A Study To Assess the Adverse Effects and Change in Condition of OnabotulinumtoxinA X Injection in Adult Participants With Forehead Lines: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Study To Assess the Adverse Effects and Change in Condition of OnabotulinumtoxinA X Injection in Adult Participants With Forehead Lines (NCT05152576), a randomized phase 2 study. The primary outcome is Number of Participants With Adverse Events.

2. Clinical Question

3. Trial Design

This completed phase 2 study used randomized allocation, triple masking, and a parallel-group design. Participants were assigned to placebo or one of three onabotulinumtoxinA X dose groups. The registry lists an enrollment of 124. Its study summary describes an anticipated enrollment of around 120 adults and approximately 10 United States sites.

Each group received a single forehead injection on Day 1, either placebo or the assigned dose of onabotulinumtoxinA X. The summary notes that participants attended regular monthly visits at the study site. The primary outcome covers Day 1 to Day 180. The study start date is 2021-11-29, the primary completion date is 2022-09-06, and the record status is completed.

The primary result is reported for the safety population. The posted group sizes for this outcome are 29 for placebo, 35 for Dose A, 31 for Dose B, and 28 for Dose C. The posted counts of participants with an adverse event are 10, 12, 18, and 13, respectively. A separate safety listing uses different at-risk counts for placebo; the reason for the difference is not reported in the registry record.

The registry record does not report the randomization sequence, allocation concealment, the identities of the masked parties, or the exact visit schedule beyond regular monthly visits. It also does not report the study's original sample-size justification or detailed statistical analysis plan. These omissions limit how fully the design and the analysis choices can be evaluated from the record.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Safety population

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.

6. Primary Endpoint

The registry lists the primary outcome as Number of Participants With Adverse Events, measured over Day 1 to Day 180.

The primary endpoint is the number of participants in the safety population who experienced an adverse event from Day 1 to Day 180. An adverse event is defined in the registry as an untoward medical occurrence in a participant who received a pharmaceutical product; the event need not have a causal relationship with the treatment. The investigator assesses the relationship of each event to study treatment.

This endpoint counts participants with an event, rather than the total number of separate events. A participant with one or more events contributes to the participant count, and the posted result does not describe event frequency, duration, or severity for every event. The endpoint is used to describe safety during the stated follow-up period. It does not, on its own, measure whether forehead lines changed.

The registry separately defines a serious adverse event as an event meeting specified serious criteria, including death, a life-threatening event, hospitalization, congenital anomaly, persistent or significant disability, or an important medical event that may require intervention. Serious events are therefore a safety category distinct from the primary count of participants with any adverse event. The registry record does not report a primary efficacy result among the posted outcomes.

7. Results Posted in the Registry

• OnabotulinumtoxinA X Dose A: 34.3% (12/35) versus 34.5% (10/29) on control; risk difference -0.2 percentage points (95% CI -23.6 to 23.2), risk ratio 0.99 (0.50–1.96); unadjusted two-proportion z-test p = 0.987.
• OnabotulinumtoxinA X Dose B: 58.1% (18/31) versus 34.5% (10/29) on control; risk difference 23.6 percentage points (95% CI -0.9 to 48.1), risk ratio 1.68 (0.94–3.02); unadjusted two-proportion z-test p = 0.067.
• OnabotulinumtoxinA X Dose C: 46.4% (13/28) versus 34.5% (10/29) on control; risk difference 11.9 percentage points (95% CI -13.4 to 37.3), risk ratio 1.35 (0.71–2.55); unadjusted two-proportion z-test p = 0.358.

8. Statistical Interpretation

9. Statistical Methods Explained

What does a risk difference mean?

A risk difference compares the proportion of participants with an event in one group with the proportion in another. Here, each dose group is compared with placebo, and the event is having at least one adverse event during Day 1 to Day 180. A positive estimate means the observed event proportion was higher in the dose group than in placebo; a negative estimate means it was lower. A value of zero represents no difference in the proportions. This is a general explanation of the measure, not a claim about causation.

The posted calculations use the participants with an event and the group denominators. For Dose A, the risk-difference estimate is -0.002; for Dose B, it is 0.236; and for Dose C, it is 0.120. These are unadjusted comparisons. They do not account for other participant characteristics, and the registry record does not report an adjusted comparison.

How should the confidence intervals be understood?

A confidence interval describes uncertainty around an estimate under the statistical method used. In general, a wider interval indicates less precision, while a narrower interval indicates greater precision. For a risk difference, an interval that includes zero is compatible with no difference under the method used, as well as with values on either side of zero. Each posted interval includes zero. This does not prove that the groups are identical; it means the estimates are imprecise enough that the data do not isolate a difference from no difference.

The interval is not a range containing every possible value, and it does not give the probability that a particular effect is correct. Its interpretation depends on the statistical method and assumptions. The registry record does not give details of the interval procedure, so readers should not infer more about its construction than is posted.

What do the p-values add?

A p-value describes how unusual data at least as incompatible with a specified null hypothesis would be if that hypothesis and the statistical assumptions were true. It does not measure the size or importance of an effect, and it is not the probability that the null hypothesis is true. The posted unadjusted p-values are 0.987 for Dose A, 0.067 for Dose B, and 0.358 for Dose C. Their interpretation depends on the comparison and analysis assumptions; they should be read alongside the estimates and confidence intervals rather than alone.

The record does not report whether the study's original analysis used a particular threshold for formal hypothesis testing. The significance level of 0.05 appears among the assumptions for the planning illustration, but that assumption is not evidence that the trial's original analysis plan used the same threshold.

Why are relative risks and odds ratios also shown?

A relative risk compares the event proportions as a ratio, while an odds ratio compares the event odds. These measures can help express a binary outcome from different perspectives. General statistical interpretation applies: a relative risk or odds ratio of one corresponds to equal values in the compared groups. These measures do not remove uncertainty, compensate for small group sizes, or provide evidence independent of the risk difference. All are based on the same event counts.

The registry comparison entries include relative-risk and odds-ratio estimates with intervals. Their intervals are broad, consistent with uncertainty in comparisons based on the posted group sizes. Because the primary outcome is common enough in these groups that the distinction between risks and odds may matter, the odds ratio should not be read as though it were a risk difference. No adjusted versions of these measures are reported.

Why does the outcome type matter?

This is a binary participant-level outcome: each participant is classified according to whether an adverse event occurred during the stated period. General methods for binary data compare event proportions or use measures such as risk differences, relative risks, and odds ratios. This differs from an outcome that counts all event episodes, measures time until an event, or records a continuous measurement. The primary result does not report the number of separate adverse-event episodes per participant.

General statistical methods may also need to account for repeated observations, clustering, or other features when a design includes them. The posted primary outcome is a participant count, and the registry record does not report a model specification or additional adjustment for such features. No particular unreported method should be assumed.

What is recalculated, and what is not known?

The comparison statistics are unadjusted re-calculations from the posted summary counts. They are descriptive comparisons derived from those counts, not a substitute for a complete trial analysis plan. The record does not report the original sample-size rationale, the trial's own full statistical methods, or whether interim analyses were conducted. It also does not report methods for missing observations or the handling of participants who may not have completed follow-up. Those details matter when assessing whether an analysis matches the trial design and how broadly its findings can be interpreted.

The reported primary endpoint population is the safety population. The record does not provide a detailed definition of that population or explain why its posted primary outcome group sizes differ from the at-risk counts in the separate serious-adverse-event listing. These counts should therefore be understood in the context of their respective registry result summaries, without assuming that they represent identical analysis sets.

10. Confidence Intervals and Precision

The primary outcome group sizes are 29 for placebo, 35 for Dose A, 31 for Dose B, and 28 for Dose C. The posted counts with an adverse event are 10, 12, 18, and 13, respectively. Confidence intervals around the risk differences include zero for all three dose-versus-placebo comparisons. This means the posted data are compatible with no difference as well as with differences in either direction under the interval method. The intervals should not be interpreted as proving that the groups are the same.

Precision is limited by the size of the groups and by the amount of information available in a binary outcome. The interval for each comparison spans a broad range of plausible risk differences, so the estimated direction and size are not pinned down closely. Dose B has a larger positive point estimate than the other dose comparisons, but its confidence interval still includes no difference. A point estimate alone gives an incomplete account of the uncertainty.

Confidence intervals describe uncertainty in the estimate under the statistical procedure; they do not capture every limitation of the trial. They do not address unreported analysis choices, missing-data handling, or the absence of posted secondary results. The registry record does not report the interval method in enough detail to assess its assumptions fully. These results are best read as estimates with substantial uncertainty, rather than as precise measurements of differences between groups.

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 planning figures are participants per arm for each two-group comparison, not total events. They are illustrations based on the observed effect, not the original trial's design justification. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set to the stated fraction of the observed effect. The trial's own original sample-size assumptions are not reported in the registry record.

The 80% power column gives the planned number of participants per arm under those assumptions to have an 80% chance of detecting the specified effect if that effect is real. The 90% power column gives the corresponding number per arm for a higher chance of detecting it. These are planning targets under a model, not guarantees about the outcome of a future study. This is not observed power.

For example, planning for the full observed Dose B effect gives 69 participants per arm for 80% power and 92 per arm for 90% power. Planning for 75% of that observed effect gives 123 and 163 per arm, respectively. For Dose C, the corresponding full-effect figures are 264 and 353 per arm. Smaller effects require more participants because they are harder to distinguish from random variation. Dose A's observed risk-difference estimate is -0.002, so planning around that very small observed difference produces extremely large participant requirements: 912,173 per arm for 80% power and 1,221,140 per arm for 90% power at the full observed effect. These illustrations do not establish what sample size the trial originally planned or was designed to detect.

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 = 0.345; treatment proportion p₁ = 0.343; average p̄ = 0.344.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6717 = 1.3166.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6717 = 0.5653.
4. n = (1.3166 + 0.5653)² / (-0.0020)² = 912,172.1, rounded up to 912,173 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 <- 0.344827586206897                          # control proportion
p1 <- 0.342857142857143                          # 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(5152576)
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 = 912,173 (80% power), 1,221,140 (90% power)
 75% of observed effect: n per arm = 1,622,193 (80% power), 2,171,656 (90% power)
 50% of observed effect: n per arm = 3,651,177 (80% power), 4,887,889 (90% power)
power.prop.test: 912172.1 
Simulated power at n = 912,173 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.

13. Multiplicity, Missing Data and Analysis Populations

The trial has three dose-versus-placebo comparisons for the primary adverse-event outcome. The posted p-values are unadjusted. The registry record does not report whether the original analysis controlled for multiple comparisons, specified a testing hierarchy, or treated the comparisons as exploratory. When several hypotheses are considered, the chance of at least one apparently unusual result can increase; general methods can address this through prespecified multiplicity procedures. Without a reported procedure, the three p-values should not be treated as if they were necessarily adjusted or independent.

The record lists three outcome measures and three analyses, but no secondary results are posted. The primary result is the number of participants with adverse events in the safety population. No posted secondary result establishes a change in forehead lines. The registry record does not report a full endpoint hierarchy or the planned role of each analysis.

Missing-data handling is not reported in the registry record. It is therefore not possible to determine from the posted results how missing visits, incomplete follow-up, or other unavailable outcome information were handled. The record also does not report whether interim analyses were planned or performed. These are unknowns, not evidence that missing data or interim analyses did or did not occur.

The primary endpoint group sizes are 29, 35, 31, and 28, while the separate serious-adverse-event listing gives at-risk counts of 30, 35, 31, and 28. The reason for the placebo difference is not reported in the registry record. The result is identified as being for the safety population, but the record does not provide a detailed definition of that population or explain how participants were included in each result summary. Consequently, the analysis populations should not be assumed to be identical across the primary outcome and safety listings.

14. 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: kidney infection (3.3%).

The serious-adverse-event listing reports at-risk counts of 30 for placebo, 35 for Dose A, 31 for Dose B, and 28 for Dose C. The counts listed as related serious adverse events are 1, 0, 0, and 0, respectively. Deaths are reported as 0 in every group. These counts are distinct from the primary endpoint counts of participants with any adverse event, and the at-risk denominator for placebo differs between the two result summaries.

The listing also reports other related adverse-event counts of 4 for placebo, 5 for Dose A, 10 for Dose B, and 9 for Dose C. The most frequent serious-event term listed is KIDNEY INFECTION, reported as 3.3%. The registry record does not give the event count associated with that term in the posted summary. These safety summaries describe reported events and investigator assessments; they do not establish that an event was caused by the injection. The reason for the differing placebo at-risk counts is not reported in the registry record.

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

The posted primary result describes how many participants in each group had at least one adverse event from Day 1 to Day 180. The counts are 10 of 29 for placebo, 12 of 35 for Dose A, 18 of 31 for Dose B, and 13 of 28 for Dose C. The unadjusted risk-difference estimates are -0.002 for Dose A, 0.236 for Dose B, and 0.120 for Dose C. The confidence intervals for all three comparisons include no difference, and the estimates are imprecise.

These findings do not determine whether an adverse event was caused by treatment. The endpoint definition includes untoward medical occurrences without requiring a causal relationship, and the investigator assesses each event's relationship to study use. The separate serious-event listing reports related serious-event counts, but those counts do not replace the primary endpoint or establish causal effects.

The primary outcome is a safety measure, not a direct measure of forehead-line change. Although the study summary describes evaluation of safety and change in condition, no secondary results are posted. The primary result therefore does not show the extent of change in forehead lines. It also does not provide a complete account of event severity, duration, recurrence, or the participant-level experience of treatment.

The comparison estimates are based on the posted counts and are unadjusted. Their uncertainty, the modest group sizes, and the unreported details of missing-data handling and multiplicity limit the conclusions that can be drawn. The registry record does not report the original sample-size rationale or full statistical plan. The data support a description of the posted event counts and their uncertain comparisons; they do not justify broader conclusions beyond those outcomes and analyses.

16. Why This Trial Matters Statistically

This trial illustrates why a clinical result needs to be read in terms of its actual endpoint. The registry summary describes both safety and change in condition, but the posted primary result is a count of participants with adverse events. That distinction matters: a safety count cannot answer a question about change in forehead lines, and no secondary results are posted to address that outcome.

The trial also shows how the point estimate and its uncertainty work together. Dose B has the largest positive risk-difference estimate among the three dose comparisons, but its confidence interval includes no difference. The other estimates also have intervals that include no difference. Reading only the point estimates or p-values would obscure how broadly uncertain the comparisons are.

Finally, the record demonstrates the importance of transparent analysis details. The comparisons are unadjusted, while the handling of multiplicity, missing data, interim analyses, and the original sample-size rationale is not reported in the registry record. Those omissions do not erase the posted counts, but they constrain what can be inferred about the analysis plan and the reliability of broader conclusions. For biostatisticians and clinical researchers, separating reported results from unreported methods is essential to a careful reading.

17. 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.

The registry record does not report the original sample-size justification, so the enrolled total cannot be assessed against the trial's planned detectable effect from the posted information. The planning illustrations based on observed effects do not fill that gap. The record also does not report the full statistical analysis plan, including the planned multiplicity approach, interim analysis details, or missing-data methods.

The posted primary endpoint is limited to whether a participant experienced an adverse event during Day 1 to Day 180. It does not provide a full account of the number, duration, severity, or recurrence of events. The primary results are for the safety population, but the registry record does not give its detailed definition. The placebo at-risk count also differs between the primary endpoint summary and the separate serious-adverse-event listing, and the reason is not reported.

The study has four groups and relatively small posted group sizes for the primary outcome. The unadjusted comparisons have wide uncertainty, and no secondary results are posted. The registry record describes approximately 10 United States sites but does not report site-level results or enough information to assess variation across sites. Further eligibility criteria and details of masking, allocation concealment, and the injection doses are not reported in the registry record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: A Study To Assess the Adverse Effects and Change in Condition of OnabotulinumtoxinA X Injection in Adult Participants With Forehead Lines — NCT05152576.
• Registry record last updated 2025-07-16; status last verified 2025-06.
• Results first posted 2025-07-16.
• 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.

21. Record Summary

NCT05152576 is a completed, randomized, triple-masked, parallel-group phase 2 study sponsored by Allergan. It enrolled 124 adults with forehead lines and compared placebo with three onabotulinumtoxinA X dose groups. The listed study start date is 2021-11-29, and the primary completion date is 2022-09-06.

The primary outcome is the number of participants with adverse events from Day 1 to Day 180 in the safety population. Posted counts were 10 of 29 for placebo, 12 of 35 for Dose A, 18 of 31 for Dose B, and 13 of 28 for Dose C. The unadjusted risk-difference comparisons have confidence intervals that include no difference. The registry record does not report secondary results, the original sample-size justification, or several details of the statistical plan.