Study to Evaluate the Safety and Efficacy of CTP-543 in Adults With Moderate to Severe Alopecia Areata: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Study to Evaluate the Safety and Efficacy of CTP-543 in Adults With Moderate to Severe Alopecia Areata (NCT03137381), a randomized phase 2 study. The primary outcome is Percentage of Participants Achieving at Least a 50% Relative Reduction in Severity of Alopecia Tool (SALT) Score From Baseline at Week 24.

2. Clinical Question

The primary question focuses on a defined threshold of improvement in scalp hair loss rather than a change in average SALT score. It compares the proportion reaching that threshold in each dose cohort with the proportion in the combined placebo group. The endpoint is assessed at Week 24, after treatment lasting up to 24 weeks.

The registry record identifies the study as randomized and quadruple masked. Its official title describes it as double-blind; further detail about the masking arrangements is not reported in the registry record. The study enrolled 149 participants overall, while the primary efficacy analysis population is described by its eligibility for analysis rather than by that overall enrollment figure.

This is an efficacy question at a specific follow-up time and under the registry's responder definition. It does not, by itself, describe changes in other aspects of alopecia areata, results at other time points, or participants' longer-term outcomes. Those results are not reported in the registry record.

3. Trial Design

The registry record describes a randomized, phase 2 study of CTP-543 in adults with moderate to severe alopecia areata. The study is marked completed, with an enrollment of 149. The recorded start date is 2017-08-09, and the primary completion date is 2019-07-08. Concert Pharmaceuticals is listed as the sponsor.

Participants were assigned to three CTP-543 dose cohorts or to combined placebo. The active cohorts received 4 mg, 8 mg, or 12 mg twice daily, and the placebo group received matching placebo twice daily. Each regimen was planned for up to 24 weeks. The placebo group combined participants from the three cohorts, rather than being listed as a separate placebo group for each dose.

The registry classifies masking as quadruple. The official title calls the study double-blind, but the operational details of who was masked are not reported in the registry record. The study model is listed as sequential; how that label was implemented is not reported in the registry record.

For the primary efficacy outcome, participants were included if they received study drug and had at least 1 post-treatment SALT assessment during the treatment period. They were analyzed according to their randomized treatment group. This description identifies the registry's efficacy population but does not establish how other analysis populations were defined.

The original protocol's sample-size justification, planned enrollment by group, allocation ratio, and statistical analysis plan are not reported in the registry record. Nor does the record explain whether there were planned interim analyses or how the sequence of dose comparisons was handled statistically. These omissions limit what can be concluded about the trial's original design decisions.

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: 235 participants were screened, out of which 149 participants who experienced an episode of hair loss due to alopecia areata were enrolled to receive CTP-543 or placebo.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Efficacy Population included all participants who received study drug and had at least 1 post-treatment SALT assessment during the treatment period. Participants were analyzed according to their randomized treatment group.

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: Randomized population included all the randomized participants.

6. Primary Endpoint

The registry lists the primary outcome as Percentage of Participants Achieving at Least a 50% Relative Reduction in Severity of Alopecia Tool (SALT) Score From Baseline at Week 24, measured over Week 24.

The primary endpoint is the percentage of participants achieving at least a 50% relative reduction in SALT score from baseline at Week 24. SALT is a quantitative assessment of scalp hair loss. Its scores range from 0, indicating no hair loss, to a maximum of 100, indicating complete hair loss. Under the registry definition, a participant counts as a responder only if their Week 24 score meets the stated relative-reduction threshold from their own baseline.

This binary responder outcome turns a continuous score into two categories: participants who meet the threshold and those who do not. In general, such endpoints can make a result easier to interpret as the proportion of participants reaching a specified level of change. However, they do not show the full range of individual score changes. Participants just short of the threshold and those with little change are both counted as nonresponders, while participants meeting the threshold are counted as responders.

The Week 24 time point anchors the comparison to a particular follow-up. The registry does not report the primary outcome at other time points in the posted results. The primary analysis population includes participants who received study drug and had at least 1 post-treatment SALT assessment, with analysis according to randomized group. The registry record does not provide further details about handling participants without an eligible Week 24 assessment.

7. Results Posted in the Registry

• Cohort 1: CTP-543 4 mg BID: 21.4% (6/28) versus 9.3% (4/43) on control; risk difference 12.1 percentage points (95% CI -5.4 to 29.6), risk ratio 2.30 (0.71–7.44); unadjusted two-proportion z-test p = 0.151.
• Cohort 2: CTP-543 8 mg BID: 47.4% (18/38) versus 9.3% (4/43) on control; risk difference 38.1 percentage points (95% CI 20.0 to 56.2), risk ratio 5.09 (1.89–13.73); unadjusted two-proportion z-test p = <0.001.
• Cohort 3: CTP-543 12 mg BID: 58.3% (21/36) versus 9.3% (4/43) on control; risk difference 49.0 percentage points (95% CI 30.7 to 67.3), risk ratio 6.27 (2.37–16.60); unadjusted two-proportion z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary: each participant either met the responder definition or did not. The reported percentage is the fraction of participants in a group who were classified as responders. For this trial, the responder definition is at least a 50% relative reduction in SALT score from baseline at Week 24. The group percentages therefore describe the frequency of that event, not the average amount of score change.

What does a risk difference express?

A risk difference is the responder proportion in one group minus the responder proportion in the comparison group. It is expressed as a difference in proportions. A positive value indicates a higher observed responder proportion in the active-dose group than in the placebo group; a negative value indicates a lower observed proportion. The recalculated estimates are 0.121 for 4 mg, 0.381 for 8 mg, and 0.490 for 12 mg. These are unadjusted comparisons from the posted event counts and group sizes, not sponsor-adjusted estimates.

In general, a risk difference keeps the comparison on the absolute scale of the event rate. It can be useful for understanding how far apart the observed group proportions are. It does not, on its own, address uncertainty, possible confounding, missing outcomes, or whether the difference is clinically meaningful. The confidence interval adds information about statistical precision, while the trial design and analysis population help determine how the comparison should be interpreted.

What does a chi-squared test assess?

The registry reports chi-squared tests for the sponsor's three comparisons with placebo. In general, a chi-squared test evaluates whether the observed distribution of a categorical outcome across groups is compatible with a null hypothesis of no association between group and outcome. Here, the outcome is responder status. The test's p-value measures how unusual the observed data, or data more extreme, would be under the null model and its assumptions. It does not give the probability that the null hypothesis is true.

The sponsor-reported p-values are 0.177 for 4 mg versus placebo and <0.001 for each of the 8 mg and 12 mg comparisons. Those values should be distinguished from recalculated p-values based on posted summary counts. The 4 mg recalculation is 0.151, and the registry flags a discrepancy. The sponsor's own result takes precedence. The registry does not report more detail about the chi-squared test implementation or its assumptions.

How do relative measures differ from absolute measures?

The recalculated risk ratios are 2.304, 5.092, and 6.271 for the 4 mg, 8 mg, and 12 mg comparisons, respectively. The corresponding recalculated odds ratios are 2.659, 8.775, and 13.65. A risk ratio compares the responder proportions as a ratio, while an odds ratio compares the odds of response. These measures describe relative contrasts and are not interchangeable with risk differences. In general, relative measures can appear large when an event is uncommon, so they are best considered alongside the actual group percentages and an absolute-scale measure.

The recalculated risk-ratio confidence intervals are 0.713 to 7.439 for 4 mg, 1.889 to 13.73 for 8 mg, and 2.369 to 16.6 for 12 mg. The recalculated odds-ratio confidence intervals are 0.676 to 10.45, 2.616 to 29.43, and 4.014 to 46.41, respectively. These are also unadjusted recalculations, not sponsor-reported estimates. The registry record does not report sponsor confidence intervals for these measures.

Why does the analysis population matter?

The primary efficacy population consists of participants who received study drug and had at least 1 post-treatment SALT assessment during the treatment period. They were analyzed according to randomized group. This defines who contributes to the posted efficacy outcome and how treatment assignment is used in the comparison. In general, exclusions or missing outcome assessments can affect the interpretation of a randomized comparison. The registry does not explain how missing Week 24 measurements were handled, whether additional analysis populations were used, or whether sensitivity analyses were performed.

None of the recalculated tests or intervals should be read as a replacement for the sponsor's analysis. They are unadjusted calculations from the posted summary counts. Because the record flags a discrepancy, the sponsor's reported analysis is the primary inferential result to cite. The registry does not report the full statistical analysis plan, so details beyond the methods explicitly listed cannot be confirmed.

10. Confidence Intervals and Precision

The recalculated risk-difference intervals provide a range of values compatible with the posted data under the calculation used, subject to its assumptions. In general, a confidence interval describes uncertainty in an estimate: wider intervals indicate less precision, while narrower intervals indicate greater precision. It is not a guarantee that the true value lies within the interval, nor is it a range of individual participant outcomes.

For 4 mg versus placebo, the recalculated risk difference is 0.121, with a confidence interval from -0.054 to 0.296. This interval includes zero, so the recalculated data do not rule out a zero risk difference under the interval method used. For 8 mg, the estimate is 0.381, with an interval from 0.200 to 0.562. For 12 mg, the estimate is 0.490, with an interval from 0.307 to 0.673. The latter two intervals do not include zero. These intervals are unadjusted recalculations, not sponsor-reported confidence intervals.

The 4 mg interval spans values on both sides of zero and is comparatively uncertain about the direction of the risk difference. The intervals for all comparisons also span a range of possible magnitudes, particularly for the relative measures. The recalculated risk-ratio and odds-ratio intervals are wide, which signals substantial uncertainty about the size of those relative contrasts. In general, relative measures can be especially sensitive to the limited event counts in groups.

The registry reports sponsor p-values but no sponsor confidence intervals for the primary comparisons. Given the flagged discrepancy, the recalculated intervals should be treated as descriptive supporting calculations rather than as the sponsor's inferential results. The registry record does not report whether the sponsor used a different interval method, adjustments, or other modeling choices.

11. Planning a Similar Trial: Sample Size

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

The sample-size estimates are planning illustrations based on the observed effect, not the original trial's design calculations. For these binary responder outcomes, the figures refer to participants per arm, not total events. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The target effect is set to the stated fraction of the observed effect: 100%, 75%, or 50%.

The 80% power column gives the estimated number of participants per arm for a future comparison to have an 80% chance of detecting the specified effect under those assumptions, if that effect is present. The 90% power column gives the corresponding estimate for a 90% chance. Power is a property of a planned study under assumed conditions; these figures are not a measure of the probability that the trial result is correct.

For example, planning for 75% of the observed effect means calculating an illustrative sample size for an effect smaller than the one observed in this trial. The posted estimates vary by dose comparison and by assumed effect fraction. Smaller effects need more participants to detect under otherwise similar assumptions. These estimates are per arm, and they do not state the total enrollment required after accounting for any other design features.

The original protocol's sample-size assumptions and justification are not reported in the registry record. These calculations are not observed power; they are planning scenarios based on the observed effect and the stated assumptions. They should not be interpreted as showing that the completed trial was adequately or inadequately powered.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

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

Worked calculation for this trial

1. Control proportion p₀ = 0.093; treatment proportion p₁ = 0.214; average p̄ = 0.154.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5100 = 0.9996.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.5027 = 0.4231.
4. n = (0.9996 + 0.4231)² / (0.1213)² = 137.6, rounded up to 138 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 <- 0.0930232558139535                          # control proportion
p1 <- 0.214285714285714                          # 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(3137381)
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 = 138 (80% power), 184 (90% power)
 75% of observed effect: n per arm = 226 (80% power), 302 (90% power)
 50% of observed effect: n per arm = 461 (80% power), 617 (90% power)
power.prop.test: 137.6 
Simulated power at n = 138 per arm: 0.811 (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.

13. Analyses Reported by the Sponsor

The sponsor's posted analyses compare each CTP-543 dose with combined placebo using chi-squared tests. The reported p-values are 0.177 for the 4 mg comparison and <0.001 for both the 8 mg and 12 mg comparisons. The registry record also includes unadjusted recalculations from the posted group counts, with p-values of 0.151, <0.001, and <0.001 for those comparisons, respectively.

The registry flags a discrepancy between the sponsor analysis and recalculation. The sponsor's own analysis takes precedence. Accordingly, the 4 mg sponsor result should be reported as p = 0.177 rather than replaced by the recalculated p-value. The posted sponsor results and recalculated values agree in being reported as <0.001 for the 8 mg and 12 mg comparisons, though agreement at that reporting threshold does not establish that the analyses used identical methods.

The registry does not explain the source of the discrepancy or provide the complete statistical analysis plan. The recalculated risk differences, risk ratios, odds ratios, and confidence intervals are simple unadjusted re-calculations from posted summary statistics; they should not be presented as sponsor estimates. For inference, use the sponsor's posted analysis while describing the recalculations as supplementary and explicitly unadjusted.

14. Multiplicity, Missing Data and Analysis Populations

The registry reports three sponsor comparisons of an active dose with combined placebo for the primary responder outcome. The corresponding p-values are 0.177 for 4 mg and <0.001 for both 8 mg and 12 mg. When several comparisons are made, the chance of at least one apparently notable result under a collection of null hypotheses can increase. In general, multiplicity procedures can control that risk by adjusting the testing strategy or the interpretation threshold.

Whether the trial used a multiplicity adjustment, a hierarchical testing procedure, or a prespecified order for the dose comparisons is not reported in the registry record. The statistical analysis plan is not reported in the registry record. Therefore, the posted p-values should be read as reported, without assuming that they were adjusted or that a particular comparison was designated as the only confirmatory test.

The registry describes the primary efficacy population as participants who received study drug and had at least 1 post-treatment SALT assessment during the treatment period, analyzed according to randomized group. The handling of participants without a Week 24 assessment, the method for missing primary outcome data, and any sensitivity analyses are not reported in the registry record. No assumptions about imputation or other missing-data procedures can be established from the posted description.

The registry lists 2 outcome measures but posts no secondary outcome results. The content and analysis of the other outcome measure are not reported in the registry record. Interim analyses and stopping rules are also not reported in the registry record. Without these details, the multiplicity and missing-data context for the primary p-values cannot be fully assessed.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: cellulitis (2.8%).

The registry reports serious adverse event figures separately from the efficacy outcome. The serious adverse event counts and at-risk denominators are 0 of 44 for combined placebo, 0 of 29 for the 4 mg cohort, 0 of 38 for the 8 mg cohort, and 1 of 36 for the 12 mg cohort. No deaths are reported in any of these groups. The top serious adverse event term listed is cellulitis, at 2.8%; the record does not identify its group in that listing.

These figures describe the serious adverse events recorded in the registry for the groups and denominators shown. They do not establish that an event was caused by the assigned treatment, and the registry extract does not provide enough detail to assess causality, severity grading, timing, or the relationship to treatment. A zero count in a group means no serious adverse event was recorded for that group in the posted results; it does not establish that the risk is absent.

The serious adverse event denominators differ from the group sizes reported for the primary efficacy outcome. The registry does not explain this difference. Other adverse events were also recorded, but they are distinct from serious adverse events and should not be conflated with the serious-event counts. The figures are a limited summary and do not replace the trial's full safety reporting.

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

The posted results show that the percentage meeting the Week 24 SALT responder definition was 9.3% with combined placebo, 21.4% with CTP-543 4 mg, 47.4% with 8 mg, and 58.3% with 12 mg. The sponsor's reported comparisons with placebo give p = 0.177 for 4 mg and p < 0.001 for 8 mg and 12 mg. These statements describe the registered endpoint, groups, population, and time point.

The results do not show the full distribution of SALT score changes. A responder percentage does not reveal how far each participant's score changed, and it does not distinguish between people who narrowly miss the threshold and those who have a different degree of change. The registry record does not report additional outcome results that would address those questions.

The results also do not establish the clinical importance of the differences, durability after treatment, or outcomes beyond Week 24. The study regimen was for up to 24 weeks, and longer-term results are not reported in the registry record. The observed percentages are specific to participants in the study and should not be assumed to apply identically to other populations or settings.

Statistical interpretation is limited by the absence of the full analysis plan, the unreported handling of missing Week 24 data, and the lack of information about multiplicity adjustments. The recalculated effect estimates and intervals are unadjusted; because the registry flags a discrepancy, the sponsor's reported analysis takes precedence for inferential interpretation. Neither a p-value nor a confidence interval alone establishes a treatment's clinical value.

17. Why This Trial Matters Statistically

Statistically, this trial illustrates why a binary responder outcome should be read alongside both the group percentages and an effect measure. The percentages communicate how often the prespecified SALT threshold was reached in each group. Risk differences express the absolute contrast, while risk ratios and odds ratios express relative contrasts. The estimates answer related but distinct questions and can convey different impressions of the same data.

The results also show why uncertainty matters. A point estimate is a single summary of the observed groups, whereas an interval indicates the range of values compatible with the data under a specified calculation. The 4 mg recalculated risk-difference interval includes zero, while the recalculated intervals for the 8 mg and 12 mg comparisons do not. Those intervals are not sponsor-reported, and the registry flags a discrepancy, so they should be interpreted as unadjusted supporting calculations.

The three dose comparisons bring attention to multiplicity. Several comparisons can complicate interpretation if the testing strategy is unknown; the registry does not report whether adjustments or an ordered procedure were planned. The registry also gives limited information about missing outcomes and the analysis plan. These gaps matter because statistical results depend not only on observed percentages but also on the prespecified analysis and how incomplete data are handled.

Finally, planning estimates based on observed effects are not substitutes for a trial's original design rationale. Their values change when the assumed effect is reduced, illustrating the general relationship between effect size and required sample size under fixed planning assumptions. They do not describe the power of this completed study.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

The primary endpoint captures whether a participant crossed a defined responder threshold at Week 24, rather than the full extent or pattern of SALT score change. The registry record does not report the score distributions or other outcome results needed to describe changes outside that binary classification.

The placebo group is combined across the three dose cohorts. The registry does not provide a separate placebo result for each cohort, so the posted comparisons use a shared combined placebo group. It is not reported whether cohort-specific features or other design details affected those comparisons.

The efficacy group sizes are 43 for placebo, 28 for 4 mg, 38 for 8 mg, and 36 for 12 mg. The registry's overall enrollment is 149, and the record does not explain the difference between that total and the listed efficacy group sizes. The serious adverse event denominators are also different from the efficacy group sizes, with no explanation reported.

Important analytic details are absent: the original sample-size justification, the full statistical analysis plan, missing-data handling, multiplicity procedures, and any interim analyses are not reported in the registry record. The registry also flags a discrepancy between sponsor results and recalculation. These limitations constrain assessment of the inferential details beyond the sponsor's posted analyses and the stated endpoint results.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Study to Evaluate the Safety and Efficacy of CTP-543 in Adults With Moderate to Severe Alopecia Areata — NCT03137381.
• Registry record last updated 2022-07-19; status last verified 2022-06.
• Results first posted 2022-07-19.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

The registry record describes a completed randomized phase 2 study sponsored by Concert Pharmaceuticals, with enrollment of 149 adults with moderate to severe alopecia areata. Participants received CTP-543 4 mg, 8 mg, or 12 mg twice daily, or combined matching placebo, for up to 24 weeks. The listed masking is quadruple; the official title describes the study as double-blind.

The primary outcome was the percentage achieving at least a 50% relative reduction in SALT score from baseline at Week 24. The posted percentages were 9.3% for placebo, 21.4% for 4 mg, 47.4% for 8 mg, and 58.3% for 12 mg. Sponsor p-values were 0.177, <0.001, and <0.001 for the respective dose comparisons with placebo. A discrepancy is flagged, so the sponsor's own analysis takes precedence over unadjusted recalculations.

The registry reports 0 serious adverse events in the placebo, 4 mg, and 8 mg groups, and 1 in the 12 mg group; no deaths are listed. Further details about the statistical plan, multiplicity, and missing-data handling are not reported in the registry record.