Safety and Efficacy of Bimatoprost Solution in Treating Eyelash Loss or Hypotrichosis in Children: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Safety and Efficacy of Bimatoprost Solution in Treating Eyelash Loss or Hypotrichosis in Children (NCT01023841), a randomized phase 4 study. The primary outcome is Percentage of Participants With Adverse Events.

2. Clinical Question

3. Trial Design

This was a randomized, parallel-group, quadruple-masked phase 4 study. The registry lists enrollment of 71 and a completed status. The study start date is 2010-06-01, and the primary completion date is 2012-11-02. These are registry-record dates; they do not by themselves describe how long each participant was followed.

The two listed groups received bimatoprost ophthalmic solution 0.03% or vehicle sterile solution. Both arm descriptions specify one drop applied to a sterile single-use-per-eye applicator and then to the upper eyelid margin once nightly for 4 months. The active-treatment description and vehicle description therefore share the stated application schedule and method.

The primary outcome was the percentage of participants with adverse events, assessed over a 5 Months timeframe. Its stated analysis population was the safety population, defined as all randomized participants who received treatment. The posted arm sizes for this outcome are 48 for bimatoprost and 23 for vehicle. The registry record does not explain the relationship between these outcome denominators and the enrollment figure, or give further participant-flow information.

The listed secondary outcomes concern change from baseline in upper eyelash length, thickness, and darkness as measured by digital image analysis. The record lists five outcome measures overall, but the three named secondary outcomes are the image-analysis measures. The trial description mentions safety and efficacy, while the available primary result addressed in the posted data is safety. Details such as the original allocation procedure, masking procedures, and the trial's original sample-size justification are not reported in the registry 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

Analysis population for the primary outcome, as defined in the registry: Safety population included all randomized participants who received treatment.

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 With Adverse Events, measured over 5 Months.

The primary endpoint is the percentage of participants with adverse events during the stated 5 Months timeframe. An adverse event is defined in the registry as an unfavorable and unintended sign, symptom, or disease associated with study-drug use, whether or not considered related to study drug. This definition means the endpoint is not restricted to events judged to have been caused by treatment.

Counting participants with at least one event gives a participant-level summary of how often an adverse event was recorded in each group. It is different from counting the total number of event episodes: one participant can have more than one event, while the percentage endpoint concerns whether participants experienced events. The posted arm values are 35.4% for bimatoprost and 43.5% for vehicle. The safety population comprises randomized participants who received treatment, and the arm denominators are 48 and 23, respectively.

This type of endpoint is used to describe safety experience across treatment groups. It does not, by itself, establish whether an event was caused by the study drug, how severe or persistent events were, or what types of events contributed to the overall percentages. Those details are not reported in the primary endpoint description. The other listed outcomes assess changes in eyelash length, thickness, and darkness with digital image analysis; they are distinct from this adverse-event endpoint.

7. Results Posted in the Registry

• Bimatoprost Ophthalmic Solution 0.03%: 35.4% (17/48) versus 43.5% (10/23) on control; risk difference -8.1 percentage points (95% CI -32.4 to 16.3), risk ratio 0.81 (0.45–1.49); unadjusted two-proportion z-test p = 0.513.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is binary at the participant level: a participant either had an adverse event counted for the endpoint or did not. A percentage summarizes the fraction of participants in an arm who experienced an event. This is distinct from a rate based on person-time and from the total number of event episodes. The outcome definition includes unfavorable and unintended signs, symptoms, or diseases associated with study-drug use, whether or not considered related to the study drug.

What does the risk difference represent?

The risk difference compares the event proportions between groups by subtracting one group's proportion from the other's. In this posted comparison, the direction is bimatoprost minus vehicle: the corresponding proportions are 0.354 and 0.435, and the risk difference is -0.081. A negative value indicates a lower observed proportion in the bimatoprost group; a value of zero would indicate equal proportions in the underlying comparison. The point estimate is an unadjusted calculation from the posted summary statistics, not an adjusted model estimate.

The arm-level percentages are reported as 35.4% and 43.5%. Their denominators are 48 and 23. The comparison also lists 17 and 10 participants with the event, respectively, according to its group ordering. These counts and denominators describe participant-level event occurrence; they do not convey how many event episodes each affected participant experienced.

How should the interval be read?

A confidence interval describes uncertainty around an estimated quantity under the method's assumptions. For the risk difference, the posted interval runs from -0.324 to 0.163. It includes zero and includes values on both sides of zero. Thus, the observed data do not sharply distinguish a negative risk difference from no difference or a positive risk difference. An interval is not a range that guarantees the true value lies within it, and its interpretation depends on the statistical method and assumptions used to construct it.

The registry record does not identify the interval method for this comparison. It also does not report an adjusted model, covariates, or a sponsor analysis entry for the primary endpoint in the listed analyses. The comparison is therefore most clearly described as an unadjusted recalculation from posted summary statistics. No discrepancy is flagged between that recalculation and a sponsor result.

What does the p value add?

The unadjusted p value is 0.513. In general, a p value measures how unusual data at least as discrepant as those observed would be under a specified null model and its assumptions. It does not give the probability that the null model is true, quantify the size of an effect, or show whether an effect matters clinically. The registry record does not specify the original analysis plan or the test used for a sponsor analysis. The p value should therefore be understood as part of the posted unadjusted comparison, not as a full account of the trial's statistical plan.

Different statistical summaries answer related but distinct questions. The percentage in each arm describes the observed event frequency. The risk difference describes the absolute contrast between those frequencies. The interval describes uncertainty around that contrast, while the p value summarizes compatibility with a null comparison under a test's assumptions. No one of these summaries replaces the others.

Why does the analysis population matter?

The stated safety population includes all randomized participants who received treatment. This definition identifies who is intended to contribute to the primary safety endpoint. It is not the same as an intention-to-treat population that necessarily includes every randomized participant regardless of treatment receipt. The record does not report the number randomized who did not receive treatment, if any, or provide further details about the handling of missing endpoint data.

For a binary endpoint, missing outcomes can affect both the arm percentages and the between-group comparison. The registry record does not describe an imputation method, a missing-data sensitivity analysis, or the amount of missingness. It is therefore not possible to tell from the reported summary whether every participant in the stated safety population had complete endpoint information.

Why can unequal group sizes affect precision?

When group sizes differ, the estimate is typically influenced by the amount of information available in each group. A smaller group often contributes less precise information about its event proportion. Here, the vehicle arm has 23 participants and the bimatoprost arm has 48. The reported interval reflects uncertainty in the comparison, but the record does not give additional details about how the unequal group sizes arose or how they were handled in the original analysis.

The trial is described as randomized and parallel-group, which means participants were assigned to one of the two treatment groups and outcomes are compared between groups. Randomization is intended to reduce systematic differences in baseline characteristics on average, but it does not guarantee balance in a particular trial. Baseline characteristics and any adjusted analyses are not reported in the registry record described for this result.

10. Confidence Intervals and Precision

The risk difference is -0.081, and its interval extends from -0.324 to 0.163. The interval covers zero, so the posted estimate does not tightly establish a direction for the underlying difference. It also includes values indicating differences in either direction. The point estimate is only one location within that broad range; interpreting it without the interval would understate the uncertainty.

The arm sizes are 48 for bimatoprost and 23 for vehicle. Estimates based on fewer participants tend to be less precise, all else being equal. The posted interval incorporates uncertainty in the comparison, but the registry record does not identify the interval method or report a separate precision assessment. The result should be read as an estimate with substantial uncertainty rather than as a precise measure of the difference.

The interval should not be interpreted as proving equivalence. Equivalence requires a prespecified margin and an analysis designed to assess whether the interval lies within that margin; neither is reported in the registry record. Likewise, the interval alone does not determine clinical importance. The record does not state a threshold for an important difference in adverse-event percentages.

The unadjusted p value of 0.513 is consistent with the uncertainty visible in the interval, but it does not quantify that uncertainty or show that the groups are identical. The event definition is broad, and no event-level breakdown is reported alongside the primary percentage. Precision about the overall participant-level contrast should therefore be distinguished from precision about particular adverse events, severity, or relatedness, which are not characterized by this endpoint summary.

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 values describe hypothetical sample sizes for a future study, not the observed enrollment in this trial. They are participants per arm, not total participants or 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 effect to detect is set to the stated fraction of the observed effect.

For planning based on 100% of the observed effect, the listed requirements are 576 participants per arm for 80% power and 771 participants per arm for 90% power. For planning based on 75% of the observed effect, the figures are 1,034 participants per arm for 80% power and 1,383 participants per arm for 90% power. For planning based on 50% of the observed effect, the figures are 2,344 participants per arm for 80% power and 3,138 participants per arm for 90% power.

Power is the chance, under a specified design and effect assumption, of detecting a difference using the chosen statistical test and threshold. The 80% column describes a design targeting 80% power under its assumptions; the 90% column targets a higher chance of detecting the assumed effect. A higher target generally requires more participants. Smaller effects also require more participants to detect with the same power, which is reflected in the listed scenarios.

These are illustrations calculated from the observed effect, not the trial's original design plan. They are not observed power. The original sample-size justification and original design assumptions are not reported in the registry record. The listed values also rely on planning assumptions that may not match a future study's population, analysis, or outcome conditions.

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 = 0.435; treatment proportion p₁ = 0.354; average p̄ = 0.394.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6912 = 1.3547.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6888 = 0.5797.
4. n = (1.3547 + 0.5797)² / (-0.0806)² = 575.8, rounded up to 576 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 <- 0.434782608695652                          # control proportion
p1 <- 0.354166666666667                          # 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(1023841)
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 = 576 (80% power), 771 (90% power)
 75% of observed effect: n per arm = 1,034 (80% power), 1,383 (90% power)
 50% of observed effect: n per arm = 2,344 (80% power), 3,138 (90% power)
power.prop.test: 575.8 
Simulated power at n = 576 per arm: 0.800 (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 registry lists three secondary outcomes: change from baseline in upper eyelash length, thickness, and darkness, each measured by digital image analysis. It also records five outcome measures overall. The listed analysis count is zero, and the registry record does not report analysis results for those secondary outcomes in the material summarized for the primary endpoint.

When a study assesses several outcomes or several statistical comparisons, the chance of obtaining at least one apparently notable result can increase. Statistical methods can account for this multiplicity, but the registry record does not report whether any adjustment was planned or used. The original multiplicity strategy, including any hierarchy among endpoints or planned contrasts, is not reported in the registry record. No conclusions about the secondary outcomes should be inferred from the adverse-event result.

The record defines the safety population as randomized participants who received treatment. It does not report a separate efficacy analysis population, a full participant disposition, or the number of participants with missing primary outcome data. The missing-data approach, including any imputation or sensitivity analyses, is not reported in the registry record. This limits assessment of whether missingness could have influenced the endpoint estimates.

The original statistical analysis plan, the primary test selected by the sponsor, any adjustment for baseline variables, and any interim analyses are not reported in the registry record. The posted unadjusted comparison can be interpreted descriptively, but it should not be mistaken for a complete account of the original analysis plan. These omissions also prevent confirmation of whether the posted endpoint and comparison followed prespecified analysis choices.

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 non-serious adverse event terms

The serious adverse-event fields list 48 participants at risk in the bimatoprost group and 23 in the vehicle group. The number affected by a serious adverse event is recorded as 0 in each group. These figures indicate that the registry lists no serious adverse events among the participants included in those group fields.

The record separately lists other adverse-event counts of 0 for bimatoprost and 1 for vehicle, with 48 and 23 participants at risk, respectively. These are counts from separate safety fields and should not be confused with the primary endpoint percentages, which summarize participants with any adverse event under the endpoint definition. The record does not provide descriptions of the other events in these fields.

Deaths are not reported in the registry record. The absence of a recorded serious event in these group fields does not establish that all possible safety risks are absent, and these counts do not describe event severity beyond the serious-event classification. They also do not show whether events were considered related to study drug. The primary endpoint explicitly includes events whether or not considered related.

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

The result describes adverse-event occurrence in the two posted treatment groups during the stated 5 Months timeframe. The recorded percentages are 35.4% for bimatoprost and 43.5% for vehicle. The unadjusted risk difference is -0.081, with an interval from -0.324 to 0.163 and an unadjusted p value of 0.513. These statistics describe the posted data and their uncertainty; they do not establish a causal treatment effect or show that the groups have identical safety experience.

The interval includes zero and values in both directions. Consequently, the estimate does not precisely resolve whether the underlying event proportion is lower or higher in either group. The p value is not a probability that the treatments are the same, and the observed percentages are not a measure of how many event episodes occurred. They describe the proportion of participants who experienced adverse events according to the endpoint definition.

The endpoint includes any unfavorable and unintended sign, symptom, or disease associated with study-drug use, regardless of whether the event was considered related to study drug. The summary does not identify event types, severity, duration, or individual relatedness. The serious adverse-event fields list zero affected participants in both arms, but those fields do not capture all possible detail about the broader primary outcome.

The record lists secondary digital image-analysis outcomes for eyelash length, thickness, and darkness, but results for those outcomes are not reported in the primary comparison. The registry record also does not report the original sample-size rationale, missing-data methods, detailed statistical analysis plan, or adjusted analysis. Those gaps constrain what can be concluded from the posted summary. The result is best understood as an imprecise, unadjusted safety comparison rather than a definitive statement about treatment effects or efficacy.

16. Why This Trial Matters Statistically

This trial illustrates why an event percentage and a between-group estimate answer different questions. The percentages, 35.4% and 43.5%, describe observed participant-level event occurrence in each arm. The risk difference, -0.081, expresses the contrast on an absolute scale. The interval from -0.324 to 0.163 then shows that the contrast is uncertain and can be interpreted in either direction.

The group sizes also matter for reading the result. The comparison involves 48 participants in the bimatoprost arm and 23 in the vehicle arm. Unequal and limited group sizes can leave considerable uncertainty around a safety estimate, especially when events are summarized as a binary participant outcome. The broad interval demonstrates why a point estimate should not be read as a precise effect.

The endpoint definition is another important statistical feature. It includes events whether or not considered related to study drug, making the primary percentage a broad safety summary rather than a count of events attributed to treatment. The separate serious adverse-event fields answer a narrower question and record zero affected participants in both groups. Neither summary alone describes the types or clinical characteristics of events.

The study's additional digital image-analysis outcomes also illustrate the need to distinguish the primary safety result from other outcomes. The registry lists measures of eyelash length, thickness, and darkness, but does not report their analysis results in the listed analysis entries. Without the original analysis plan and multiplicity details, the statistical role of those outcomes cannot be reconstructed. Taken together, these features make uncertainty, endpoint definition, analysis population, and completeness of reporting central to interpreting the posted comparison.

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 posted group sizes are 48 and 23, and the interval around the unadjusted risk difference is broad. This limits precision for the between-group comparison. The registry record does not explain why the group sizes differ or provide participant-flow details that would clarify the outcome denominators in relation to the enrollment figure of 71.

The primary endpoint uses a broad adverse-event definition, including events whether or not considered related to study drug. The primary summary does not give event types, severity, duration, or participant-level event histories. The serious adverse-event fields list zero affected participants in both groups, while the record does not report deaths. These fields are not enough to characterize the full safety profile.

The record does not report the missing-data approach, the number of missing primary outcomes, or sensitivity analyses. It also does not report the original statistical analysis plan, the sponsor's primary test, covariate adjustment, interim analyses, or the trial's original sample-size justification. The unadjusted comparison therefore cannot establish whether its methods match the original prespecified plan.

The registry lists three secondary image-analysis outcomes but does not report their analysis results in the listed analysis entries. It does not report a multiplicity strategy or detailed results for those outcomes. Finally, the summary concerns one randomized study with the stated group sizes and timeframe; the registry record alone does not establish how broadly its estimates apply beyond the participants studied.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Safety and Efficacy of Bimatoprost Solution in Treating Eyelash Loss or Hypotrichosis in Children — NCT01023841.
• Registry record last updated 2019-04-17; status last verified 2019-04.
• Results first posted 2013-09-13.
• 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

The registry record describes a completed, randomized, quadruple-masked, parallel-group phase 4 study of bimatoprost ophthalmic solution 0.03% versus vehicle sterile solution in children with eyelash loss or hypotrichosis. Enrollment is listed as 71. Both treatments were applied nightly to the upper eyelid margin for 4 months. The primary endpoint was the percentage of participants with adverse events over 5 Months in the safety population of randomized participants who received treatment.

The posted percentages were 35.4% for bimatoprost and 43.5% for vehicle. The unadjusted risk difference was -0.081, with an interval from -0.324 to 0.163; the unadjusted p value was 0.513. Serious adverse-event counts were 0 in both groups. The record lists three secondary digital image-analysis outcomes, but their results, missing-data methods, original analysis plan, and original sample-size justification are not reported in the registry record.