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 Tofacitinib In Psoriatic Arthritis Subjects With Inadequate Response to TNF Inhibitors (NCT01882439), a randomized phase 3 study. The primary outcome is Percentage of Participants Meeting American College of Rheumatology Response Criteria Greater Than or Equal to (≥) 20% (ACR20): Month 3.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01882439 |
| Phase | Phase 3 |
| Condition | Psoriatic Arthritis |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Triple |
| Enrollment | 395 |
| Arms in the primary outcome | 3 |
| Lead sponsor | Pfizer |
| Results posted | Yes |
2. Clinical Question
Population
Participants had active psoriatic arthritis and an inadequate response to at least one TNF inhibitor, either because of inadequate efficacy or an adverse event. The primary endpoint population comprised randomized participants who received at least one dose of study drug.
Intervention
Tofacitinib was given twice daily at 5 mg or 10 mg. The trial included treatment sequences that continued tofacitinib for 6 months and sequences that began with placebo for 3 months before switching to tofacitinib.
Comparator
For the Month 3 primary comparison, the comparator was placebo. The two tofacitinib dose groups were compared separately with the placebo group.
Primary question
Among participants in the primary endpoint population, what percentage met ACR20 at Month 3 in each tofacitinib group and in the placebo group? ACR20 requires improvement in joint counts and in at least three of five other core measures.
3. Trial Design
This was a phase 3, randomized, parallel-group study of tofacitinib in people with active psoriatic arthritis and an inadequate response to at least one TNF inhibitor. The registry record lists 395 participants enrolled and identifies Pfizer as the sponsor. The study status is completed. Its start is recorded as 2013-08 and its primary completion as 2016-04.
The treatment sequences included tofacitinib 5 mg twice daily for 6 months, tofacitinib 10 mg twice daily for 6 months, and two sequences that began with placebo for 3 months before switching to tofacitinib at either dose for 3 months. For the primary Month 3 comparison, the placebo group had not yet switched treatment. The primary endpoint population was described as all participants who were randomized and received at least one dose of study drug.
The registry record identifies the study as triple-masked, while the official title describes it as double-blind. Both descriptions are present in the record; further detail about who was masked is not reported in the registry record. The record identifies randomized allocation and a parallel model, but details of the randomization procedure, allocation concealment, and the original sample-size justification are not reported in the registry record.
The primary outcome was the percentage meeting ACR20 at Month 3. Secondary outcomes included other ACR response thresholds, disability, and components of the ACR response criteria at specified follow-up times. The registry lists 38 outcome measures, with 36 secondary results posted. The results and interpretation below concern the posted Month 3 primary comparison and the broad pattern of the posted secondary measures.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Before assignment: Of 546 participants screened for entry into the study, 395 were enrolled and randomized, 394 received treatment.
Overall Study
| Stage | Tofacitinib, 5 mg Twice Daily | Tofacitinib, 10 mg, Twice Daily | Placebo/Tofacitinib, 5 mg, Twice Daily | Placebo/Tofacitinib, 10 mg, Twice Daily |
|---|---|---|---|---|
| STARTED | 131 | 132 | 66 | 65 |
| COMPLETED | 122 | 111 | 56 | 56 |
| NOT COMPLETED | 9 | 21 | 10 | 9 |
Reasons for not completing this period:
| Reason | Tofacitinib, 5 mg Twice Daily | Tofacitinib, 10 mg, Twice Daily | Placebo/Tofacitinib, 5 mg, Twice Daily | Placebo/Tofacitinib, 10 mg, Twice Daily |
|---|---|---|---|---|
| Adverse event related to study drug | 3 | 8 | 1 | 2 |
| Pregnancy | 0 | 1 | 0 | 0 |
| Protocol Violation | 2 | 2 | 0 | 1 |
| No longer willing to participate | 1 | 4 | 2 | 3 |
| Medication error with no associated AE | 0 | 0 | 2 | 0 |
| Insufficient clinical response | 1 | 4 | 4 | 2 |
| Adverse event unrelated to study drug | 2 | 2 | 1 | 1 |
Analysis population for the primary outcome, as defined in the registry: All participants who were randomized and received at least 1 dose of study drug.
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: All participants who received at least 1 dose of study drug.
| Characteristic | Unit | Tofacitinib, 5 mg Twice Daily | Tofacitinib, 10 mg, Twice Daily | Placebo/Tofacitinib, 5 mg, Twice Daily | Placebo/Tofacitinib, 10 mg, Twice Daily | Total |
|---|---|---|---|---|---|---|
| Participants analysed | 131 | 132 | 66 | 65 | 394 | |
| Age, Continuous | Years | 49.5 (SD 12.3) | 51.3 (SD 10.9) | 48.7 (SD 11.2) | 49.3 (SD 14.0) | 50.0 (SD 12.0) |
| Sex: Female, Male: Female | Participants | 64 | 74 | 38 | 42 | 218 |
| Sex: Female, Male: Male | Participants | 67 | 58 | 28 | 23 | 176 |
6. Primary Endpoint
The registry lists the primary outcome as Percentage of Participants Meeting American College of Rheumatology Response Criteria Greater Than or Equal to (≥) 20% (ACR20): Month 3, measured over Month 3.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | Percentage of participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint was the percentage of participants meeting ACR20 at Month 3. ACR20 is a composite response criterion: it requires at least 20% improvement from baseline in both tender or painful joint counts and swollen joint counts, together with at least 20% improvement in three of the five other ACR core set measures. Those five measures are the participant’s global assessment of arthritis, physician’s global assessment of arthritis, participant’s assessment of arthritis pain, the Health Assessment Questionnaire–Disability Index (HAQ-DI), and C-reactive protein (CRP).
A composite endpoint combines several aspects of disease activity and function into one response definition. It is used to classify whether an individual meets the specified improvement threshold across multiple measures, rather than relying on change in just one measure. The endpoint is reported as a percentage, so the comparison describes the proportion meeting the criterion in each group. The Month 3 result is an early, defined-time assessment; it does not by itself describe later outcomes or each component’s separate contribution.
The posted primary population includes randomized participants who received at least one dose of study drug. Details about how participants with missing endpoint measurements were treated are not reported in the registry record. The criterion also does not, by itself, show the size of improvement among participants who met it or the distribution of changes among those who did not.
7. Results Posted in the Registry
- Tofacitinib, 5 mg Twice Daily: 49.6% (65/131) versus 23.7% (31/131) on control; risk difference 26.0 percentage points (95% CI 14.7 to 37.2), risk ratio 2.10 (1.47–2.98); unadjusted two-proportion z-test p = <0.001.
- Tofacitinib, 10 mg, Twice Daily: 47.0% (62/132) versus 23.7% (31/131) on control; risk difference 23.3 percentage points (95% CI 12.1 to 34.5), risk ratio 1.98 (1.39–2.84); unadjusted two-proportion z-test p = <0.001.
Risk difference: Tofacitinib, 5 mg Twice Daily
95% CI: 14.7 to 37.2 percentage points
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Change From Baseline in American College of Rheumatology (ACR) Response Criteria Components: C-reactive Protein (CRP) Levels: Month 3 | Continuous Endpoint | Mean difference | -6.49 (-11.52 to -1.46) | 161 per arm |
| Change From Baseline in American College of Rheumatology (ACR) Response Criteria Components Score: Patient's Assessment of Arthritis Pain: Month 3 | Continuous Endpoint | Mean difference | -13.94 (-19.96 to -7.92) | 50 per arm |
| Change From Baseline in American College of Rheumatology (ACR) Response Criteria Components Score: Patient's Global Assessment of Arthritis: Month 3 | Continuous Endpoint | Mean difference | -14.45 (-20.65 to -8.25) | 49 per arm |
Change From Baseline in American College of Rheumatology (ACR) Response Criteria Components: C-reactive Protein (CRP) Levels: Month 3
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Tofacitinib, 5 mg Twice Daily: mean -5.47 versus 1.02 on control; difference -6.49 (95% CI -11.52 to -1.46), standardized effect d = -0.31; z-test p = 0.011.
- Tofacitinib, 10 mg, Twice Daily: mean -5.92 versus 1.02 on control; difference -6.94 (95% CI -12.01 to -1.87), standardized effect d = -0.33; z-test p = 0.007.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Tofacitinib, 5 mg Twice Daily than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Tofacitinib, 10 mg, Twice Daily than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Change From Baseline in American College of Rheumatology (ACR) Response Criteria Components Score: Patient's Assessment of Arthritis Pain: Month 3
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Tofacitinib, 5 mg Twice Daily: mean -21.66 versus -7.72 on control; difference -13.94 (95% CI -19.96 to -7.92), standardized effect d = -0.56; z-test p = <0.001.
- Tofacitinib, 10 mg, Twice Daily: mean -20.88 versus -7.72 on control; difference -13.16 (95% CI -19.22 to -7.10), standardized effect d = -0.52; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Tofacitinib, 5 mg Twice Daily than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Tofacitinib, 10 mg, Twice Daily than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Change From Baseline in American College of Rheumatology (ACR) Response Criteria Components Score: Patient's Global Assessment of Arthritis: Month 3
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Tofacitinib, 5 mg Twice Daily: mean -21.59 versus -7.14 on control; difference -14.45 (95% CI -20.65 to -8.25), standardized effect d = -0.57; z-test p = <0.001.
- Tofacitinib, 10 mg, Twice Daily: mean -19.88 versus -7.14 on control; difference -12.74 (95% CI -18.97 to -6.51), standardized effect d = -0.49; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Tofacitinib, 5 mg Twice Daily than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Tofacitinib, 10 mg, Twice Daily than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The posted secondary outcomes cover ACR response thresholds, disability, CRP, pain assessment, and global assessments. Across the continuous Month 3 components with posted results, the estimated changes in both tofacitinib groups generally move in the direction of greater improvement than the placebo estimates. The pattern is broadly consistent with the primary endpoint’s higher ACR20 response percentages in the tofacitinib groups. These results provide context across several aspects of the ACR response framework rather than an independent confirmation of every dimension of the primary finding.
Secondary outcomes differ in scale and meaning. A change in a continuous measure describes an average estimated change, whereas an ACR response percentage counts participants who meet a composite threshold. Similar directions across measures do not mean the outcomes are equivalent, and a result for one component cannot establish the result for another. The registry lists additional outcomes and assessment times, but the posted results do not cover every listed endpoint in the same detail.
The recalculated secondary comparisons are unadjusted and use summary statistics. The registry record does not report sponsor analyses for these comparisons. Their p-values therefore should not be treated as if they came from the same fully specified analysis as the primary endpoint. In addition, the record does not report a multiplicity adjustment across the many secondary measures and time points. When many outcomes are examined, some may appear notable by chance. The secondary findings are best read as supporting context and as a description of the observed pattern, while the prespecified primary endpoint and sponsor analysis carry greater interpretive weight.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Percentage of Participants Meeting American College of Rheumatology Response Criteria ≥50% (ACR50) at Week 2 and Months 1, 2, 3, 4, and 6
- Percentage of Participants Meeting American College of Rheumatology Response Criteria ≥70% (ACR70) at Week 2 and Months 1, 2, 3, 4, and 6
- Percentage of Participants Meeting American College of Rheumatology Response Criteria Greater Than or Equal to (≥) 20% (ACR20): Week 2 and Months 1, 2, 4, and 6
- Change From Baseline in Health Assessment Questionnaire - Disability Index (HAQ-DI) Score: Week 2 and Months 1, 2, 4, and 6
- Change From Baseline in American College of Rheumatology (ACR) Response Criteria Components: C-reactive Protein (CRP) Levels: Month 3
- Change From Baseline in American College of Rheumatology (ACR) Response Criteria Components Score: Patient's Assessment of Arthritis Pain: Month 3
- Change From Baseline in American College of Rheumatology (ACR) Response Criteria Components Score: Patient's Global Assessment of Arthritis: Month 3
- Change From Baseline in American College of Rheumatology (ACR) Response Criteria Components Score: Physician's Global Assessment of Arthritis: Month 3
9. Statistical Interpretation
At Month 3, 49.62% of participants in the tofacitinib 5 mg twice-daily group met ACR20, compared with 23.66% in the placebo group. For the 10 mg twice-daily group, the corresponding percentages were 46.97% and 23.66%. The posted sponsor analyses report risk differences of 25.95 percentage points for the 5 mg comparison and 23.31 percentage points for the 10 mg comparison. Both sponsor analyses report p < 0.001.
The risk difference expresses the difference in response percentages between a tofacitinib group and placebo. The positive estimates indicate a higher observed ACR20 response percentage in each tofacitinib group in this comparison. The confidence intervals reported by the sponsor are 14.72 to 37.19 percentage points for 5 mg and 12.10 to 34.51 percentage points for 10 mg. Both intervals are entirely above zero, so the posted estimates are compatible with a positive difference under the reported analysis. The intervals also show that the result is not a single precisely known value: a range of effects remains compatible with the data and method.
The posted percentages for the two doses are numerically close, but these placebo comparisons do not establish whether the doses differ from each other. No direct comparison between the two tofacitinib groups is reported in the registry record. Nor should the separate placebo comparisons be treated as proof of a dose-response pattern. The outcome is a threshold-based composite at a single assessment time, not a complete account of symptoms, function, durability, or each ACR component.
The recalculated unadjusted comparisons produce risk differences of 0.260 and 0.233 on the proportion scale, with p < 0.001 for each. These correspond to the sponsor’s reported percentage-point differences when expressed as percentages. The sponsor’s own analysis takes precedence; the recalculations are simple unadjusted checks from posted summary statistics and do not replace the reported analysis.
These results describe the randomized trial groups and the endpoint as defined in the registry. They do not establish that an individual participant will experience the group-level response, and they do not settle questions that the registry results do not address, such as comparative safety over longer follow-up, the handling of missing measurements, or the impact of multiplicity across the many outcomes and assessments.
10. Statistical Methods Explained
The primary endpoint is binary at the participant level: each person either met ACR20 at Month 3 or did not. The posted group result is a percentage, which describes the proportion of participants meeting that criterion. A risk difference compares two such proportions by subtracting the placebo response proportion from the tofacitinib response proportion. It is expressed in percentage points when the proportions are written as percentages. A positive risk difference in this setting means the observed response proportion was higher in the tofacitinib group.
The registry’s sponsor analyses use a large-sample approximation for the risk difference and report a 95% confidence interval and a p-value for each placebo comparison. A confidence interval describes the range of effect estimates reasonably compatible with the observed data under the analysis method. It is not a guarantee that the true effect lies within the interval, nor does it describe how much responses vary among individual participants. A p-value measures how inconsistent the observed results, or more extreme results, would be with a null hypothesis of no group difference under the test’s assumptions. It is not the probability that the null hypothesis is true, and it does not measure clinical importance.
The registry also allows a simple unadjusted recalculation from group summaries. These recalculations are not a substitute for a trial’s prespecified model or analysis plan. They do not account for features that cannot be reconstructed from the summary statistics, such as covariate adjustment or missing-data procedures. In this record, the sponsor’s posted estimates and the recalculated estimates align in their expressed risk differences and direction; the sponsor’s own analysis takes precedence.
Several secondary outcomes are continuous rather than binary. For those outcomes, the posted group estimates are least-squares means, with standard errors. A mean difference compares the estimated change in one group with the estimated change in placebo. The standard error conveys the estimated uncertainty of a mean estimate; it is not the same as the spread of individual participant measurements. The recalculated continuous comparisons use approximations from the posted means and standard errors. The record does not post sponsor analyses for the secondary continuous comparisons described in the results, so those recalculations should be read as exploratory rather than as replacements for a sponsor model.
For a continuous outcome, a standardized effect expresses a mean difference relative to an estimate of the outcome’s variability. This can aid comparison across measures with different units, but it is an approximation in these recalculations and should not be mistaken for the trial’s reported analysis. When a continuous outcome has a negative mean change, the direction’s meaning depends on the scale and definition; interpretation should follow the measure’s meaning rather than treating negative values as inherently good or bad. The registry record does not report detailed analysis specifications for the secondary outcomes.
General statistical point: the large-sample approximation is intended to estimate uncertainty using a distributional approximation that is more useful as sample sizes grow. It may be less reliable in settings with sparse events or highly unusual data patterns. General statistical point: over-dispersion occurs when outcome variability exceeds what a model assumes; if present and not accommodated, uncertainty can be understated. The registry’s stated method for the primary comparisons is a large-sample approximation, and over-dispersion handling is not reported in the registry record.
The recalculated planning illustrations use the observed effect as a starting point and then consider smaller fractions of that effect. They use a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. They are not the original trial’s design justification, which is not reported in the registry record. The arithmetic uses the posted summary estimates and should be interpreted as a planning illustration rather than as a reconstruction of the original protocol.
The registry identifies the primary endpoint population as randomized participants who received at least one dose of study drug. That definition is not necessarily identical to an analysis of every randomized participant regardless of treatment receipt. The registry record does not report how missing Month 3 outcomes were handled, whether all randomized participants were included in the endpoint analysis, or what sensitivity analyses were conducted. These omissions matter because the interpretation of a response percentage can depend on which participants contribute data and how unavailable measurements are treated.
The record lists many outcome measures and repeated assessment times. General statistical point: when many hypotheses are tested, the chance of at least one apparently notable result can increase unless the analysis plan accounts for multiplicity. The registry record does not report a multiplicity strategy for the secondary outcomes. For that reason, isolated secondary p-values or apparent differences should be treated more cautiously than the primary result, particularly when they are not accompanied by a reported sponsor analysis.
11. Confidence Intervals and Precision
The sponsor’s 95% confidence interval for the Month 3 risk difference between tofacitinib 5 mg twice daily and placebo is 14.72 to 37.19 percentage points. For tofacitinib 10 mg twice daily versus placebo, it is 12.10 to 34.51 percentage points. Each interval lies above zero, indicating that the reported analysis is compatible with a positive difference in response percentages. The intervals are still wide enough to include a range of possible effect sizes, so the point estimates should not be read as exact values.
Precision concerns uncertainty around an estimate, not whether a treatment is important or whether an individual participant will respond. The point estimate is the center of the reported interval, while the interval communicates how much uncertainty remains under the statistical method. These confidence intervals apply to the risk differences at Month 3 and do not describe later response, safety, or changes in individual ACR components.
The sponsor’s p-values are reported as p < 0.001. The recalculated unadjusted comparisons report p < 0.001. These are distinct reported formats and should not be conflated: the sponsor analyses use the registry’s reported large-sample method, while the recalculations are simple checks based on summary statistics. The confidence intervals and p-values address sampling uncertainty under their respective methods; they do not account for questions that are not described in the registry record, such as missing-data handling or adjustment for multiple outcomes.
12. Planning a Similar Trial: Sample Size
This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 53 | 71 |
| 75% of the observed effect | 91 | 122 |
| 50% of the observed effect | 196 | 261 |
The planning illustrations describe participants per arm for 80% power and participants per arm for 90% power. They are based on the primary binary endpoint’s observed effect and compare two groups under equal allocation. For planning for 100% of the observed effect, the illustration gives 53 participants per arm for 80% power and 71 for 90% power for the 5 mg comparison; for the 10 mg comparison, it gives 65 and 87 participants per arm, respectively. Planning for 75% of the observed effect gives 91 and 122 for 5 mg, and 112 and 149 for 10 mg. Planning for 50% of the observed effect gives 196 and 261 for 5 mg, and 240 and 320 for 10 mg.
In plain terms, the 80% power column is the approximate group size associated with an 80% chance of detecting the specified effect under the stated planning assumptions, if that effect is present. The 90% column uses a higher target chance of detection and therefore requires more participants for the same effect. As the effect to be detected becomes smaller, more participants are needed to distinguish it from random variation.
The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect set to the stated fraction of the observed effect. These are planning illustrations computed from the observed result, not the original trial’s design assumptions, which are not reported in the registry record. This is not observed power; it is an illustration of sample sizes under specified assumptions, not a measure of what the completed 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 is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.
Worked calculation for this trial
- Control proportion p0 = 0.237; treatment proportion p1 = 0.496; average p̄ = 0.366.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6814 = 1.3355.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6562 = 0.5523.
- n = (1.3355 + 0.5523)2 / (0.2595)2 = 52.9, rounded up to 53 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 <- 0.236641221374046 # control proportion
p1 <- 0.49618320610687 # 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(1882439)
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 = 53 (80% power), 71 (90% power)
75% of observed effect: n per arm = 91 (80% power), 122 (90% power)
50% of observed effect: n per arm = 196 (80% power), 261 (90% power)
power.prop.test: 52.9
Simulated power at n = 53 per arm: 0.813 (20000 replicates)
The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Large sample approximation | Risk Difference (RD) 25.95 | 14.72 to 37.19 | < 0.001 |
| Large sample approximation | Risk Difference (RD) 23.31 | 12.10 to 34.51 | < 0.001 |
The sponsor reports risk differences of 25.95 percentage points for tofacitinib 5 mg twice daily versus placebo and 23.31 percentage points for tofacitinib 10 mg twice daily versus placebo. The reported 95% confidence intervals are 14.72 to 37.19 and 12.10 to 34.51 percentage points, respectively, and both p-values are reported as p < 0.001. The analyses are identified as large-sample approximations.
The unadjusted recalculations from the posted response percentages give risk differences of 0.260 and 0.233 on the proportion scale, with p < 0.001 for each comparison. Expressed as percentage points, these estimates align with the sponsor’s reported differences. No discrepancy is identified between the sponsor results and the recalculations in the registry record. The sponsor’s own analysis takes precedence, since the recalculations are simple and unadjusted and cannot reproduce any unreported details of the sponsor’s analysis.
The agreement supports reading the basic comparison consistently: both analyses indicate a higher Month 3 ACR20 response percentage in each tofacitinib group than in placebo. It does not mean the calculations are interchangeable in every respect or resolve missing-data, multiplicity, and model-specification questions that are not reported in the registry record.
15. Multiplicity, Missing Data and Analysis Populations
The primary endpoint population is described as participants who were randomized and received at least one dose of study drug. The registry record does not report whether the primary analysis included every participant meeting that definition, how many endpoint measurements were missing, or how missing Month 3 outcomes were handled. It also does not report imputation procedures, sensitivity analyses, or other checks on the effect of missing data. Without those details, the posted response percentages cannot be used to assess how alternative missing-data assumptions might affect the estimates.
The trial assessed multiple secondary outcomes at multiple time points. The registry record does not report a multiplicity strategy, such as an ordering of hypotheses or an adjustment to control the chance of false-positive findings across these assessments. This does not invalidate the posted observations, but it limits how strongly isolated secondary results should be interpreted. An unadjusted p-value addresses a single comparison under its assumptions; it does not account for the broader set of outcomes and analyses.
The record also does not report the original statistical analysis plan, detailed endpoint-analysis model, or the original sample-size justification. The planning illustrations based on observed effects are separate from those unknown protocol details. The sponsor’s primary analysis method is identified as a large-sample approximation, but the record does not provide enough detail to assess all modeling decisions or whether additional adjustments were made.
The primary endpoint population should not be casually relabeled as an intention-to-treat population: the registry’s definition requires receipt of at least one dose. The registry record does not report the handling of participants who were randomized but did not receive study drug, nor the exact number contributing to each endpoint analysis beyond the arm summaries. These reporting gaps affect assessment of robustness and transparency, rather than changing the values that are posted.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Tofacitinib, 5 mg Twice Daily | 5 | 131 | 3.8% |
| Tofacitinib, 10 mg, Twice Daily | 8 | 132 | 6.1% |
| Placebo/Tofacitinib, 5 mg, Twice Daily | 2 | 66 | 3.0% |
| Placebo/Tofacitinib, 10 mg, Twice Daily | 1 | 65 | 1.5% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Tofacitinib, 5 mg Twice Daily | 49 of 131 |
| Tofacitinib, 10 mg, Twice Daily | 48 of 132 |
| Placebo/Tofacitinib, 5 mg, Twice Daily | 19 of 66 |
| Placebo/Tofacitinib, 10 mg, Twice Daily | 19 of 65 |
Most frequent serious adverse event terms
| Event term | Organ system | Tofacitinib, 5 mg Twice Daily | Tofacitinib, 10 mg, Twice Daily | Placebo/Tofacitinib, 5 mg, Twice Daily | Placebo/Tofacitinib, 10 mg, Twice Daily |
|---|---|---|---|---|---|
| Acute myocardial infarction | Cardiac disorders | 1 of 131 | 0 of 132 | 0 of 66 | 0 of 65 |
| Angina pectoris | Cardiac disorders | 1 of 131 | 0 of 132 | 0 of 66 | 0 of 65 |
| Atrial flutter | Cardiac disorders | 0 of 131 | 0 of 132 | 1 of 66 | 0 of 65 |
| Hyperthyroidism | Endocrine disorders | 0 of 131 | 1 of 132 | 0 of 66 | 0 of 65 |
| Inguinal hernia | Gastrointestinal disorders | 0 of 131 | 1 of 132 | 0 of 66 | 0 of 65 |
| Oral candidiasis | Infections and infestations | 1 of 131 | 0 of 132 | 0 of 66 | 0 of 65 |
| Parotitis | Infections and infestations | 0 of 131 | 1 of 132 | 0 of 66 | 0 of 65 |
| Pneumonia | Infections and infestations | 1 of 131 | 0 of 132 | 0 of 66 | 0 of 65 |
| Pyelonephritis | Infections and infestations | 0 of 131 | 1 of 132 | 0 of 66 | 0 of 65 |
| Femur fracture | Injury, poisoning and procedural complications | 0 of 131 | 1 of 132 | 0 of 66 | 0 of 65 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Tofacitinib, 5 mg Twice Daily | Tofacitinib, 10 mg, Twice Daily | Placebo/Tofacitinib, 5 mg, Twice Daily | Placebo/Tofacitinib, 10 mg, Twice Daily |
|---|---|---|---|---|---|
| Nasopharyngitis | Infections and infestations | 14 of 131 | 12 of 132 | 4 of 66 | 1 of 65 |
| Upper respiratory tract infection | Infections and infestations | 12 of 131 | 7 of 132 | 4 of 66 | 7 of 65 |
| Headache | Nervous system disorders | 10 of 131 | 12 of 132 | 3 of 66 | 4 of 65 |
| Diarrhoea | Gastrointestinal disorders | 10 of 131 | 8 of 132 | 2 of 66 | 2 of 65 |
| Nausea | Gastrointestinal disorders | 5 of 131 | 7 of 132 | 5 of 66 | 4 of 65 |
| Hypertension | Vascular disorders | 8 of 131 | 5 of 132 | 2 of 66 | 2 of 65 |
| Sinusitis | Infections and infestations | 3 of 131 | 5 of 132 | 4 of 66 | 2 of 65 |
| Bronchitis | Infections and infestations | 3 of 131 | 7 of 132 | 1 of 66 | 2 of 65 |
| Dizziness | Nervous system disorders | 7 of 131 | 1 of 132 | 0 of 66 | 1 of 65 |
Serious events with the highest arm-level rate: syncope (1.5%), atrial flutter (1.5%), asthma (1.5%), hypertensive crisis (1.5%), acute myocardial infarction (0.8%).
The posted serious adverse event counts are 5 of 131 participants in the tofacitinib 5 mg twice-daily group, 8 of 132 in the 10 mg twice-daily group, 2 of 66 in the placebo/tofacitinib 5 mg sequence, and 1 of 65 in the placebo/tofacitinib 10 mg sequence. The registry also lists serious-event terms with reported percentages, including syncope, atrial flutter, asthma, and hypertensive crisis at 1.5% each, and acute myocardial infarction and angina pectoris at 0.8% each.
These figures describe the posted counts and terms; they do not establish that events were caused by a particular treatment or allow a complete comparison of risk. The two placebo sequences switched to tofacitinib after 3 months, so their listed groups represent treatment sequences rather than a full-period placebo-only comparison. The registry record does not report deaths in the posted safety summary. Further detail about event timing, exposure-adjusted rates, severity beyond the serious-event classification, or attribution is not reported in the registry record.
17. What the Result Does, and Does Not, Mean
The Month 3 primary result shows that a larger percentage of participants met ACR20 in each tofacitinib group than in the placebo group. The sponsor-reported risk differences and confidence intervals quantify the size and uncertainty of those group contrasts under the reported analysis. The findings are specific to participants with active psoriatic arthritis who had an inadequate response to at least one TNF inhibitor, to the endpoint’s definition, and to the Month 3 assessment.
The results do not guarantee an individual response. Group percentages describe what occurred across trial participants, not the probability of benefit for a particular person in a different setting. ACR20 is a composite threshold, so the percentage meeting it does not show the size of improvement for each responder, the reasons other participants did not meet it, or how every component changed. It also does not answer whether effects continued after Month 3.
The separate comparisons with placebo do not establish a difference between the two tofacitinib doses. No direct dose-to-dose analysis is reported in the registry record. The results also do not determine whether the observed difference is important to every participant, since the registry results do not provide a threshold for clinical importance or participants’ preferences.
Finally, the primary efficacy comparison is not a complete benefit-risk assessment. Serious adverse event counts are posted, but the registry record does not provide enough detail to attribute events or establish a comprehensive safety comparison. Missing-data methods, multiplicity procedures, and several original design details are also not reported. These limits should accompany interpretation of the observed Month 3 contrast.
18. Why This Trial Matters Statistically
This trial presents a clear statistical comparison of a binary, clinically defined response at a specified time. Its randomized, parallel-group design and placebo comparator allow the Month 3 response percentages to be contrasted across groups. Reporting the risk difference alongside a confidence interval is useful because it communicates both the estimated separation between groups and uncertainty around that estimate, rather than relying on a p-value alone.
The comparison also illustrates why an endpoint definition matters. ACR20 is not a single symptom score: it requires improvement in joint counts and several additional core measures. The outcome therefore condenses multiple dimensions into a response classification. That makes the group percentage readily interpretable as a proportion meeting a criterion, but it also means the aggregate result does not reveal the pattern of change in every component or the range of individual experiences.
Statistically, the posted sponsor results and simple unadjusted recalculations agree in direction and estimated risk difference. The recalculations are useful as a transparent check, while the sponsor’s analysis remains the primary reported analysis. The record also provides a basis for recognizing the limits of summary results: detailed missing-data and multiplicity methods are not reported, and secondary outcomes must be interpreted with less confidence than the primary comparison.
The study’s treatment sequences make the Month 3 timing important. The placebo groups were scheduled to switch to tofacitinib after 3 months, so the primary comparison concerns the period before that switch. The results should not be generalized to later follow-up by assuming the Month 3 placebo contrast persisted unchanged.
19. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
- Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.
The registry record leaves several trial-specific uncertainties. Although the primary endpoint population is defined as randomized participants who received at least one dose, the record does not describe missing Month 3 outcome handling, the number of missing endpoint measurements, or sensitivity analyses. The reported arm counts and percentages cannot establish whether alternative missing-data assumptions would change the result.
The record identifies the primary analysis method as a large-sample approximation but does not report the full statistical analysis plan or detailed model specifications. It does not report a strategy for multiplicity across the many secondary outcomes and time points. The secondary recalculations are unadjusted and should not be treated as confirmatory sponsor analyses.
The primary comparisons are each against placebo; a direct comparison between tofacitinib doses is not reported. The Month 3 response threshold also provides limited information about durability, individual changes, or the contribution of separate components. The treatment sequences switched from placebo to tofacitinib after 3 months, limiting the interpretation of those groups as placebo comparators beyond the primary time point.
The record uses both triple-masked and double-blind descriptions and does not explain the masking roles. It does not report the original sample-size justification, detailed randomization procedures, or allocation concealment. Safety reporting includes serious adverse event counts and selected terms, but the registry record does not provide sufficient detail on event timing, attribution, exposure-adjusted rates, or deaths to support a comprehensive safety assessment.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Tofacitinib In Psoriatic Arthritis Subjects With Inadequate Response to TNF Inhibitors — NCT01882439.
- Registry record last updated 2017-09-15; status last verified 2017-09.
- Results first posted 2017-09-15.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
Continue through the Clinical Biostats statistical pathway
Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.
23. Record Summary
NCT01882439 is a completed phase 3 randomized, parallel-group trial sponsored by Pfizer. It enrolled 395 participants with active psoriatic arthritis and an inadequate response to at least one TNF inhibitor. Treatment sequences included tofacitinib 5 mg or 10 mg twice daily and placebo for 3 months followed by tofacitinib.
The primary endpoint was the percentage meeting ACR20 at Month 3 among randomized participants who received at least one dose. The sponsor reported risk differences versus placebo of 25.95 percentage points for 5 mg and 23.31 percentage points for 10 mg, with both reported p-values below < 0.001. Confidence intervals for both estimates were above zero.
Interpretation is limited by unreported details about missing data, multiplicity, and the original design and analysis plans. The posted secondary outcomes and serious adverse event counts provide additional context but do not resolve those limitations or establish a direct comparison between the two tofacitinib doses.