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Rheumatoid Arthritis Phase 2 Binary Endpoint NCT01285310

Study of Apremilast to Evaluate the Safety and Effectiveness for Patients With Rheumatoid Arthritis: Complete Statistical Analysis

This analysis examines a randomized, placebo-controlled Phase 2 trial of apremilast in people with active rheumatoid arthritis and an inadequate response to methotrexate. The primary result is the Week 16 ACR 20 response, with secondary outcomes and safety results offering additional context.

Trial start: 2010-12-09  ·  Enrollment: 237  ·  Sponsor: Amgen
Scope of this record

This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.

1. Trial at a Glance

This page covers the registry results for Study of Apremilast to Evaluate the Safety and Effectiveness for Patients With Rheumatoid Arthritis (NCT01285310), a randomized phase 2 study. The primary outcome is Percentage of Participants With an American College of Rheumatology 20% Improvement (ACR 20) Response at Week 16.

237
Enrollment
Phase 2
3
Arms
In the primary outcome
-7.4 pts
Risk difference
Apremilast 20 mg
-21.7 to 7.0 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT01285310
PhasePhase 2
ConditionRheumatoid Arthritis
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment237
Arms in the primary outcome3
Lead sponsorAmgen
Results postedYes

2. Clinical Question

Population

Participants had active rheumatoid arthritis and an inadequate response to methotrexate. The primary analysis population was the full analysis set: participants randomized as specified in the protocol, excluding those randomized in error who did not receive any study drug. Participants who withdrew early or lacked enough information for a definitive response determination were also addressed in the endpoint definition, although the specific handling of their missing response data is not reported in the registry record.

Intervention

The study compared two apremilast doses: 20 mg and 30 mg. The registry record describes the trial as randomized, double-blind, and placebo-controlled. Further details about dose administration, adherence, or treatment duration are not reported in the registry record.

Comparator

Both apremilast groups were compared with placebo. The primary endpoint was assessed at Week 16. Secondary outcomes included measures at Week 16 and Week 24, but the posted record does not provide a complete account of how participants were managed after the study ended or how treatment exposure varied over time.

Primary question

The primary question was whether the percentage of participants meeting the ACR 20 response criteria at Week 16 differed between each apremilast dose and placebo. A response required at least 20% improvement in both tender and swollen joint counts, plus at least 20% improvement in at least three of five additional clinical and patient-reported measures. The registry reports response percentages and sponsor analyses for each comparison. These estimates describe the recorded results; they do not, on their own, establish why the trial ended or explain the complete benefit-risk profile.

3. Trial Design

The registry record describes a Phase 2, multicenter, randomized, double-blind, placebo-controlled, parallel-group study. It lists quadruple masking, meaning the record classifies four participant or study roles as masked, but the specific roles and procedures are not reported in the registry record. The randomized groups received apremilast 20 mg, apremilast 30 mg, or placebo. The stated enrollment was 237 participants.

The study concerned rheumatoid arthritis in participants who had an inadequate response to methotrexate. The primary endpoint was the percentage meeting the ACR 20 response definition at Week 16. Listed secondary endpoints included disability, physical functioning, disease activity, and joint-count measures, with assessments at Week 16 or Week 24. The registry lists 73 outcome measures and 80 analyses, and reports 72 secondary outcomes.

The record gives a start date of 2010-12-09 and a primary completion date of 2012-02-21. Its status is TERMINATED. The reason for termination, the date on which the decision was made, and whether the study ended early relative to its intended schedule are not reported in the registry record. The originally intended duration, planned enrollment rationale, randomization procedure, allocation ratio, and any stratification factors are also not reported in the registry record.

Enrollment totals and the denominators for individual outcomes are not identical in every reported analysis. For example, the primary endpoint groups include 79 placebo participants, 82 assigned to apremilast 20 mg, and 76 assigned to apremilast 30 mg. The registry's definition of the primary analysis population excludes participants randomized in error who received no study drug. Further details about participant flow, treatment discontinuation, and the analysis of incomplete records are not reported in the registry record. These details matter when interpreting how the posted outcome denominators relate to the enrollment total.

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.

Placebo Controlled Phase: Weeks 0-24

StagePlaceboApremilast 20 mgApremilast 30 mgPlacebo/Apremilast 20mg EEPlacebo / Apremilast 20 mg XO
STARTED79827600
COMPLETED70676100
NOT COMPLETED9151500

Reasons for not completing this period:

ReasonPlaceboApremilast 20 mgApremilast 30 mgPlacebo/Apremilast 20mg EEPlacebo / Apremilast 20 mg XO
Adverse Event34600
Lack of Efficacy17300
Non-compliance10200
Withdrawal by Subject33200
Lost to Follow-up01100
Other10100

Active Treatment Phase: Weeks 25-52

StagePlaceboApremilast 20 mgApremilast 30 mgPlacebo/Apremilast 20mg EEPlacebo / Apremilast 20 mg XO
STARTED063602742
COMPLETED031341723
NOT COMPLETED032261019

Reasons for not completing this period:

ReasonPlaceboApremilast 20 mgApremilast 30 mgPlacebo/Apremilast 20mg EEPlacebo / Apremilast 20 mg XO
Adverse Event02302
Lack of Efficacy04310
Withdrawal by Subject03022
Study Termination by sponsor02119615
Other01000
Non-compliance01110

Analysis population for the primary outcome, as defined in the registry: Full analysis set consisting of all participants randomized as specified in the protocol; participants who were randomized in error and did not receive any dose of study drug were excluded. Participants who withdrew early or who did not have sufficient data for a definitive determination of response status at Week 16 were counted as non-responders.

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: Full Analysis Set (FAS) The FAS consisted of all participants who were randomized as specified per protocol during the placebo controlled period.

CharacteristicUnitPlaceboApremilast 20 mgApremilast 30 mgTotal
Participants analysed798276237
Age, Continuousyears56.5 (SD 12.45)58.6 (SD 11.84)52.6 (SD 11.87)56.0 (SD 12.26)
Sex: Female, Male: FemaleParticipants626555182
Sex: Female, Male: MaleParticipants17172155
Duration of Rheumatoid Arthritis Diagnosisyears11.98 (SD 12.104)8.46 (SD 6.856)7.76 (SD 7.833)9.41 (SD 9.351)

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants With an American College of Rheumatology 20% Improvement (ACR 20) Response at Week 16, measured over Baseline and Week 16.

ElementRegistry entry
Result typeNumber
Measure of spreadnot applicable
Unitpercentage of participants
Endpoint classificationBinary Endpoint

The primary endpoint is the percentage of participants with an ACR 20 response at Week 16. ACR 20 is a composite response definition, not a single symptom score. To qualify, a participant had to meet all of the following: at least 20% improvement from baseline in the 68 tender-joint count; at least 20% improvement in the 66 swollen-joint count; and at least 20% improvement in at least three of five other measures. Those measures were pain, participant and physician global assessments of disease activity, physical function measured with the HAQ-DI, and C-reactive protein.

Composite response endpoints are used to represent improvement across several aspects of a condition rather than relying on one measurement alone. Requiring improvement in both joint counts and in several additional measures makes the response definition more demanding than improvement in only one component. At the same time, the result compresses diverse information into a responder or non-responder classification. It does not show how much each individual component changed, nor whether a participant who did not meet the full definition had meaningful change in some components.

The endpoint is reported as the percentage of participants meeting this definition in each randomized group. The registry reports 35.4% for placebo, 28.0% for apremilast 20 mg, and 34.2% for apremilast 30 mg. The comparison estimates and their uncertainty are more informative than considering these percentages alone because the observed group rates are subject to sampling variability. The endpoint definition describes what counted as a response; it does not establish that the response is important to every participant or explain the clinical relevance of changes in individual components.

7. Results Posted in the Registry

Risk difference: Apremilast 20 mg

-7.4

95% CI: -21.7 to 7.0 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals16.823.329.736.242.749.1Placebo (n=79)Apremilast 20 mg (n=82)Apremilast 30 mg (n=76)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Apremilast 20 mgApremilast 30 mg-25-16-8.100.138.3717risk difference (percentage points) vs control (95% CI)

8. Secondary Efficacy Endpoints

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

Secondary outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Change From Baseline in Health Assessment Questionnaire-Disability Index (HAQ-DI) at Week 16Continuous EndpointMean difference-0.01 (-0.15 to 0.14)52,584 per arm
Percentage of Participants With an American College of Rheumatology 20% Improvement (ACR 20) Response at Week 24Binary EndpointRisk difference-4.5 pts (-17.3 to 8.2)1,298 per arm
Change From Baseline in Health Assessment Questionnaire - Disability Index (HAQ-DI) at Week 24Continuous EndpointMean difference-0.01 (-0.15 to 0.13)26,219 per arm

Change From Baseline in Health Assessment Questionnaire-Disability Index (HAQ-DI) at Week 16

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Apremilast 20 mgApremilast 30 mg-0.27-0.18-0.10-0.010.080.17mean difference vs control (95% CI)

Percentage of Participants With an American College of Rheumatology 20% Improvement (ACR 20) Response at Week 24

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)Apremilast 20 mgApremilast 30 mg-20-12-3.984.061220risk difference (percentage points) vs control (95% CI)

Change From Baseline in Health Assessment Questionnaire - Disability Index (HAQ-DI) at Week 24

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Apremilast 20 mgApremilast 30 mg-0.34-0.24-0.14-0.040.060.16mean difference vs control (95% CI)

The secondary outcomes cover several related domains, including physical function, disease activity, and response status at a later assessment. This range can help describe whether the primary endpoint's pattern is accompanied by observations in other clinical measures. The outcomes are not independent repetitions of one question: they measure different constructs, use different scales, and are assessed at different time points. Taken together, they provide context, not a single unified estimate of treatment effect.

The registry's secondary results do not overturn the primary interpretation. The primary Week 16 ACR 20 comparisons have broad confidence intervals that include zero. Secondary findings may point in different directions across outcomes, but the registry record does not provide enough information about a prespecified hierarchy or multiplicity adjustment to interpret every result as confirmatory evidence. The outcome list is broad, and the record reports 80 analyses overall. In that setting, apparent differences among secondary estimates can arise from sampling variation as well as from real differences in the measured outcomes.

Unadjusted secondary results carry less weight than a clearly prespecified primary analysis because multiple outcomes and comparisons create more opportunities for chance patterns. General statistical explanation: multiplicity procedures can control or otherwise address the increased false-positive risk associated with examining many hypotheses. The applicable strategy for this trial is not reported in the registry record. The secondary results should therefore be treated as exploratory or descriptive unless a separate analysis plan establishes their intended inferential role.

Some sponsor-reported secondary analyses provide estimates without confidence intervals or p-values. For those results, readers cannot assess precision and statistical compatibility in the same way as for the primary endpoint. Recalculated comparisons based on posted summary statistics can provide a simple unadjusted perspective, but they may not match sponsor model-based estimates. Missing-data methods and the analysis population for each secondary outcome are not fully reported in the registry record, further limiting direct comparisons across outcomes. The overall pattern is best understood as additional context around the primary result rather than as a separate basis for a definitive conclusion.

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

9. Statistical Interpretation

Clinical Biostats interpretation

At Week 16, the registry reports an ACR 20 response in 35.4% of the placebo group, 28.0% of the apremilast 20 mg group, and 34.2% of the apremilast 30 mg group. These are observed percentages in the primary analysis population. The point estimates show that the recorded response percentage was lower with 20 mg than with placebo and similar with 30 mg to the placebo percentage. Those descriptive comparisons do not by themselves account for uncertainty.

For the 20 mg comparison, the sponsor-reported risk difference was -7.4 percentage points, with a 95% confidence interval from -27.1 to 7.0 and p = 0.313. For the 30 mg comparison, the reported risk difference was -1.2 percentage points, with a 95% confidence interval from -16.2 to 13.8 and p = 0.872. Both intervals include zero, the value corresponding to no difference in response percentages. The data therefore do not sharply distinguish either comparison from no difference, and the intervals also encompass differences in either direction.

The p-values describe how compatible the observed data are with a specified no-difference statistical model, subject to the analysis assumptions. They are not the probability that a treatment is effective or ineffective. The confidence intervals convey a range of estimates compatible with the data and model; their breadth indicates that the comparisons are imprecise. Neither the point estimates nor the p-values justify a categorical conclusion about the treatment effect.

The overall trial status is TERMINATED, but the reason for termination and its relationship, if any, to these results are not reported in the registry record. It would be inappropriate to infer a reason from the endpoint estimates, the p-values, or the status alone. The record also does not report whether an interim analysis occurred or whether the primary analysis was changed during the study.

Secondary outcomes extend the assessment to function and disease activity, but they do not replace the primary endpoint. Their results require caution because many outcomes and analyses are listed, and the record does not report a multiplicity-adjustment strategy. The secondary results are useful as descriptive context, while their evidential weight depends on the analysis plan, missing-data handling, and prespecification details that are not reported in the registry record. Overall, the posted primary results show uncertainty around both comparisons and should be read as estimates with limited precision rather than as definitive proof in either direction.

10. Statistical Methods Explained

The primary endpoint is binary: each participant either met the ACR 20 response criteria at Week 16 or did not. General statistical explanation: for a binary endpoint, a risk difference compares the proportion of responders in one group with the proportion in another. A risk difference of zero represents equal response proportions. A negative estimate for an apremilast-versus-placebo comparison indicates a lower observed response proportion in the apremilast group; a positive estimate indicates a higher observed proportion. The sponsor reports risk differences in percentage points.

What does the confidence interval add?

General statistical explanation: an estimate from a trial is subject to sampling variation because a different set of participants could produce a different estimate. A confidence interval communicates the uncertainty around an estimate under the method used. A broad interval indicates that the data are compatible with a wide range of effect sizes. If an interval for a risk difference includes zero, it includes no difference as one value compatible with the data and analysis assumptions. It does not prove that the true difference is zero.

For the Week 16 primary comparisons, the sponsor used a Chi-squared method and reported 95% confidence intervals. The placebo-versus-20 mg comparison has a reported risk difference of -7.4, interval -27.1 to 7.0, and p = 0.313. The placebo-versus-30 mg comparison has a reported risk difference of -1.2, interval -16.2 to 13.8, and p = 0.872. These reported intervals include zero. The registry also posts participant counts and group percentages, while recalculated comparisons use simple unadjusted methods based on the posted summaries. They are not a substitute for a fuller model-based analysis.

Why might the analysis method matter?

General statistical explanation: a simple unadjusted comparison treats the groups' observed summary data as the basis for estimating a difference. An adjusted analysis can account for prespecified baseline variables or other design features. Adjusted and unadjusted estimates can differ because they use different information or models. The registry's primary analysis is reported as a Chi-squared comparison, while the details of covariate adjustment, if any, are not reported in the registry record. The two primary sponsor estimates and their confidence intervals are the most direct record of the sponsor's reported analysis.

For continuous outcomes such as HAQ-DI, the registry reports group means and standard deviations, while the recalculated comparisons are unadjusted mean differences. General statistical explanation: a mean difference compares average changes between groups. Standard deviation describes variation among participants, whereas a confidence interval for a mean difference describes uncertainty in the estimated comparison. These quantities answer different questions. The sponsor's HAQ-DI results are described as least-squares mean differences, which are model-based estimates; their model details, confidence intervals, and p-values are not reported in the registry record. A simple difference calculated from posted group means should therefore not be treated as an identical estimand to a least-squares mean difference.

What does a p-value tell the reader?

General statistical explanation: a p-value measures how unusual the observed data, or data more extreme, would be under a specified null hypothesis and statistical model. It is not a measure of the size or clinical importance of an effect, and it is not the probability that the null hypothesis is true. The primary p-values are 0.313 and 0.872 in the sponsor-reported analyses. Interpretation should consider the estimates and intervals as well as the p-values, and should account for whether multiple comparisons were planned.

The record lists 73 outcome measures, 80 analyses, and 72 posted secondary outcomes. It does not report a multiplicity strategy, so the extent to which reported inferential results were adjusted for examining multiple outcomes or comparisons is not reported in the registry record. General statistical explanation: evaluating many outcomes can increase the chance that some results appear notable by chance. That is one reason to give the prespecified primary endpoint priority and to interpret secondary findings cautiously unless an analysis plan addresses multiplicity.

Missing outcome data also affect interpretation. The primary endpoint description refers to participants who withdrew early or lacked sufficient data for a definitive response determination, but the specific imputation or classification rule for those cases is not reported in the registry record. General statistical explanation: different missing-data assumptions can change estimated response rates, particularly if missingness is related to participants' outcomes. The registry record's stated analysis population definition is useful, but it does not fully specify the handling of every incomplete observation.

Finally, the comparison methods should be kept distinct from the study design. Randomization supports comparisons by reducing systematic differences between groups on average, but the registry record alone does not establish that all analysis assumptions were satisfied. The record does not report an interim-analysis plan, stopping boundary, detailed statistical analysis plan, or original sample-size justification. Those details cannot be inferred from the outcome results or from the planning illustrations.

11. Confidence Intervals and Precision

The precision of the primary comparisons is reflected in the reported 95% confidence intervals. For apremilast 20 mg versus placebo, the sponsor-reported risk difference is -7.4 percentage points, with an interval from -27.1 to 7.0. For apremilast 30 mg versus placebo, the difference is -1.2 percentage points, with an interval from -16.2 to 13.8. Each interval includes zero, so the record's results are compatible with no difference as well as with effects in either direction.

The intervals are wide relative to their point estimates. This means the trial's observed data do not locate the underlying comparison with high precision. The 20 mg interval includes a lower response percentage as well as a higher one relative to placebo; the same is true of the 30 mg interval. The uncertainty should not be reduced to a statement that the groups are equivalent. Equivalence would require a prespecified margin and an analysis designed to assess it, and such details are not reported in the registry record.

Confidence intervals are not guarantees that a particular range contains the true effect. General statistical explanation: under the assumptions of a method, a confidence interval procedure has a stated long-run coverage property across repeated studies. For an individual study, the interval describes uncertainty under that method and model. It does not include every possible source of uncertainty, such as uncertainty about missing-data assumptions, outcome selection, or model choice.

The reported p-values, 0.313 for 20 mg and 0.872 for 30 mg, are consistent with the broad uncertainty indicated by the intervals. The group percentages are useful descriptive summaries, but their separation should not be mistaken for a precise estimate of the difference. The registry does not report a confidence interval for every secondary analysis. Where uncertainty intervals are unavailable, the precision of those estimates cannot be evaluated from the posted results in the same way.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

Effect to detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect621831
75% of the observed effect1,1221,501
50% of the observed effect2,5613,428
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect5001,0002,0005,00010,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, pooled-variance normal approximation for two proportions. Counts were reconstructed from the posted percentages and arm sizes, so small rounding differences are possible. Calculated for the comparison: Apremilast 20 mg.

The planning figures are participants per arm for each comparison, not total events. The planning calculation assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses the observed effect as a reference and considers detecting the stated fraction of that effect. These are planning illustrations based on observed results, not the trial's original design calculations; the original sample-size assumptions and justification are not reported in the registry record.

The 80% power column describes the number of participants per arm that the illustration estimates would be needed to have an 80% chance of detecting the stated effect under those assumptions, if that effect were the true effect and the model assumptions held. The 90% power column represents a higher chance of detecting the same stated effect under the same assumptions, and therefore generally requires more participants per arm. Power is a design probability under assumptions, not a measure of how likely a result is to be true.

For the primary 20 mg comparison, planning for 100% of the observed effect gives 621 participants per arm for 80% power and 831 participants per arm for 90% power. Planning for 75% of the observed effect gives 1,122 participants per arm for 80% power and 1,501 participants per arm for 90% power. Planning for 50% of the observed effect gives 2,561 participants per arm for 80% power and 3,428 participants per arm for 90% power. The pattern illustrates that smaller effects require more participants to detect under the same assumptions.

These estimates are particularly sensitive to the observed effect. A small observed difference can produce very large planning counts when the calculation asks a future study to detect that same small difference. The figures should not be read as a recommendation or as a reconstruction of the intended trial size. They are not observed power: observed power is not a useful replacement for interpreting the estimates and their confidence intervals, and these figures are conditional planning illustrations rather than a description of what the trial achieved.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n = [ z1−α/2 √(2p̄(1−p̄)) + z1−β √(p0(1−p0) + p1(1−p1)) ]2 / (p1 − p0)2

n is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

  1. Control proportion p0 = 0.354; treatment proportion p1 = 0.280; average p̄ = 0.317.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6583 = 1.2902.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6562 = 0.5523.
  4. n = (1.2902 + 0.5523)2 / (-0.0739)2 = 620.9, rounded up to 621 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 <- 0.354430379746835                          # control proportion
p1 <- 0.280487804878049                          # 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(1285310)
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 = 621 (80% power), 831 (90% power)
 75% of observed effect: n per arm = 1,122 (80% power), 1,501 (90% power)
 50% of observed effect: n per arm = 2,561 (80% power), 3,428 (90% power)
power.prop.test: 620.9 
Simulated power at n = 621 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

MethodEstimate95% CIP-value
Chi-squaredRisk Difference (RD) -7.4-27.1 to 7.00.313
Chi-squaredRisk Difference (RD) -1.2-16.2 to 13.80.872

The sponsor's reported primary comparisons use a Chi-squared method and express the result as risk differences. For apremilast 20 mg versus placebo, the reported difference is -7.4 percentage points, with a 95% confidence interval from -27.1 to 7.0 and p = 0.313. For apremilast 30 mg versus placebo, it is -1.2 percentage points, with a 95% confidence interval from -16.2 to 13.8 and p = 0.872. These are the sponsor's own reported estimates and inferential results for the primary endpoint.

The unadjusted recalculations use posted group-level summaries and are intended as a simple cross-check, not as a replacement for the sponsor's analysis. The registry indicates no discrepancy for the primary results. Recalculation and sponsor analysis can nevertheless differ in methods, rounding, or the information included, so the sponsor's analysis remains the appropriate reference for what the trial reported.

For continuous HAQ-DI outcomes, the sponsor reports least-squares mean differences. The simple recalculations compare posted group means without adjustment. Those are not necessarily the same estimand: least-squares means generally arise from a statistical model, while the unadjusted calculation uses the displayed group summaries. The sponsor's HAQ-DI estimates are reported without confidence intervals or p-values in the registry record, and the model specifications are not reported. The registry's numeric results should therefore be read according to the method identified for each analysis rather than treating every estimate as interchangeable.

15. Multiplicity, Missing Data and Analysis Populations

The registry record lists 73 outcome measures, 80 analyses, and 72 posted secondary outcomes. It does not report a multiplicity-adjustment plan, an outcome hierarchy, or a detailed statistical analysis plan. It is therefore not possible to determine from the record whether the primary endpoint was the sole confirmatory test, whether some secondary outcomes were intended to be confirmatory, or how the sponsor accounted for testing multiple outcomes and comparisons.

General statistical explanation: when many hypotheses are examined, the probability of obtaining at least one apparently unusual result by chance can increase. Prespecified testing strategies can address that issue by defining which comparisons are primary and how evidence across multiple tests will be interpreted. Without the strategy being reported, unadjusted secondary p-values should not be treated as if each were the only planned test. The primary endpoint remains the most direct focus because it is identified as primary in the registry record, but the record does not show the full prespecification history.

The primary outcome description identifies a full analysis set consisting of participants randomized as specified in the protocol, excluding participants randomized in error who received no study drug. It also refers to participants who withdrew early or lacked sufficient data for a definitive response determination. The method used to classify or impute those participants' responses is not reported in the registry record. The number of participants with missing primary outcome data, the reasons for missingness, and any sensitivity analyses are also not reported.

General statistical explanation: excluding participants with missing outcomes, classifying them as non-responders, or using an imputation model can lead to different estimates, depending on the assumptions and the pattern of missingness. Randomization does not by itself resolve missing outcome data. The registry supplies the analysis-population description but not enough detail to evaluate the missing-data assumptions.

The record does not report whether interim analyses occurred, whether stopping rules were used, or whether the primary analysis was modified. It also does not report the rationale for termination. These omissions do not establish that any particular procedure was or was not used; they limit what can be concluded about the planned analysis and the context of the final results.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Week 24: Placebo1791.3%
Week 24: Apremilast 20 mg6827.3%
Week 24: Apremilast 30 mg4765.3%
Study Termination: Apremilast 20 mg1615310.5%
Study Termination: Apremilast 30 mg7769.2%
Participants with at least one serious adverse event
Serious adverse events by armWeek 24: Placebo1.3%Week 24: Apremilast 20 mg7.3%Week 24: Apremilast 30 mg5.3%Study Termination: Apremilast…10.5%Study Termination: Apremilast…9.2%% of participants with at least one serious adverse event

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5.0% reporting threshold.

ArmParticipants affected of at risk
Week 24: Placebo15 of 79
Week 24: Apremilast 20 mg26 of 82
Week 24: Apremilast 30 mg23 of 76
Study Termination: Apremilast 20 mg49 of 153
Study Termination: Apremilast 30 mg29 of 76

Most frequent serious adverse event terms

Event termOrgan systemWeek 24: PlaceboWeek 24: Apremilast 20 mgWeek 24: Apremilast 30 mgStudy Termination: Apremilast 20 mgStudy Termination: Apremilast 30 mg
AppendicitisInfections and infestations0 of 791 of 820 of 761 of 1531 of 76
Transient ischaemic attackNervous system disorders0 of 791 of 820 of 762 of 1530 of 76
CellulitisInfections and infestations0 of 790 of 821 of 760 of 1531 of 76
Staphylococcal abscessInfections and infestations0 of 790 of 821 of 760 of 1531 of 76
Lung neoplasmNeoplasms benign, malignant and unspecified (incl cysts and polyps)0 of 790 of 821 of 760 of 1531 of 76
Basal cell carcinomaNeoplasms benign, malignant and unspecified (incl cysts and polyps)0 of 791 of 820 of 761 of 1530 of 76
Diabetes mellitusMetabolism and nutrition disorders0 of 791 of 820 of 761 of 1530 of 76
Bipolar disorderPsychiatric disorders0 of 790 of 821 of 760 of 1531 of 76
Suicidal ideationPsychiatric disorders0 of 790 of 821 of 760 of 1531 of 76
Atrial fibrillationCardiac disorders0 of 791 of 820 of 761 of 1530 of 76

Most frequent non-serious adverse event terms

Event termOrgan systemWeek 24: PlaceboWeek 24: Apremilast 20 mgWeek 24: Apremilast 30 mgStudy Termination: Apremilast 20 mgStudy Termination: Apremilast 30 mg
NauseaGastrointestinal disorders6 of 797 of 8210 of 7613 of 15310 of 76
HeadacheNervous system disorders1 of 799 of 827 of 7612 of 1538 of 76
DiarrhoeaGastrointestinal disorders2 of 797 of 826 of 7614 of 1536 of 76
NasopharyngitisInfections and infestations4 of 796 of 823 of 7611 of 1536 of 76
Upper respiratory tract infecetionInfections and infestations2 of 793 of 825 of 769 of 1537 of 76
Abdominal pain upperGastrointestinal disorders3 of 793 of 825 of 763 of 1535 of 76
Decreased appetiteMetabolism and nutrition disorders0 of 792 of 824 of 764 of 1534 of 76
VomitingGastrointestinal disorders1 of 791 of 823 of 763 of 1535 of 76
HypertensionVascular disorders0 of 792 of 820 of 769 of 1531 of 76

Serious events with the highest arm-level rate: cellulitis (1.3%), staphylococcal abscess (1.3%), appendicitis (1.3%), lung neoplasm (1.3%), bipolar disorder (1.3%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The registry reports serious adverse event counts in groupings labelled Week 24 and Study Termination. At Week 24, serious events were reported for 1 participant in the placebo group, 6 participants in the apremilast 20 mg group, and 4 participants in the apremilast 30 mg group. The corresponding at-risk counts were 79, 82, and 76. At Study Termination, the registry lists 16 serious events among 153 at risk in the apremilast 20 mg group and 7 among 76 at risk in the apremilast 30 mg group. These are the counts as recorded in their respective groupings; the record does not explain why the termination denominators differ from the Week 24 groupings.

The listed serious-event terms include cellulitis, staphylococcal abscess, appendicitis, lung neoplasm, bipolar disorder, and suicidal ideation, each reported as 1.3%. The group attribution and further clinical detail for those terms are not reported in the registry record. Death counts are not reported in the registry record.

These figures describe reported events and denominators, not a complete comparative safety analysis. The registry does not report exposure-adjusted rates, event timing, severity beyond the serious-event classification, causal attribution, or a full account of treatment discontinuation due to adverse events. The counts should not be interpreted as proving or excluding a safety difference between groups.

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

The posted results establish what was recorded for the primary endpoint: the Week 16 ACR 20 response percentages were 35.4% with placebo, 28.0% with apremilast 20 mg, and 34.2% with apremilast 30 mg. The sponsor's risk-difference estimates for the apremilast groups compared with placebo have 95% confidence intervals that include zero. These results leave substantial uncertainty about the size and direction of the differences represented by the trial data.

They do not establish that the groups are equivalent. A failure to distinguish a difference from zero is not the same as evidence that any possible difference is small enough to be unimportant. The registry record does not report an equivalence or non-inferiority margin, and the confidence intervals include a range of possible effects. Nor do these estimates establish that apremilast does or does not work. The statistical results describe the observed comparisons and their uncertainty; they are not medical advice.

The trial's terminated status is relevant context, but the reason for termination is not reported in the registry record. It cannot be assumed that termination was caused by efficacy findings, safety findings, recruitment, or any other particular factor. Likewise, the record does not establish whether an interim analysis informed the decision.

Secondary outcome results and serious adverse event counts add context, but they have limitations. The registry does not report a multiplicity strategy, complete missing-data methods, or detailed statistical models for all outcomes. The serious event counts are not a complete safety profile, and the record does not report exposure-adjusted comparisons or deaths. Readers should distinguish the registry entries reported from questions the registry does not answer.

The most defensible interpretation is that this Phase 2 trial reports uncertain primary comparisons at Week 16, with additional functional and disease-activity outcomes that require cautious interpretation. The posted record does not support a firm conclusion about the clinical meaning of the estimated differences or about the reason the study was terminated. Those questions require information beyond the reported results and registry entries.

18. Why This Trial Matters Statistically

This trial illustrates a central issue in clinical biostatistics: the observed group percentages are only the starting point for interpretation. The primary comparisons are expressed as risk differences with confidence intervals. The intervals show that estimates can be compatible with a range of effects, including no difference, and that the observed data do not provide a precise estimate. Reporting uncertainty alongside point estimates is essential when group percentages alone might invite an overly definite reading.

The study also shows why a composite endpoint needs to be understood before its statistical results are interpreted. ACR 20 combines joint counts with patient, physician, function, and laboratory measures. A single response percentage summarizes that composite rule, but does not reveal which components contributed to participants' responses. The result is interpretable only in relation to the specified criteria and assessment time.

Another statistical lesson is that design and analysis information matter as much as a list of results. The record describes randomization and masking, but does not report the full analysis plan, missing-data procedures, multiplicity strategy, or original sample-size justification. Those omissions limit the ability to assess how all outcomes were intended to be interpreted. The distinction between sponsor model-based estimates and simple unadjusted recalculations is also important: numerical similarity does not make different estimands identical.

Finally, planning illustrations based on observed effects are not evidence of the trial's original design or a measure of achieved power. They demonstrate how sample-size requirements depend on the effect a study aims to detect and the assumptions used. Reading these figures alongside confidence intervals encourages focus on precision and design assumptions rather than treating a p-value as the whole result.

19. Limitations

The registry record is limited in its description of why the study was terminated. It gives the status as TERMINATED but does not report the reason, the decision date, or whether termination occurred earlier than planned. That missing context prevents interpretation of study completion as an efficacy or safety signal.

Important design and analysis details are also not reported in the registry record. These include the original sample-size justification, allocation ratio, randomization procedures, stratification factors, detailed masking procedures, analysis plan, interim-analysis procedures, and any stopping rules. The registry's primary endpoint definition describes the full analysis set and mentions participants without definitive response data, but does not explain the missing-data method or report the number of missing outcomes.

The breadth of outcomes creates interpretive limits. The record lists 73 outcome measures and 80 analyses, but does not report how multiplicity was addressed or whether secondary outcomes followed a hierarchy. Some sponsor-reported secondary comparisons lack confidence intervals and p-values. This makes it difficult to assess their precision or inferential role. The number of secondary outcomes posted is 72, but the record does not explain the difference between that count and the total outcome measures.

For HAQ-DI, the sponsor reports least-squares mean differences without model details or uncertainty measures. Recalculations from posted group means are unadjusted and do not necessarily estimate the same quantity. Secondary endpoint denominators also vary, and the record does not fully report participant flow or outcome-specific missingness. Safety reporting gives serious event counts in separate Week 24 and Study Termination groupings, but does not explain the differing denominators or provide exposure-adjusted comparisons, detailed event timing, or death counts. These limitations restrict the conclusions that can be drawn from the registry record alone.

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23. Record Summary

The registry record describes NCT01285310, a Phase 2 randomized, double-blind, placebo-controlled, parallel-group study of apremilast in participants with active rheumatoid arthritis and an inadequate response to methotrexate. It lists 237 enrolled participants and three groups: placebo, apremilast 20 mg, and apremilast 30 mg. The recorded study status is TERMINATED.

The primary endpoint was the percentage of participants with an ACR 20 response at Week 16. The sponsor reported risk differences of -7.4 percentage points for 20 mg versus placebo and -1.2 percentage points for 30 mg versus placebo; both reported 95% confidence intervals include zero. Secondary outcomes covered function and disease activity. Serious adverse events were reported in Week 24 and Study Termination groupings.

The registry does not report the reason for termination, the original sample-size justification, full missing-data and multiplicity methods, or a detailed statistical analysis plan. Those omissions limit interpretation beyond the posted endpoint estimates, intervals, secondary results, and safety counts.

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