Safety and Efficacy Study of Botulinum Toxin Type A for the Treatment of Crow's Feet Lines and Frown Lines: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Safety and Efficacy Study of Botulinum Toxin Type A for the Treatment of Crow's Feet Lines and Frown Lines (NCT01224015), a randomized phase 3 study. The primary outcome is Percentage of Participants Achieving a Grade of None or Mild at Maximum Smile Based on the Investigator Facial Wrinkle Scale Assessment of the Severity of Crow's Feet Lines.

2. Clinical Question

The registry describes this as a safety and efficacy study of botulinum toxin type A for crow’s feet and frown lines in people who had completed an earlier study. The primary endpoint focuses specifically on crow’s feet lines, rather than combining crow’s feet and frown-line assessments into one outcome. The reported comparison is therefore about the distribution of this particular Day 30 severity category, not every feature of facial appearance or every outcome that might matter to participants.

The record reports a randomized, double-masked, parallel-group trial and a planned total enrollment of 684. The posted outcome results cover the 44 U group, the 24 U group, and the normal saline placebo group. Randomization and masking describe features of the trial design, but details such as the randomization procedure, how masking was maintained, and how treatment allocation was concealed are not reported in the registry record.

3. Trial Design

NCT01224015 is recorded as a phase 3 randomized, double-masked, parallel-group study sponsored by Allergan. The registry lists the start as 2011-05, primary completion as 2011-10, and the study status as completed. Enrollment is recorded as 684. The registry record does not give the number of participants screened, the number who completed follow-up, or the reasons participants may have left the study.

Three groups are described: onabotulinumtoxinA 44 U, onabotulinumtoxinA 24 U, and placebo consisting of normal saline. The 44 U group received the stated total dose in the bilateral crow’s feet and frown-line areas. The 24 U description specifies 24 units total and placebo injections in those areas. The placebo group received normal saline injections in the same areas. Each group description allows for up to 2 treatments during the study; the number of treatments actually received by participants is not reported in the registry record.

The endpoint population is described as the intent-to-treat population, consisting of all randomized participants with data available for analysis. The posted group sizes for this endpoint are 349 for the 44 U group, 223 for the 24 U group, and 95 for placebo. These are the denominators reported with the endpoint results. The registry’s planned enrollment is a separate design figure and should not be treated as the denominator for every posted outcome.

The record does not report the trial’s original sample-size justification, the planned statistical analysis methods, the detailed visit schedule, or whether interim analyses were planned or conducted. It also does not describe how missing endpoint measurements were handled beyond defining the analysis population as randomized participants with data available. Those omissions limit what can be said about the protocol’s planned statistical approach.

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: Extension study for patients who participated in study 191622-099

Overall Study

Analysis population for the primary outcome, as defined in the registry: Participants from the Intent-to-treat population, consisting of all randomized participants with data available for analysis.

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 Percentage of Participants Achieving a Grade of None or Mild at Maximum Smile Based on the Investigator Facial Wrinkle Scale Assessment of the Severity of Crow's Feet Lines, measured over Day 30.

The primary endpoint is the percentage of participants whose investigator-assessed crow’s feet lines were graded none or mild at maximum smile on Day 30. Investigators used a four-point Facial Wrinkle Scale: 0 means none, 1 means mild, 2 means moderate, and 3 means severe. The reported endpoint combines the first two categories into a single outcome: a score of none or mild.

This endpoint represents a categorical summary of a clinical rating at a specified facial expression and time point. It is not a continuous measure of the amount of wrinkle change, nor does it report how far an individual’s score moved from an earlier assessment. The endpoint description does not report a baseline score or a change-from-baseline analysis. It also does not show the separate percentages for none and mild, since those categories are reported together.

In general, a binary endpoint such as this makes it possible to compare the proportion of participants who meet a defined threshold between groups. It can be straightforward to interpret as a share of participants meeting the stated criterion. At the same time, combining categories means that different scores within the none-or-mild group are treated alike for this outcome, and scores of moderate and severe are both outside the reported success category.

The endpoint is limited to crow’s feet severity, as assessed by an investigator. Although the study also concerns frown lines, the posted primary outcome does not report a combined assessment of crow’s feet and frown lines. The relevance of the threshold to participants’ own experience, and whether the result corresponds to a change they would notice, is not reported in the registry record.

7. Results Posted in the Registry

• onabotulinumtoxinA 44U: 63.6% (222/349) versus 1.1% (1/95) on control; risk difference 62.6 percentage points (95% CI 57.1 to 68.0), risk ratio 60.43 (8.59–425.27); unadjusted two-proportion z-test p = <0.001.
• onabotulinumtoxinA 24U: 56.5% (126/223) versus 1.1% (1/95) on control; risk difference 55.4 percentage points (95% CI 48.6 to 62.3), risk ratio 53.68 (7.61–378.42); unadjusted two-proportion z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The main outcome is binary for the purpose of the posted comparison: each participant either had a score of none or mild at maximum smile on Day 30, or did not. In general, a percentage for a binary endpoint is the proportion of participants in a group meeting the stated criterion. The posted percentages are 63.6% for onabotulinumtoxinA 44 U, 56.5% for onabotulinumtoxinA 24 U, and 1.1% for placebo. The corresponding endpoint group sizes are 349, 223, and 95.

What does a risk difference express?

A risk difference compares two proportions by subtracting one group’s proportion from the other’s. It is expressed on the probability scale, with zero representing equal proportions. A positive value in a treatment-versus-placebo comparison means the observed proportion meeting the endpoint was higher in the treatment group. The registry reports an unadjusted risk difference of 0.626 for 44 U versus placebo, and 0.554 for 24 U versus placebo. These are the posted estimates; no conversion or alternative adjusted estimate is needed to describe them.

Risk differences are often useful because they express the absolute separation between group proportions. They should be distinguished from relative measures, which compare proportions as a ratio. The registry also includes relative-risk and odds-ratio values, but the interpretation above emphasizes the risk differences as the posted comparison metric. Neither an absolute nor relative measure, on its own, describes how individual participants changed over time.

How should the p-values be read?

The posted p-values are unadjusted and are <0.001 for each treatment-versus-placebo comparison. In general, a p-value measures how incompatible the observed data are with a specified null hypothesis under a statistical model. It is not the probability that the null hypothesis is true, and it does not measure the size or practical importance of an effect. A small p-value does not remove the need to consider the estimate, interval limits, outcome definition, and study limitations.

The registry record does not state the original analysis test, model, or null-hypothesis specification in detail. It also does not report whether the posted p-values came from a prespecified sponsor analysis. The p-values should therefore be described as the posted unadjusted values, without attributing an unreported method to them.

What do the interval limits add?

A confidence interval is, in general, a way to express the precision of an estimate by giving a range of values compatible with the data and the method used. Narrower intervals indicate greater precision than wider intervals, all else equal. Here, the recorded interval limits are 0.571 to 0.680 for 44 U versus placebo and 0.486 to 0.623 for 24 U versus placebo. The confidence level and exact interval method are not reported in the registry record. The limits should not be read as a guarantee that the true value lies within them, nor as a range of outcomes for individual participants.

What does the analysis population mean?

The endpoint population is called intent-to-treat in the registry, but its definition is specific: all randomized participants with data available for analysis. This wording means the posted endpoint result is not described as including randomized participants who lacked the required data. The record does not explain how many participants lacked endpoint data, why data may have been missing, or what method was used to address missingness. Consequently, the possible influence of missing data cannot be assessed from the posted description.

In general, analyzing randomized participants according to their assigned group can preserve important features of randomization. Restricting an outcome analysis to those with available data can, however, introduce uncertainty if data availability is related to treatment assignment or outcome. That is a general concern, not evidence that such a problem occurred in this trial. The registry does not provide enough information to evaluate that possibility.

Why does over-dispersion matter for some outcomes?

Over-dispersion is a general issue in count data when observed variability exceeds what a simple statistical model expects. It can affect standard errors and interval estimates if a model assumes less variability than the data contain. The primary outcome in this record is a percentage based on whether participants met a binary criterion, not a count of repeated events per participant. The registry does not report an over-dispersion parameter or a count-data model for this endpoint, so over-dispersion is not part of the reported primary comparison.

For this binary endpoint, the main statistical features to keep in view are the group proportions, the risk-difference estimates, their interval limits, and the unadjusted p-values. The record does not report enough detail to reproduce or verify the sponsor’s original inferential procedure. The posted comparisons should be read as the estimates and tests recorded, with those methodological details left unspecified.

10. Confidence Intervals and Precision

The registry reports risk-difference estimates with interval limits for both dose-versus-placebo comparisons. For onabotulinumtoxinA 44 U, the estimate is 0.626 and the interval runs from 0.571 to 0.680. For onabotulinumtoxinA 24 U, the estimate is 0.554 and the interval runs from 0.486 to 0.623. The interval limits convey uncertainty around each estimated difference; the estimates are not exact descriptions of a fixed underlying value.

In general, a confidence interval reflects both the observed data and assumptions of the statistical method used to construct it. A wider interval indicates less precision, while a narrower interval indicates more precision, all else equal. The registry record does not state the confidence level or the interval calculation method, so those details cannot be characterized further. The interval limits should not be mistaken for the full range of possible results or for a prediction interval for participants.

The posted percentages are 63.6% for 44 U, 56.5% for 24 U, and 1.1% for placebo. Their endpoint denominators are 349, 223, and 95, respectively. The placebo group is smaller than either treatment group, which is relevant when considering the amount of information available in each arm; no precision estimate for each standalone percentage is reported in the registry record. The interval limits provided are for the risk differences, not for each group’s percentage separately.

Both unadjusted p-values are <0.001, but a p-value is not a substitute for the interval limits or a measure of precision. It does not show how close the estimate might be to another plausible value, and it does not communicate the size of the estimated difference by itself. Together, the estimates, interval limits, and group percentages describe the posted result more fully than a significance threshold alone.

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 display gives planning illustrations in participants per arm, not total event counts. The registry’s planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set as a stated fraction of the observed effect. These assumptions describe the posted planning illustration; the trial’s own original design assumptions are not reported in the registry record.

The 80% power column gives the planned number of participants per arm for a hypothetical study to have an 80% chance of detecting the specified effect under those assumptions, if that effect were the true one and the other assumptions held. The 90% power column gives the corresponding planning number for a 90% chance. Power is a property of a planned design under assumptions, not a statement about the probability that the trial result is correct.

For example, planning for 100% of the observed effect in the 44 U comparison gives 8 participants per arm for 80% power and 10 participants per arm for 90% power. Planning for 50% of the observed effect gives 22 participants per arm for 80% power and 28 participants per arm for 90% power. For the 24 U comparison, the corresponding 100% effect illustrations are 10 and 12 participants per arm, while planning for 50% of the observed effect gives 25 and 33 participants per arm. These figures are hypothetical planning outputs, not the size of the actual trial groups.

Smaller effects are harder to distinguish from random variation under otherwise similar assumptions, so detecting a smaller fraction of the observed effect requires more participants in these illustrations. This is not observed power: it is a planning exercise that uses the observed effect as its reference point. The registry does not report whether these assumptions were used when the trial was designed or whether the trial’s planned enrollment was based on a different justification.

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 = 0.011; treatment proportion p₁ = 0.636; average p̄ = 0.323.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6615 = 1.2965.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.4918 = 0.4139.
4. n = (1.2965 + 0.4139)² / (0.6256)² = 7.5, rounded up to 8 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 <- 0.0105263157894737                          # control proportion
p1 <- 0.636103151862464                          # 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(1224015)
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 = 8 (80% power), 10 (90% power)
 75% of observed effect: n per arm = 12 (80% power), 16 (90% power)
 50% of observed effect: n per arm = 22 (80% power), 28 (90% power)
power.prop.test: 7.5 
Simulated power at n = 8 per arm: 0.859 (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 posted primary outcome is the Day 30 percentage of participants rated none or mild for crow’s feet lines at maximum smile. The registry reports no secondary outcome measures and no analysis results beyond this primary outcome. The record therefore offers no basis for describing a broader set of endpoint findings or for determining how many statistical comparisons were planned in the full protocol.

Multiplicity arises in general when multiple hypotheses or outcomes are tested: the chance of at least one false-positive result can increase as more tests are performed. Statistical plans may address this through a prespecified hierarchy or adjustment, among other approaches. The registry record does not report whether multiplicity was considered, whether any adjustment was planned, or whether the two dose-versus-placebo comparisons formed part of a larger testing strategy. The posted p-values are unadjusted, so they should not be described as multiplicity-adjusted.

The analysis population is described as all randomized participants with data available for analysis. The record does not give the number of randomized participants without endpoint data, the reasons data were unavailable, or the methods used to handle missing observations. It does not report whether missingness was assessed by treatment group or whether sensitivity analyses were performed. These omissions prevent an evaluation of how missing data may have affected the endpoint estimates.

The original statistical analysis plan, the detailed analysis model, any interim analyses, and any prespecified subgroup analyses are not reported in the registry record. Their absence from the record does not establish that they were not conducted; it means their methods and results cannot be assessed from the posted information. Interpretation should remain focused on the reported endpoint, its defined available-data population, and the unadjusted comparisons, without assuming unreported safeguards or analyses.

14. Safety Results

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

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: diarrhoea (1.1%), dehydration (1.1%), breast cancer (0.4%), intestinal obstruction (0.3%), gastrointestinal infection (0.3%).

The registry reports serious adverse events affecting 6 participants in the onabotulinumtoxinA 44 U group, 1 in the 24 U group, and 1 in the placebo group. The corresponding groups at risk are reported as 349, 223, and 95. These are counts of participants affected, not counts of all serious-event episodes. The registry does not report deaths for these groups; the death entries are not populated, so death information is not reported in the registry record.

The listed serious adverse-event terms include diarrhoea and dehydration, each reported as 1.1%, as well as breast cancer at 0.4%, intestinal obstruction at 0.3%, gastrointestinal infection at 0.3%, and infected bites at 0.3%. The record does not provide enough detail to determine how these terms were distributed across groups, whether a participant could contribute to more than one term, or whether the events were considered related to treatment.

Other adverse events affected 44 participants in the 44 U group, 23 in the 24 U group, and 15 in placebo; the corresponding at-risk group sizes are the same as those stated for the serious-event figures. These summaries do not describe severity, duration, timing, or treatment relationship for every event. They also do not establish a complete comparison of safety, because the registry record does not report all such details or the method used to collect and summarize events.

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

The posted result describes a higher percentage of participants meeting the none-or-mild crow’s feet criterion at Day 30 in each onabotulinumtoxinA group than in the normal saline placebo group. The recorded risk differences are positive, and each posted unadjusted p-value is <0.001. The interval limits quantify uncertainty around those risk-difference estimates, although the confidence level and construction method are not stated in the registry record.

This result concerns one investigator-rated endpoint at one time point, in an analysis population defined as randomized participants with data available. It does not report the separate frequencies of none and mild ratings, the magnitude of change for individual participants, or results at other time points. It also does not provide a primary outcome measure for frown lines, despite the study’s broader focus on crow’s feet and frown lines.

Statistical evidence against a null comparison is not the same as evidence about every aspect of a treatment’s effects. The p-values do not measure clinical importance, and the posted endpoint does not by itself tell readers whether the observed rating differences correspond to a meaningful experience for participants. The registry does not report participant-reported outcomes or a threshold for a change considered meaningful to participants.

The result also does not settle questions about durability, the full safety profile, or the balance between outcomes and adverse events. The adverse-event summaries provide counts and selected terms, but not the detailed context needed for a comprehensive assessment. Missing endpoint data and the methods for handling those data are not described. These limits apply to interpretation of the registry record and should not be filled in by assuming unreported methods or outcomes.

16. Why This Trial Matters Statistically

This trial illustrates several statistical issues that arise in clinical research with a categorical rating endpoint. The outcome is defined by a threshold on a four-point investigator scale: none or mild counts as meeting the endpoint, while moderate or severe does not. That makes the result readily expressible as a percentage, but it also means the reported summary does not preserve distinctions within the combined categories or describe the size of changes for individual participants.

The three-arm design makes two active-treatment comparisons available against a placebo group. The placebo group has fewer endpoint observations than either active-treatment group, which is important context for interpreting the information contributed by each comparison. The risk-difference estimates and interval limits communicate both the direction and uncertainty of the reported contrasts, while the unadjusted p-values give a separate measure of statistical compatibility with a null comparison.

The study also shows why statistical significance should not be used as a complete interpretation. A small p-value does not establish clinical importance, explain the rating’s relevance to participants, or answer questions about longer-term outcomes and safety. Those judgments depend on the endpoint’s meaning and other evidence that is not included in the primary result.

Finally, the record defines the analysis population as randomized participants with data available, yet does not report the extent or handling of missing endpoint data. It also does not state the confidence level, analysis model, or multiplicity strategy. These reporting gaps do not negate the posted results, but they limit independent assessment of the analysis choices and the robustness of the findings. Separating what the result estimates from what the record leaves unspecified is central to careful statistical 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.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

The primary endpoint is a single investigator assessment of crow’s feet severity at maximum smile on Day 30. The registry does not report baseline values for this endpoint, change from baseline, participant-reported assessments, or results at other time points. It therefore cannot show from this outcome alone how ratings changed over time or how participants perceived their own results.

The analysis population includes randomized participants with data available, but the record does not report how many randomized participants lacked Day 30 data, the reasons for missing data, or how missingness was handled. This leaves uncertainty about whether the posted analysis represents all randomized participants in a way that is robust to unavailable observations.

The registry does not report the original statistical analysis plan, the exact test or model, the confidence level for the interval limits, or the multiplicity strategy for the dose comparisons. It also does not report the original sample-size justification. The planning illustration should not be treated as evidence of the design rationale for this completed trial.

The record describes participants as people who successfully completed Study 191622-099. The posted result therefore applies to the population described in this trial record; the record does not establish how well it generalizes to people outside that study-completer group. It also does not report detailed information about treatment adherence, the number of treatments actually received, or the reasons participants may not have received up to 2 treatments.

Finally, the safety summaries do not provide detailed event timing, severity, treatment relationship, or group-specific breakdowns for the listed serious-event terms. The record does not provide enough information to make a comprehensive safety comparison or to infer causation for an event.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Safety and Efficacy Study of Botulinum Toxin Type A for the Treatment of Crow's Feet Lines and Frown Lines — NCT01224015.
• Registry record last updated 2014-02-25; status last verified 2014-02.
• Results first posted 2014-02-25.
• 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

NCT01224015 is a completed randomized, double-masked, parallel phase 3 study sponsored by Allergan. The registry lists enrollment of 684 and describes participants as people who successfully completed Study 191622-099. The treatment groups were onabotulinumtoxinA 44 U, onabotulinumtoxinA 24 U, and normal saline placebo.

The primary endpoint was the percentage with an investigator rating of none or mild crow’s feet lines at maximum smile on Day 30. The reported percentages were 63.6% for 44 U, 56.5% for 24 U, and 1.1% for placebo. The unadjusted risk-difference estimates versus placebo were 0.626 and 0.554, respectively; both unadjusted p-values were <0.001.

The registry does not report the original analysis plan, confidence level, multiplicity strategy, or detailed handling of missing endpoint data. The results should be interpreted as findings for the posted endpoint and its available-data analysis population, with these reporting limits in mind.