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Arthritis, Rheumatoid Phase 3 Binary Endpoint NCT00856544

A Study Comparing 2 Doses Of CP-690,550 Vs. Placebo For The Treatment Of Rheumatoid Arthritis In Patients On Other Background Arthritis Medications: Complete Statistical Analysis

This Phase 3 trial compared two doses of CP-690,550 with placebo for Month 6 ACR20 response in adults with rheumatoid arthritis receiving background DMARDs. The registry record also reports selected secondary outcomes and adverse-event counts.

Trial start: 2009-05  ·  Enrollment: 795  ·  Sponsor: Pfizer
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 A Study Comparing 2 Doses Of CP-690,550 Vs. Placebo For The Treatment Of Rheumatoid Arthritis In Patients On Other Background Arthritis Medications (NCT00856544), a randomized phase 3 study. The primary outcome is Percentage of Participants Achieving American College of Rheumatology 20% (ACR20) Response at Month 6.

795
Enrollment
Phase 3
3
Arms
In the primary outcome
+21.5 pts
Risk difference
CP-690,550 5 mg
12.4 to 30.7 pts
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00856544
PhasePhase 3
ConditionArthritis, Rheumatoid
AllocationRandomized
Design modelParallel
MaskingQuadruple
Enrollment795
Arms in the primary outcome3
Lead sponsorPfizer
Results postedYes

2. Clinical Question

Population

Adults with active rheumatoid arthritis who were taking background disease-modifying antirheumatic drugs (DMARDs). The primary endpoint description identifies the full analysis set as randomized participants who received at least one dose of study medication; the number evaluable could vary by measure.

Intervention

CP-690,550 at 5 mg or 10 mg. The study summary describes both doses as twice daily and used with traditional DMARDs.

Comparator

Placebo alongside background arthritis medication. For the Month 6 primary comparison, the two placebo sequences were combined into one reporting group. The registry describes later movement from placebo to active treatment for some participants.

Primary question

What percentage of participants achieved an ACR20 response at Month 6 in each CP-690,550 dose group and the placebo group? The endpoint requires specified improvements in tender and swollen joint counts and in at least three of five other ACR core measures.

The primary comparison is about the proportion meeting a defined response threshold at a specified follow-up time. It is not a comparison of average change in every symptom, nor does the endpoint by itself capture all dimensions of rheumatoid arthritis or treatment experience. The registry lists 795 participants enrolled overall, while the analyzed counts for the primary outcome are reported separately by group. Those outcome counts are the relevant denominators for interpreting the posted Month 6 percentages.

The clinical question is framed against placebo on background medication, rather than against no treatment. The trial’s stated purpose was to assess safety and efficacy of two CP-690,550 doses in people with active rheumatoid arthritis who were using other arthritis medications. The posted primary results describe the response proportions and the sponsor’s group comparisons; they do not establish how the results apply to patients outside the study population or to different treatment settings.

3. Trial Design

This was a Phase 3 randomized, double-blind, placebo-controlled, parallel-group study. The registry describes masking as quadruple. The sponsor was Pfizer, the condition was rheumatoid arthritis, and the study status is completed. The record lists enrollment of 795 participants, a start in 2009-05, and primary completion in 2011-01.

The study compared CP-690,550 5 mg, CP-690,550 10 mg, and placebo among participants receiving background DMARDs. The primary Month 6 comparison combines the two placebo sequences into a single placebo reporting group. The arm descriptions indicate that placebo non-responders advanced to a specified active dose at the Month 3 visit; all participants in each placebo sequence advanced to that dose at the Month 6 visit. These changes in treatment assignment matter when interpreting outcomes after the placebo-controlled period.

The primary endpoint was the percentage achieving ACR20 at Month 6. The record also lists ACR20 at other visits, ACR50 and ACR70 at multiple visits, and DAS28-3 using CRP. Across the registry record, 47 outcome measures and six analyses are listed. Those entries indicate a broader set of measurements than the primary comparison alone, but the detailed statistical plan for the trial is not reported in the registry record.

Enrollment is not the same as the number evaluated for every outcome. The primary outcome description says its full analysis set included randomized participants who received at least one dose, and defines the analyzed number as participants evaluable for that measure. The posted outcome counts are 311 for the 5 mg group, 309 for the 10 mg group, and 157 for placebo. The record does not give the original design’s sample-size justification or its planned allocation details, so the enrollment total should not be read as evidence of a particular power target.

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.

Overall Study

StageCP-690,550 5 mgCP-690,550 10 mgPlacebo Then CP-690,550 5 mgPlacebo Then CP-690,550 10 mg
STARTED3183187980
Treated3153187980
COMPLETED2612527167
NOT COMPLETED5766813

Reasons for not completing this period:

ReasonCP-690,550 5 mgCP-690,550 10 mgPlacebo Then CP-690,550 5 mgPlacebo Then CP-690,550 10 mg
Randomized but not treated3000
Death0200
Adverse Event202923
Lack of Efficacy161233
Other91616
Lost to Follow-up1220
Withdrawal by Subject8501

Analysis population for the primary outcome, as defined in the registry: Full analysis set (FAS) population included all randomized participants who received at least 1 dose of study medication. N (number of participants analyzed)=participants who were evaluable for this measure. Missing values due to withdrawal, advancement to active treatment before Month 6 were imputed using non-responder imputation (NRI) method.

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.

CharacteristicUnitCP-690,550 5 mgCP-690,550 10 mgPlacebo Then CP-690,550 5 mgPlacebo Then CP-690,550 10 mgTotal
Participants analysed3153187980792
Age ContinuousYears52.7 (SD 11.7)51.9 (SD 11.8)50.8 (SD 11.2)53.3 (SD 10.8)52.3 (SD 11.6)
Sex: Female, Male: FemaleParticipants2642586360645
Sex: Female, Male: MaleParticipants51601620147

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants Achieving American College of Rheumatology 20% (ACR20) Response at Month 6, measured over Month 6.

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

The primary endpoint is the percentage of participants achieving an American College of Rheumatology 20% (ACR20) response at Month 6. It is a binary outcome: each participant either meets the response definition or does not. The definition requires at least 20% improvement in tender joint count and at least 20% improvement in swollen joint count, together with at least 20% improvement in at least three of five additional ACR core measures.

Those five measures are participant assessment of pain, participant global assessment of disease activity, physician global assessment of disease activity, self-assessed disability using the Health Assessment Questionnaire disability index, and C-reactive protein. This combination makes ACR20 a structured response criterion spanning joint findings, assessments of disease and pain, function, and an inflammatory marker. It is used to express how many participants met a prespecified level of improvement rather than to report an average change on one measure.

The percentage is useful for a group comparison because it describes the frequency of reaching the defined threshold. It does not show the size of improvement among responders beyond the threshold, or the distribution of changes among those who did not meet it. Nor does it replace the other outcomes listed in the registry. Interpretation therefore depends on the stated response definition, follow-up time, analysis population, and treatment changes during follow-up.

The primary description says placebo sequences were combined for the Month 6 comparison. It also notes that missing values due to withdrawal or advancement to active treatment before Month 6 were imputed, but the description is cut off and does not fully specify the imputation approach. Further details on the method for handling missing outcomes are not reported in the registry record.

7. Results Posted in the Registry

Risk difference: CP-690,550 5 mg

+21.5

95% CI: 12.4 to 30.7 percentage points

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals20.630.039.448.758.167.5CP-690,550 5 mg (n=311)CP-690,550 10 mg (n=309)Placebo (n=157)% of participants (95% CI)
Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)CP-690,550 5 mgCP-690,550 10 mg-2.895.4914223139risk 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
Disease Activity Score Using 28-Joint Count and Erythrocyte Sedimentation Rate (4 Variables) (DAS28-4 [ESR]) at Month 12Continuous EndpointMean difference0.06 (-0.31 to 0.43)7,395 per arm
Number of Participants With Optimal Sleep Assessed Using Medical Outcomes Study Sleep Scale (MOS-SS) at Month 12Binary EndpointRisk difference-0.9 pts (-14.1 to 12.3)46,344 per arm
Functional Assessment of Chronic Illness Therapy (FACIT)-Fatigue Scale at Month 12Continuous EndpointMean difference-1.91 (-4.37 to 0.55)405 per arm

Disease Activity Score Using 28-Joint Count and Erythrocyte Sedimentation Rate (4 Variables) (DAS28-4 [ESR]) at Month 12

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)CP-690,550 5 mgCP-690,550 10 mg-0.70-0.46-0.210.030.270.51mean difference vs control (95% CI)

Number of Participants With Optimal Sleep Assessed Using Medical Outcomes Study Sleep Scale (MOS-SS) at Month 12

Treatment effect versus the control arm
Forest plot of risk difference (percentage points) vs control (95% CI)CP-690,550 5 mgCP-690,550 10 mg-17-9.24-1.805.641321risk difference (percentage points) vs control (95% CI)

Functional Assessment of Chronic Illness Therapy (FACIT)-Fatigue Scale at Month 12

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)CP-690,550 5 mgCP-690,550 10 mg-4.87-3.43-1.99-0.540.902.34mean difference vs control (95% CI)

The registry lists a broad set of secondary outcomes, including ACR response thresholds at several visits and disease activity measures. It reports 42 secondary outcomes, but only selected outcome details are described in the available record. Among the Month 12 results with arm-level values, the pattern is mixed across measures and treatment sequences. This is not a contradiction of the Month 6 primary result: the secondary outcomes measure different constructs, use later follow-up, and in some cases compare participants who had moved from placebo to active treatment.

The Month 12 DAS28-4 using ESR, MOS-SS sleep measure, and FACIT-Fatigue results provide additional descriptions of disease activity, sleep, and fatigue. They should be considered alongside, rather than substituted for, the ACR20 primary endpoint. The registry does not report sponsor inferential analyses for these selected secondary outcomes. The recalculated comparisons are unadjusted and should not be mistaken for prespecified confirmatory findings.

Secondary outcomes help show whether results extend across different measures and time points. They can also raise questions for further analysis when patterns differ, but interpretation is constrained by the number of outcomes, the incompleteness of the statistical plan, and the absence of reported adjustment details. When many comparisons are examined, some nominally notable results may arise by chance. This is why unadjusted secondary findings generally carry less evidential weight than a prespecified primary analysis that is fully defined in the protocol and analysis plan.

The registry does not report whether secondary testing followed a hierarchy, whether multiplicity adjustments were applied, or which secondary outcomes were intended as confirmatory. Accordingly, the secondary results are best read as descriptive context. They do not independently settle the main clinical question, and they should not be combined into a single overall conclusion without a defined analysis strategy.

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

9. Statistical Interpretation

Clinical Biostats interpretation

At Month 6, ACR20 response was reported for 52.73% of participants in the CP-690,550 5 mg group, 58.25% in the 10 mg group, and 31.21% in the combined placebo group. These are the posted proportions for participants evaluable for the measure. The registry’s sponsor analyses report positive percent differences for each active-dose comparison with placebo, with 95% confidence intervals that do not include zero and p-values of < 0.001.

The recalculated, unadjusted risk differences are 0.215 for CP-690,550 5 mg versus placebo, with a 95% confidence interval from 0.124 to 0.306, and 0.270 for 10 mg versus placebo, with a 95% confidence interval from 0.179 to 0.361. Both recalculated comparisons have p-values of <0.001. These are simple unadjusted comparisons based on the posted summary counts, not replacements for the trial’s own analysis. The registry’s reported analyses use a normal approximation and give percent differences of 21.52 and 27.04, respectively.

The two active-dose groups have different observed response proportions, but the primary comparisons presented are each against placebo. A direct inferential comparison of 5 mg with 10 mg is not reported in the registry record. The results therefore do not establish whether the doses differ from one another. Likewise, the posted p-values concern the stated active-versus-placebo comparisons; they do not account for the full set of outcomes and analyses unless the statistical plan says so, and that plan is not reported.

The placebo sequences later changed treatment according to the arm descriptions. This is important for reading results at later visits: after participants switch to active treatment, those later results no longer represent a continuing placebo comparison in the same sense as the Month 6 primary comparison. The posted primary analysis deliberately combines placebo sequences at Month 6, while the record’s descriptions also indicate advancement to active treatment around that period.

The evidence in the registry record is specific to this endpoint, follow-up time, analysis population, and comparison. ACR20 is a threshold measure and should not be treated as a complete account of symptoms, function, safety, or longer-term outcomes. The reported statistical results quantify the observed group contrast and its uncertainty; they do not by themselves determine clinical importance, establish a dose-response relationship, or support conclusions outside the studied setting.

10. Statistical Methods Explained

The primary outcome is binary because participants are classified as meeting or not meeting the ACR20 response definition. The registry reports the percentage meeting that definition in each group. A group percentage is a descriptive summary, while a comparison such as a risk difference expresses the contrast between two group proportions. These summaries answer related but distinct questions: the percentages describe each arm, and the contrast describes how far apart the groups were on the outcome scale.

What does the risk difference represent?

A risk difference is the proportion with the outcome in one group minus the proportion in the comparison group, with the ordering determined by the stated contrast. It is expressed on the proportion scale in the recalculated comparisons. A value above zero for these active-versus-placebo contrasts indicates a higher observed ACR20 response proportion in the active group. This measure is directly tied to the event probabilities and does not have the same interpretation as a risk ratio or odds ratio.

The posted recalculations are labeled unadjusted. They use the summary counts and do not incorporate covariates, stratification, repeated measurements, or other model adjustments. An unadjusted contrast can be informative, but it may not reproduce the trial’s planned estimand or analysis model. The registry analyses are reported separately and use a normal approximation for the percent difference. The statistical plan, including whether other adjustments were prespecified, is not reported in the registry record.

How should a confidence interval be read?

A confidence interval describes uncertainty around an estimate under the method used to calculate it. In general, a narrower interval indicates greater precision than a wider interval on the same scale. The interval is not a range containing every individual participant’s outcome, nor does it describe the spread of responses among participants. It concerns uncertainty in the group contrast. The registry’s sponsor analyses report 95% confidence intervals, and the recalculated intervals are based on the posted summary statistics.

A confidence interval that excludes zero for a risk difference is consistent with a statistically distinguishable contrast under the stated interval procedure. That conclusion depends on the assumptions of the method and does not itself establish clinical importance. The point estimate and the interval should be read together: the point estimate gives the central estimate, while the interval shows how much uncertainty remains around it.

What do the p-values say?

A p-value is a measure of how compatible the observed data are with a specified null model, under the assumptions of the analysis. It is not the probability that the null hypothesis is true, nor is it a measure of the magnitude or importance of an effect. The sponsor reports p-values of < 0.001 for both primary comparisons; the unadjusted recalculations report p-values of <0.001. The methods and analysis plan needed to judge whether the reported tests account for multiplicity are not reported in the registry record.

Results from multiple outcomes and visits create a multiplicity issue: when many hypotheses are examined, a nominal p-value may not have the same overall error interpretation as a single prespecified test. The registry lists multiple outcome measures and analyses, but whether the sponsor adjusted for multiplicity, used a testing hierarchy, or designated some analyses as exploratory is not reported in the registry record. The primary outcome remains the natural focus because it is specifically identified as primary, but the absence of a complete analysis plan limits assessment of the broader testing context.

Why does the analysis population matter?

The primary outcome description identifies a full analysis set of randomized participants who received at least one dose of study medication. It further says the analyzed number is the number evaluable for that measure. The arm counts for the primary outcome are therefore outcome-specific, rather than simply the total enrollment. The record’s primary outcome description says missing values caused by withdrawal or advancement to active treatment before Month 6 were imputed, but the entry is incomplete. The detailed imputation rule, sensitivity analyses, and handling of other missingness are not reported in the registry record.

Missing-data choices can affect a binary response estimate because participants without an observed Month 6 assessment need a rule for whether and how their outcomes contribute. A general statistical point is that imputation relies on assumptions about unobserved outcomes; different assumptions can lead to different estimates. Without the full method and sensitivity analyses, the robustness of the result to missing-data assumptions cannot be judged from the registry record alone.

Why can over-dispersion matter?

Over-dispersion is a general issue in count or probability models when the observed variability exceeds what a model assumes. It can make standard errors and confidence intervals too optimistic if ignored. The primary outcome is a binary response summarized as proportions, and the posted analyses are described using a normal approximation; the registry does not report an over-dispersion assessment. This general concept should not be taken to imply that over-dispersion was present in this trial.

For a binary endpoint, the underlying uncertainty depends in part on the number of participants and the event proportions. This helps explain why confidence intervals accompany the group estimates. It does not justify deriving a new analysis from the percentages alone or assuming that the sponsor used the same method as the unadjusted recalculation.

The sponsor’s analysis and the simple recalculation serve different roles. The sponsor result is the inferential result reported by the trial. The recalculation is an independent, unadjusted check using posted summary statistics. The registry indicates no discrepancy between those results. Even when estimates are aligned, the recalculation cannot recover details such as covariate adjustment, stratification, missing-data rules, or multiplicity control that are not fully reported.

11. Confidence Intervals and Precision

The sponsor reports a 95% confidence interval of 12.39 to 30.65 for the percent difference between CP-690,550 5 mg and placebo. For CP-690,550 10 mg versus placebo, the reported 95% confidence interval is 17.94 to 36.13. The registry reports p-values of < 0.001 for both comparisons. The recalculated risk-difference intervals are 0.124 to 0.306 for 5 mg and 0.179 to 0.361 for 10 mg, with p-values of <0.001.

These intervals convey uncertainty in the group contrasts, not variation in individual responses. In general, a confidence interval is interpreted in relation to its estimate and the scale on which it is expressed. The sponsor intervals are reported as percent differences, while the recalculated intervals are expressed as risk differences on the proportion scale. The registry’s analyses use a normal approximation; the recalculations are unadjusted summary-statistic comparisons.

Both sponsor intervals lie above zero, as do the recalculated intervals. Under the respective methods, that is consistent with a positive active-versus-placebo contrast for the primary outcome. The interval limits still allow a range of possible contrast sizes, so the point estimates should not be interpreted as exact effects. Statistical precision is also distinct from clinical importance, which requires contextual judgment not resolved by the interval alone.

Precision depends on the amount of information contributing to each estimate, including the number evaluated and the outcome frequency. The primary analyzed counts were 311, 309, and 157 across the two active groups and placebo. The smaller placebo count is relevant context for interpreting the estimate, although the interval already reflects uncertainty calculated by the stated method. No additional confidence intervals for the arm-specific response percentages are reported in the registry record.

Because details of the full analysis plan and missing-data method are incomplete, the posted intervals should be read as uncertainty under the analyses reported, not as a full accounting of all possible sources of uncertainty. The registry record does not report whether the sponsor’s intervals were adjusted for multiple comparisons.

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 effect82109
75% of the observed effect143191
50% of the observed effect314419
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect501002005001,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
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: CP-690,550 5 mg.

The sample-size illustrations are planning calculations based on the observed effect, not the trial’s original design assumptions. For these binary outcomes, the figures are participants per arm, not total participants across the comparison. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The calculations consider detecting the stated fraction of the observed effect. The trial’s own sample-size justification is not reported in the registry record.

The 80% power column describes the number of participants per arm that the planning calculation estimates would be needed for an 80% chance of detecting the selected effect under those assumptions, if that effect and model assumptions were correct. The 90% power column uses a higher target chance of detecting the selected effect and therefore generally requires more participants per arm. Power is a design property under specified assumptions, not a guarantee that a result will be statistically significant.

Rows for planning at 100%, 75%, and 50% of the observed effect show how the assumed effect size changes the required sample size. Smaller effects are harder to distinguish from random variation and therefore require more participants. The same planning logic underlies the sample-size curve: it illustrates the relationship between assumed effect and the number needed, rather than reporting participant enrollment or outcomes from the trial.

These figures are not observed power. They are prospective planning illustrations calculated from the observed effect, and may be sensitive to the underlying estimate and assumptions. They should not be read as evidence that the trial was designed with these targets, since the original design’s assumptions are not reported in the registry record.

13. How the Sample Size Is Derived

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

Formula

n = [ 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 = 0.312; treatment proportion p1 = 0.527; average p̄ = 0.420.
  2. First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6979 = 1.3679.
  3. Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6811 = 0.5733.
  4. n = (1.3679 + 0.5733)2 / (0.2152)2 = 81.3, rounded up to 82 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 <- 0.312101910828025                          # control proportion
p1 <- 0.527331189710611                          # 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(856544)
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 = 82 (80% power), 109 (90% power)
 75% of observed effect: n per arm = 143 (80% power), 191 (90% power)
 50% of observed effect: n per arm = 314 (80% power), 419 (90% power)
power.prop.test: 81.3 
Simulated power at n = 82 per arm: 0.801 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

14. Analyses Reported by the Sponsor

MethodEstimate95% CIP-value
Normal approximationPercent difference 27.0417.94 to 36.13< 0.001
Normal ApproximationPercent Difference 21.5212.39 to 30.65< 0.001

The registry reports the sponsor’s own primary analyses as normal-approximation comparisons of percent differences. For CP-690,550 10 mg versus placebo, the reported difference is 27.04, with a 95% confidence interval from 17.94 to 36.13 and p < 0.001. For CP-690,550 5 mg versus placebo, the reported difference is 21.52, with a 95% confidence interval from 12.39 to 30.65 and p < 0.001.

The recalculation uses the posted arm-level summary counts to estimate unadjusted risk differences. It reports 0.270 for the 10 mg comparison and 0.215 for the 5 mg comparison, each with an interval and p-value calculated from those summaries. The sponsor reports percent differences, whereas the recalculated contrasts are on the proportion scale, so the numeric scales differ. The registry indicates no discrepancy between the posted sponsor analysis and the recalculations.

The sponsor’s analysis is the trial’s reported inferential analysis. The recalculation is a useful check based on the available summary statistics, but it cannot reproduce unreported model adjustments or analysis details. The registry record does not provide enough information to determine whether such adjustments were part of the sponsor’s method. Since the discrepancy indicator is false, there is no identified conflict requiring the sponsor estimate to be displaced by the simple recalculation.

15. Multiplicity, Missing Data and Analysis Populations

The primary outcome is identified as ACR20 response at Month 6. The registry also lists multiple ACR thresholds, follow-up visits, disease activity measures, and other secondary outcomes. With many outcomes and time points, the interpretation of nominal p-values depends partly on how the analysis plan addressed multiplicity. The statistical plan, including any adjustment procedure, testing hierarchy, or distinction between confirmatory and exploratory analyses, is not reported in the registry record.

The reported sponsor p-values for the two primary comparisons are each < 0.001. The record does not state whether the two dose-versus-placebo tests were adjusted for one another or for the broader set of outcomes. The recalculated p-values are unadjusted. They should therefore be understood as results for individual comparisons, not as family-wise conclusions across every endpoint and visit in the study.

The primary outcome description names the full analysis set as randomized participants who received at least one dose. It says the analyzed number is the number evaluable for the measure. For Month 6, the posted analyzed counts are 311 for CP-690,550 5 mg, 309 for CP-690,550 10 mg, and 157 for placebo. The record does not give a complete participant flow by reason for missingness or a full accounting of exclusions from each analysis population.

The primary description says missing values due to withdrawal or advancement to active treatment before Month 6 were imputed, but the registry text ends before the method is fully specified. The imputation model, assumptions, and sensitivity analyses are not reported in the registry record. In general, missing-data methods rely on assumptions about outcomes that were not observed; the effect of those assumptions cannot be assessed without the method and supporting analyses.

The registry also does not report whether the primary analysis used additional covariate adjustment or other features beyond the described population and comparison. These omissions limit the ability to reconstruct the planned statistical approach or judge robustness across alternative assumptions. They do not change what the posted descriptive proportions say, but they matter when interpreting inferential claims and the totality of the outcome findings.

16. Safety Results

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

ArmParticipants with serious adverse eventsParticipants at riskPercentage
CP-690,550 5 mg (Up To Month 3)93152.9%
CP-690,550 10 mg (Up To Month 3)83182.5%
Placebo (Up To Month 3)61593.8%
CP-690,550 5 mg (Month 3 to 6)53151.6%
CP-690,550 10 mg (Month 3 to 6)73182.2%
Placebo (Month 3 to 6)0810.0%
Placebo, Then CP-690,550 5 mg (Month 3 to 6)0380.0%
Placebo, Then CP-690,550 10 mg (Month 3 to 6)0400.0%
CP-690,550 5 mg (Post Month 6)73152.2%
CP-690,550 10 mg (Post Month 6)93182.8%
Placebo, Then CP-690,550 5 mg (Post Month 6)2792.5%
Placebo, Then CP-690,550 10 mg (Post Month 6)0800.0%
Participants with at least one serious adverse event
Serious adverse events by armCP-690,550 5 mg (Up To Month …2.9%CP-690,550 10 mg (Up To Month…2.5%Placebo (Up To Month 3)3.8%CP-690,550 5 mg (Month 3 to 6)1.6%CP-690,550 10 mg (Month 3 to …2.2%Placebo (Month 3 to 6)0.0%Placebo, Then CP-690,550 5 mg…0.0%Placebo, Then CP-690,550 10 m…0.0%% 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 2% reporting threshold.

ArmParticipants affected of at risk
CP-690,550 5 mg (Up To Month 3)95 of 315
CP-690,550 10 mg (Up To Month 3)89 of 318
Placebo (Up To Month 3)51 of 159
CP-690,550 5 mg (Month 3 to 6)69 of 315
CP-690,550 10 mg (Month 3 to 6)73 of 318
Placebo (Month 3 to 6)12 of 81

Most frequent serious adverse event terms

Event termOrgan systemCP-690,550 5 mg (Up To Month 3)CP-690,550 10 mg (Up To Month 3)Placebo (Up To Month 3)CP-690,550 5 mg (Month 3 to 6)CP-690,550 10 mg (Month 3 to 6)Placebo (Month 3 to 6)
Rheumatoid arthritisMusculoskeletal and connective tissue disorders1 of 3150 of 3182 of 1590 of 3150 of 3180 of 81
CholecystitisHepatobiliary disorders1 of 3150 of 3180 of 1591 of 3150 of 3180 of 81
PneumoniaInfections and infestations0 of 3152 of 3180 of 1590 of 3150 of 3180 of 81
Tendon ruptureInjury, poisoning and procedural complications0 of 3152 of 3180 of 1590 of 3150 of 3180 of 81
Angina pectorisCardiac disorders1 of 3150 of 3180 of 1590 of 3150 of 3180 of 81
BradycardiaCardiac disorders1 of 3150 of 3180 of 1590 of 3150 of 3180 of 81
ConstipationGastrointestinal disorders0 of 3151 of 3180 of 1590 of 3150 of 3180 of 81
PancreatitisGastrointestinal disorders1 of 3150 of 3180 of 1590 of 3150 of 3180 of 81
Chest painGeneral disorders1 of 3150 of 3180 of 1590 of 3150 of 3180 of 81
Biliary dyskinesiaHepatobiliary disorders0 of 3150 of 3181 of 1590 of 3150 of 3180 of 81

Most frequent non-serious adverse event terms

Event termOrgan systemCP-690,550 5 mg (Up To Month 3)CP-690,550 10 mg (Up To Month 3)Placebo (Up To Month 3)CP-690,550 5 mg (Month 3 to 6)CP-690,550 10 mg (Month 3 to 6)Placebo (Month 3 to 6)
Upper respiratory tract infectionInfections and infestations19 of 31523 of 3187 of 15913 of 3159 of 3180 of 81
NasopharyngitisInfections and infestations16 of 3157 of 31812 of 1596 of 3159 of 3180 of 81
HeadacheNervous system disorders12 of 31510 of 3186 of 1592 of 3155 of 3182 of 81
NauseaGastrointestinal disorders11 of 3158 of 3184 of 1596 of 3154 of 3181 of 81
DiarrhoeaGastrointestinal disorders14 of 31510 of 3186 of 1590 of 3150 of 3180 of 81
BronchitisInfections and infestations6 of 3153 of 3184 of 1593 of 3154 of 3183 of 81
Alanine aminotransferase increasedInvestigations6 of 3156 of 3184 of 1591 of 3155 of 3180 of 81
HypertensionVascular disorders4 of 3157 of 3181 of 1593 of 3154 of 3181 of 81
DyspepsiaGastrointestinal disorders4 of 3158 of 3182 of 1594 of 3151 of 3180 of 81
Back painMusculoskeletal and connective tissue disorders4 of 3158 of 3180 of 1592 of 3153 of 3182 of 81

Serious events with the highest arm-level rate: chest pain (1.3%), tendon injury (1.3%), rheumatoid arthritis (1.3%), biliary dyskinesia (0.6%), pneumonia (0.6%).

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 events and other adverse events for several treatment periods and sequences. For the period up to Month 3, serious adverse events affected 9 of 315 participants in the 5 mg group, 8 of 318 in the 10 mg group, and 6 of 159 in the placebo group. Other adverse events affected 95 of 315, 89 of 318, and 51 of 159 participants, respectively. These are counts of participants affected as recorded for those groups and periods.

From Month 3 to Month 6, the record distinguishes continued active treatment, placebo, and placebo sequences that advanced to active treatment. For example, the placebo groups that advanced to 5 mg or 10 mg each report zero serious adverse events during that period, with other adverse events affecting 16 of 38 and 18 of 40 participants, respectively. The treatment sequence and time window should be kept in view when comparing these entries.

After Month 6, the registry also reports serious and other adverse-event counts across active treatment and sequences that began on placebo. It lists selected serious event terms with percentages, including chest pain, tendon injury, and rheumatoid arthritis at 1.3% each, and biliary dyskinesia, pneumonia, and tendon rupture at 0.6% each. Deaths are not reported in the registry record.

These figures are descriptive. The record does not provide a complete statistical comparison of safety between groups or enough information to establish causal attribution. Different group sizes and exposure periods also require careful interpretation.

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

The posted Month 6 results show that the recorded ACR20 response percentages were higher in each CP-690,550 dose group than in the combined placebo group. The sponsor’s reported percent differences and the simple unadjusted recalculations are consistent with that descriptive pattern. The confidence intervals quantify uncertainty in the group contrasts under the reported methods, while the p-values address compatibility with a null comparison under their respective assumptions.

That statistical pattern does not, on its own, establish whether the size of the difference is clinically important. ACR20 is a threshold outcome: it distinguishes participants who satisfy a defined response criterion from those who do not, but it does not show the full range of improvement or worsening. Additional outcome measures and patient context are needed to understand the broader meaning of a treatment response.

The findings also do not establish a difference between the two active doses. The registry reports each dose against placebo, not a direct inferential comparison of 5 mg versus 10 mg. A higher observed percentage in one active group cannot by itself establish that one dose is superior to the other, particularly without a direct comparison and its uncertainty.

Interpretation is limited by the incomplete description of missing-data handling and the absence of the full statistical plan. The record notes imputation related to withdrawal and advancement to active treatment before Month 6, but does not fully specify the procedure. The record also does not state whether multiplicity adjustments were used across the primary comparisons and wider outcome set.

Finally, the trial question concerns adults with active rheumatoid arthritis receiving background DMARDs in this randomized, placebo-controlled study. The registry results should not be generalized automatically to other populations, treatment contexts, outcomes, or follow-up periods. The posted data describe results within this particular study and do not constitute individual medical advice.

18. Why This Trial Matters Statistically

This trial illustrates why outcome definition and analysis population matter in clinical research. ACR20 is not a single symptom score: it combines joint-count changes with several additional core measures and sets a threshold for classifying response. The resulting percentage is easy to interpret as a group frequency, but it compresses a range of participant experiences into a responder/non-responder outcome.

The contrast between the arm percentages and the risk-difference estimates also shows how effect measures describe the same comparison on different scales. The sponsor reports percent differences using a normal approximation, while the recalculation presents unadjusted risk differences based on the posted summary counts. The two forms of reporting can be read together, but the methods and scales should not be conflated.

The record also highlights the importance of follow-up and treatment sequence. The primary comparison combines placebo sequences at Month 6, while the descriptions indicate that placebo participants could advance to active treatment around that time. Results after such changes answer a different question from a continuing placebo-controlled comparison, and should be interpreted with that transition in mind.

Finally, the registry lists many outcome measures and analyses, yet does not report key details of the statistical plan, missing-data procedure, or multiplicity handling. These details are essential for evaluating how confidently to interpret a group of results, especially when several outcomes and visits are examined. The trial is therefore a useful example of both what a clearly defined primary outcome can show and what registry summaries alone cannot fully establish.

19. Limitations

The registry record does not report the full statistical analysis plan, including the original sample-size justification, planned power, covariate adjustment, or procedures for multiplicity. The planning illustrations based on observed effects are not evidence of the trial’s original design assumptions. Without those protocol details, the reported analyses cannot be fully reconstructed.

The primary outcome description is incomplete where it discusses imputation. It says missing values due to withdrawal or advancement to active treatment before Month 6 were imputed, but does not state how. The record does not provide sensitivity analyses showing whether conclusions change under other missing-data assumptions. This limits assessment of potential bias from missing outcome data.

The placebo sequences later advanced to active treatment, according to the arm descriptions. That makes interpretation of longer-term outcomes more complex than the initial placebo comparison, because treatment exposure differs by period and sequence. The Month 6 primary comparison combines placebo sequences, but the registry does not provide all details needed to evaluate the impact of switching on subsequent outcomes.

Although many outcomes are listed, the record offers detailed values for only selected secondary measures. Sponsor inferential analyses are not listed for those selected secondary outcomes. The broader pattern across measures cannot therefore be evaluated comprehensively from the posted results. The absence of reported multiplicity handling further limits the weight that can be placed on unadjusted secondary comparisons.

Safety results are separated by treatment period and sequence, but the registry record does not provide a complete comparative safety analysis or deaths. The adverse-event counts are descriptive and should not be treated as a formal estimate of relative risk. These limitations are specific to the information reported in the registry and do not establish that additional analyses were not conducted.

20. Related Tutorials

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23. Record Summary

NCT00856544 is a completed Phase 3 randomized, quadruple-masked, parallel-group study sponsored by Pfizer. It enrolled 795 participants with active rheumatoid arthritis receiving background DMARDs. The study compared CP-690,550 5 mg and 10 mg with placebo. The primary outcome was ACR20 response at Month 6.

Reported response percentages were 52.73% for 5 mg, 58.25% for 10 mg, and 31.21% for placebo. The sponsor reported positive percent differences for each active-versus-placebo comparison, with 95% confidence intervals excluding zero and p-values of < 0.001. Unadjusted recalculations from the posted summaries are consistent with those results.

The record lists multiple secondary measures and adverse-event findings, while details of the statistical plan, multiplicity handling, and missing-data procedure are incomplete. The primary result is therefore best interpreted alongside its endpoint definition, analysis population, treatment sequence, and the limits of the registry record.

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