tocilizumab alone, 1.855 for tocilizumab alone versus methotrexate alone, and 1.996 for combination treatment versus methotrexate alone.
Unadjusted recalculations use posted group summaries and yield risk differences and unadjusted p-values. They do not necessarily reproduce the sponsor’s stratified method or other details that may have been part of the sponsor’s analysis. The registry record flags a discrepancy, so the sponsor’s own analysis takes precedence. The recalculations are useful as a separate check of the summary data, but they should not be presented as if they were the sponsor’s stated analysis or as a correction to it.
The registry does not report enough detail to determine the source of every difference. In particular, the strata and full statistical analysis plan are not reported in the registry record. That limitation makes it inappropriate to infer that any particular analytic choice explains the discrepancy. Interpretations should therefore identify which result is sponsor-reported and avoid blending it with the unadjusted recalculation.
15. Multiplicity, Missing Data and Analysis Populations
The primary endpoint is identified, but the registry record does not report a complete statistical analysis plan or a formal hierarchy for the many secondary measures and pairwise comparisons. It also does not report whether the sponsor adjusted secondary p-values for multiplicity. This matters because testing multiple outcomes can increase the chance of obtaining one or more small p-values even when the corresponding null hypotheses are true. A prespecified testing sequence or adjustment can address that issue, but the record does not establish that either approach was used.
The primary population is described as the intent-to-treat population comprising randomized participants who received at least one dose of study infusion or capsules and performed at least one post-baseline efficacy measurement. That definition is available, but it is narrower than an assertion that every randomized participant contributed to the endpoint. The registry does not report the number excluded from this population or the reasons for any exclusions.
The sustained-remission definition requires information over time, including the handling of in-between DAS28 values. Missing visits or measurements could affect whether a participant satisfies such a rule. The specific methods for missing Week 104 measurements, missing intervening assessments, treatment discontinuation, protocol deviations, or imputation are not reported in the registry record. No assumptions about these procedures should be inferred from the endpoint definition alone.
Interim analyses, stopping rules, and any associated adjustment of significance thresholds are not reported in the registry record. Details of randomization, allocation concealment, stratification factors, and subgroup analysis plans are likewise not reported. These omissions do not demonstrate that procedures were absent; they limit what can be verified from the record. The sponsor’s reported method is named, but the details needed to reproduce it are not all available.
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 |
|---|---|---|---|
| Tocilizumab + Methotrexate | 16 | 106 | 15.1% |
| Tocilizumab + Placebo Methotrexate | 19 | 103 | 18.4% |
| Methotrexate + Placebo Tocilizumab | 13 | 108 | 12.0% |
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 |
|---|---|
| Tocilizumab + Methotrexate | 105 of 106 |
| Tocilizumab + Placebo Methotrexate | 99 of 103 |
| Methotrexate + Placebo Tocilizumab | 106 of 108 |
Most frequent serious adverse event terms
| Event term | Organ system | Tocilizumab + Methotrexate | Tocilizumab + Placebo Methotrexate | Methotrexate + Placebo Tocilizumab |
|---|---|---|---|---|
| Pneumonia | Infections and infestations | 0 of 106 | 2 of 103 | 2 of 108 |
| Osteoarthritis | Musculoskeletal and connective tissue disorders | 1 of 106 | 2 of 103 | 0 of 108 |
| Cholelithiasis | Hepatobiliary disorders | 3 of 106 | 0 of 103 | 0 of 108 |
| Myocardial infarction | Cardiac disorders | 1 of 106 | 1 of 103 | 0 of 108 |
| Wrist fracture | Injury, poisoning and procedural complications | 1 of 106 | 1 of 103 | 0 of 108 |
| Bursitis infective | Infections and infestations | 1 of 106 | 0 of 103 | 0 of 108 |
| Cystitis | Infections and infestations | 0 of 106 | 0 of 103 | 1 of 108 |
| Gastroenteritis | Infections and infestations | 1 of 106 | 0 of 103 | 0 of 108 |
| Helicobacter gastritis | Infections and infestations | 0 of 106 | 1 of 103 | 0 of 108 |
| Herpes zoster | Infections and infestations | 1 of 106 | 0 of 103 | 0 of 108 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Tocilizumab + Methotrexate | Tocilizumab + Placebo Methotrexate | Methotrexate + Placebo Tocilizumab |
|---|---|---|---|---|
| Nasopharyngitis | Infections and infestations | 38 of 106 | 40 of 103 | 37 of 108 |
| Nausea | Gastrointestinal disorders | 27 of 106 | 20 of 103 | 48 of 108 |
| Fatigue | General disorders | 30 of 106 | 25 of 103 | 34 of 108 |
| Alanine aminotransferase increased | Investigations | 25 of 106 | 16 of 103 | 28 of 108 |
| Headache | Nervous system disorders | 20 of 106 | 15 of 103 | 22 of 108 |
| Diarrhoea | Gastrointestinal disorders | 19 of 106 | 12 of 103 | 20 of 108 |
| Cough | Respiratory, thoracic and mediastinal disorders | 14 of 106 | 10 of 103 | 18 of 108 |
| Influenza | Infections and infestations | 18 of 106 | 13 of 103 | 10 of 108 |
| Dizziness | Nervous system disorders | 12 of 106 | 12 of 103 | 17 of 108 |
| Mouth ulceration | Gastrointestinal disorders | 15 of 106 | 12 of 103 | 5 of 108 |
Serious events with the highest arm-level rate: cholelithiasis (2.8%), pneumonia (1.9%), osteoarthritis (1.9%), helicobacter gastritis (1.0%), osteomyelitis (1.0%).
The registry reports serious adverse events for 16 of 106 participants in the tocilizumab-plus-methotrexate group, 19 of 103 participants in the tocilizumab-plus-placebo-methotrexate group, and 13 of 108 participants in the methotrexate-plus-placebo-tocilizumab group. These are participant counts with serious adverse events and their corresponding group denominators. They should be read as descriptive counts, not as a complete safety comparison or as evidence about causation.
The registry also reports other adverse events affecting 105 of 106 participants, 99 of 103 participants, and 106 of 108 participants, respectively. The serious-event terms listed as most frequent are cholelithiasis at 2.8%, pneumonia at 1.9%, osteoarthritis at 1.9%, Helicobacter gastritis at 1.0%, osteomyelitis at 1.0%, and pelvic infection at 1.0%. The record does not specify arm-specific counts for those listed terms in the information.
Death counts are not reported in the registry record. The adverse-event figures do not, by themselves, describe event timing, duration, relatedness to treatment, exposure time, or the statistical uncertainty around between-group differences. They provide a limited summary of reported safety events and should not be used to infer an overall safety ranking.
17. What the Result Does, and Does Not, Mean
The primary result describes how often participants in each analyzed group met a particular sustained-remission definition at Week 104. The sponsor’s reported analyses show risk ratios above 1 for both tocilizumab-containing groups compared with methotrexate alone, with 95% confidence intervals above 1 and p-values below 0.001. The reported comparison between combination treatment and tocilizumab alone is much closer to 1, and its confidence interval includes 1. These statements concern the endpoint and comparisons recorded in the registry.
The result does not establish that every participant experienced the group average or that the same pattern applies to outcomes not measured by this endpoint. It does not explain the mechanism behind a group difference. It also does not prove that an observed difference is free from bias, missing-data effects, or unreported analysis choices. The registry’s information about analysis populations and missing-data methods is limited.
A statistical comparison is not a personal prediction. Group percentages and risk ratios summarize outcomes across participants; they do not determine what will happen for a particular person. The results also do not substitute for evidence on every aspect of treatment, including outcomes that are not reported in the registry record. No treatment recommendation follows from these statistics alone.
The primary endpoint’s requirement for persistence makes it distinct from a single-visit remission measure. The secondary outcomes extend the picture to other disease activity and remission features, but the record does not establish a multiplicity plan for those measures. Their results should therefore be interpreted with more caution than the designated primary comparison. Overall, the registry supports a statistical description of the recorded endpoint and sponsor analyses, while leaving important details of conduct and analysis undocumented.
18. Why This Trial Matters Statistically
Statistically, the trial is informative because it includes three randomized groups that permit more than one direct comparison: combination treatment against each monotherapy, and the two monotherapies against each other. The matching placebo design and double blinding are relevant safeguards against some forms of expectation and assessment bias. The primary outcome also asks about sustained remission rather than a single measurement, making the estimand more specific to persistence over time.
The pattern of sponsor-reported primary comparisons is not uniform across all contrasts. The two tocilizumab-containing groups have a reported risk ratio close to 1 with a confidence interval that includes 1, whereas both comparisons with methotrexate alone have reported confidence intervals above 1. This illustrates why a study with several groups should not be reduced to a single claim that one regimen is “better” across every comparison. Each estimate addresses a distinct contrast and has its own uncertainty.
The record also illustrates why the reported analysis method matters. Sponsor-reported Cochran-Mantel-Haenszel risk ratios and simple unadjusted recalculations are not interchangeable. When a discrepancy is flagged, clear separation of the sponsor’s analysis from summary-statistic recalculation preserves the distinction between an analysis reported by the trial sponsor and a secondary check.
Finally, the case highlights the importance of documenting multiplicity, missing-data methods, and analysis populations. A long list of outcomes can add useful context, but without a reported hierarchy and missing-data strategy, the evidential weight of secondary comparisons is harder to judge. The registry provides a useful record of estimates and design features, while also demonstrating where fuller protocol and analysis documentation is needed for independent interpretation.
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 limitations follow from what the registry record does not document. Although it names the Cochran-Mantel-Haenszel method for the sponsor’s primary comparisons, it does not report the strata, the full statistical analysis plan, or enough detail to reproduce the sponsor’s calculations. The record flags a discrepancy between sponsor analyses and unadjusted recalculations, but it does not establish its source. The sponsor-reported results therefore take precedence, while the reason for the difference remains unclear from the registry record.
The primary population definition requires receipt of at least one dose and at least one post-baseline efficacy measurement. The record does not report how many randomized participants fell outside that definition or why. It does not describe the method used for missing Week 104 data or intervening measurements, although these observations are relevant to the sustained-remission rule. It also does not report how discontinuations or protocol deviations were handled.
The registry lists many secondary measures but does not report a multiplicity strategy or a testing hierarchy. This limits the strength of conclusions drawn from unadjusted secondary findings. The available numerical secondary results include duration outcomes, but the sponsor-reported analysis fields for those comparisons are empty. Their posted summary values cannot be treated as a substitute for a documented confirmatory analysis.
Safety information is also bounded: death counts are not reported in the registry record, and the listed serious-event terms lack arm-specific counts in the record information summarized. The registry does not provide all details needed to compare event timing, exposure, or relatedness. These are reporting limitations, not evidence that the corresponding information was never collected.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: A Study of Tocilizumab and Methotrexate in Combination or as Monotherapy in Treatment-Naïve Patients With Early Rheumatoid Arthritis — NCT01034137.
- Registry record last updated 2016-07-11; status last verified 2016-06.
- Results first posted 2016-07-11.
- 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
NCT01034137 is a completed randomized, double-blind, parallel-group phase 3 study sponsored by Hoffmann-La Roche. It enrolled 317 treatment-naïve participants with early rheumatoid arthritis and compared tocilizumab plus methotrexate, tocilizumab alone, and methotrexate alone using matching placebos. The recorded start was 2010-01, and primary completion was 2014-09.
The primary endpoint was the percentage achieving sustained remission at Week 104. Sponsor-reported analyses found risk ratios above 1 for both tocilizumab-containing groups compared with methotrexate alone; the comparison between the two tocilizumab-containing groups was close to 1 and had a confidence interval including 1. The registry record flags a discrepancy, so sponsor analyses take precedence over unadjusted recalculations.
Important details—including the original sample-size assumptions, missing-data methods, multiplicity strategy, and full analysis plan—are not reported in the registry record. Secondary and safety results provide additional context but have their own reporting and interpretation limits.