A Study to Evaluate the Efficacy of Lastacaft® Compared to Pataday™ and Placebo in Patients With Acute Allergic Conjunctivitis: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Study to Evaluate the Efficacy of Lastacaft® Compared to Pataday™ and Placebo in Patients With Acute Allergic Conjunctivitis (NCT01732757), a randomized phase 4 study. The primary outcome is Ocular Itching Evaluated by the Subject 3 Minutes Post Challenge on Day 0.

2. Clinical Question

3. Trial Design

The registry identifies this as a completed Phase 4 study sponsored by Allergan. It was randomized, double-masked, and used a parallel-group design. The record lists enrollment as 157. The study start is recorded as 2012-11 and primary completion as 2012-12. Further details about the randomization procedure, the people masked, or the timing and conduct of challenge procedures are not reported in the registry record.

Participants were assigned to Lastacaft®, Pataday™, or placebo. Each was administered as one drop in both eyes on Day 0. The active treatments were alcaftadine 0.25% and olopatadine 0.2%; the placebo formulation was dextran 70 0.1%/hydroxypropyl methylcellulose 0.3%. The registry describes the study objective as evaluating the treatments against one another and placebo for prevention of ocular itching associated with allergic conjunctivitis.

The primary outcome was measured at 3 minutes post challenge on Day 0. The posted group summaries each report 52 subjects for this outcome. The primary population is defined as all randomized subjects with data at that time point, so the outcome summaries do not represent an analysis of every enrolled participant by definition. Reasons that some enrolled or randomized participants may not have contributed primary outcome data are not reported in the registry record.

The registry lists 11 outcome measures, including the primary itching outcome and secondary measures of itching and ocular signs. Ten secondary outcomes are posted, but secondary results are not included in the record summarized by these primary comparisons. The detailed protocol, original analysis plan, and 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

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: All randomized subjects with data at this time point

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 Ocular Itching Evaluated by the Subject 3 Minutes Post Challenge on Day 0, measured over Day 0 at 3 Minutes Post Challenge.

The primary endpoint is the subject-rated ocular itching score at 3 minutes post challenge on Day 0. Subjects rated itching on a 9-point numeric analog scale ranging from 0=None to 4=Incapacitating Itch with an Irresistible Urge to Rub, with 0.5 increments allowed. The score for both eyes was averaged to produce one score per subject. Lower scores indicate less itching.

This endpoint focuses on the symptom named in the study objective and captures a specific, early post-challenge time point. A subject-reported rating reflects the participant’s experience of itching, while averaging the scores from both eyes gives one outcome value per subject for the analysis. The registry records the outcome as a mean with standard deviation, which describes the group’s average score and the spread of individual scores around that average.

The primary endpoint is narrow in timing and content: it represents itching at a single post-challenge time point, rather than change over a longer period or an overall measure of allergic conjunctivitis. Secondary outcomes listed in the registry include itching at other post-challenge times and investigator assessments of redness and chemosis. Results for those measures are not included in the posted primary outcome comparisons.

7. Results Posted in the Registry

• Lastacaft®: mean 0.40 versus 2.00 on control; difference -1.60 (95% CI -1.94 to -1.26), standardized effect d = -1.81; z-test p = <0.001.
• Pataday™: mean 0.76 versus 2.00 on control; difference -1.24 (95% CI -1.60 to -0.88), standardized effect d = -1.31; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: each subject has a numeric itching score, and the registry reports group means and standard deviations. The posted comparisons are mean differences between each active-treatment group and the placebo group. A mean difference expresses the separation between two group averages in the original score units. Because lower scores indicate less itching, a negative active-treatment-minus-placebo difference corresponds to a lower average score in the active-treatment group.

What does a mean and standard deviation describe?

General statistical explanation: the mean gives the center of a group’s observed scores, while the standard deviation describes how dispersed those scores are around the mean. The standard deviation is not the uncertainty of the mean itself. It describes participant-level variation; precision of an estimated group difference is conveyed more directly by its confidence interval. The posted primary summaries report standard deviations of 0.582 for Lastacaft®, 0.752 for Pataday™, and 1.109 for placebo.

How should the mean differences be read?

The recalculated comparison for Lastacaft® is a mean difference of -1.6 versus placebo, and the recalculated comparison for Pataday™ is -1.24 versus placebo. These are simple unadjusted recalculations from the posted summary statistics. They use the reported group means and sample sizes; they do not incorporate adjustment for other variables or account for a more complex analysis model. The registry record does not report whether the trial’s own primary analysis used these same calculations or another method.

The reported p-values for both comparisons are unadjusted and are given as p < 0.001. A p-value describes how compatible the observed data are with a specified null hypothesis under the assumptions of the statistical test. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of the difference. The registry record does not report the sponsor’s test specification or a multiplicity adjustment for these comparisons.

What do confidence intervals add?

General statistical explanation: a confidence interval gives a range of values compatible with the data and the method used to construct the interval. It helps readers judge the precision of an estimate as well as its direction. The reported interval for the Lastacaft® comparison is -1.94 to -1.26; for Pataday™, it is -1.604 to -0.876. The confidence level and construction method for these intervals are not reported in the registry record, so they should be interpreted as posted without assuming an unreported method.

What does an unadjusted comparison leave out?

An unadjusted mean difference compares group summaries directly. It does not, by itself, account for baseline characteristics, stratification, repeated measurements, or other potential design features. The registry record identifies randomization and a parallel-group design, but does not describe covariate adjustment or the precise analysis model. General statistical explanation: random allocation can support a fair comparison on average, but it does not eliminate the need to understand the analysis population, missing observations, and planned handling of multiple outcomes.

The record lists 11 outcome measures and 10 posted secondary outcomes. Testing multiple outcomes or time points can increase the chance of at least one small p-value if many tests are interpreted together. Whether and how the study controlled that risk is not reported in the registry record. The primary comparison results should therefore be distinguished from claims about a broader family of outcomes.

How should the standardized effect and planning calculations be understood?

The recalculated summaries also include a pooled standard deviation and a standardized effect estimate for each active-treatment comparison. General statistical explanation: standardization expresses a difference relative to the variability of scores, which can help compare effects measured on different scales. It does not replace the original-unit difference, which is more directly interpretable on the itching scale. The registry record does not provide a clinical interpretation threshold for either measure.

The sample-size illustrations use the observed effect or a stated fraction of it as a planning target. General statistical explanation: planning calculations show how a proposed study size relates to a chosen effect, significance level, allocation, and power target. They are sensitive to those assumptions and are not a description of the study’s original design. The original design assumptions and sample-size justification are not reported in the registry record.

10. Confidence Intervals and Precision

The posted mean difference for Lastacaft® versus placebo is -1.6, with a reported interval from -1.94 to -1.26. For Pataday™ versus placebo, the mean difference is -1.24, with a reported interval from -1.604 to -0.876. Each interval lies below zero, matching the direction of the posted group means: the active-treatment group average is lower than the placebo average for this outcome and time point.

General statistical explanation: an interval communicates uncertainty around an estimate. A narrower interval indicates greater precision than a wider interval when the same kind of estimate and method are being compared. The interval endpoints also show a range of differences compatible with the data under the method used. The confidence level and interval construction method are not reported in the registry record, so no specific coverage level should be assumed.

The posted standard deviations are 0.582 for Lastacaft®, 0.752 for Pataday™, and 1.109 for placebo. These values describe variation in individual scores, not the uncertainty of the mean difference. The outcome summaries report 52 subjects in each group, and the primary population is defined as randomized subjects with data at the time point. The handling of missing data is not reported in the registry record.

The reported p-values are unadjusted and both are p < 0.001. They indicate that the observed differences are inconsistent with the null comparison under the calculation used, but do not express the size of the effect or the precision as directly as the difference and interval. The record does not report a confidence level, a clinically important difference threshold, or a direct interval for Lastacaft® versus Pataday™.

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 are participants per arm, not total events. They are illustrative calculations based on the observed comparisons, not the sample-size assumptions used to design the completed trial. The registry record does not report the trial’s original design assumptions or sample-size justification.

The stated 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 the stated fraction of the observed effect: 100%, 75%, or 50%. The values apply to planning for a comparison between two arms. For example, planning for 75% of the observed Lastacaft® effect gives 9 participants per arm for 80% power and 12 participants per arm for 90% power. Planning for 75% of the observed Pataday™ effect gives 17 participants per arm for 80% power and 22 participants per arm for 90% power.

In plain terms, the 80% power column gives the illustrative number of participants per arm for a design with an 80% chance of detecting the specified effect under the stated assumptions, if that effect is present. The 90% power column gives the corresponding planning number for a 90% chance. Smaller target effects require more participants under these assumptions, which is why planning for 50% of the observed effect gives larger sample-size figures than planning for the full observed effect. These values are not observed power and should not be read as a retrospective measure of the completed trial.

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, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -1.600; pooled standard deviation σ = 0.886.
2. n = 2 × (1.96 + 0.842)² × 0.886² / -1.600² = 4.8, rounded up to 5 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
delta <- -1.6                      # observed difference in means
sigma <- 0.885608547835893                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^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 (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(1732757)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 5 (80% power), 7 (90% power)
 75% of observed effect: n per arm = 9 (80% power), 12 (90% power)
 50% of observed effect: n per arm = 20 (80% power), 26 (90% power)
power.t.test: 5.9 
Simulated power at n = 5 per arm: 0.710 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-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 11 outcome measures, including the primary itching score at 3 minutes post challenge and secondary itching and ocular-sign outcomes. Ten secondary outcomes are posted. The primary comparisons are for each active treatment versus placebo, and their p-values are unadjusted. Whether the trial planned a hierarchy of outcomes, a multiplicity correction, or another strategy for interpreting several comparisons is not reported in the registry record.

General statistical explanation: when many hypotheses are tested, the chance of at least one apparently unusual result can increase. Adjustment methods or a prespecified testing hierarchy can help control that issue, but the registry record does not identify such a method. The unadjusted p-values should therefore be read as results for the individual posted comparisons, not as evidence that a family-wide error rate was controlled.

The primary outcome population is described as all randomized subjects with data at the time point. The posted primary summaries list 52 subjects per group, while the record reports enrollment of 157. The reasons for the difference between enrollment and outcome sample sizes are not reported. The registry record does not describe imputation, exclusion rules beyond the stated population, sensitivity analyses, or other missing-data procedures.

The record identifies a randomized, double-masked, parallel-group design, but does not report the statistical analysis plan, the exact inferential test, or whether the primary analysis was adjusted for baseline measures or other covariates. It also does not report interim analyses or stopping rules. Those details cannot be inferred from the posted summaries. The recalculated comparisons are unadjusted calculations from the summary statistics and should be kept distinct from any sponsor analysis that may have been conducted.

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.

The registry reports zero serious adverse events in the Lastacaft® group, zero in the Pataday™ group, and zero in the placebo group. For other adverse events, it also reports zero in each group. The corresponding numbers at risk are 53 for Lastacaft®, 52 for Pataday™, and 52 for placebo for both reported categories.

These figures describe the adverse-event counts recorded in the registry, not proof that no events of any kind occurred outside the reported categories or observation period. The registry does not report the adverse-event observation period or additional detail about how events were collected. Death counts are not reported in the registry record. The safety figures should be read separately from the primary itching outcome, which has its own analysis population and posted group sample sizes.

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

The posted primary results describe lower average ocular itching scores in each active-treatment group than in the placebo group at 3 minutes post challenge on Day 0. The reported unadjusted mean differences and intervals quantify those comparisons in the original scale units. They apply to the primary outcome population described in the registry: randomized subjects with data at that time point.

These results do not establish what happened at other time points, on every secondary outcome, or in participants without primary outcome data. The registry lists additional measures of itching and investigator-rated ocular signs, but their numerical results are not included in the posted primary comparisons. The record also does not provide a direct statistical comparison between Lastacaft® and Pataday™. Separate comparisons against placebo cannot substitute for that direct comparison.

Statistical evidence and clinical importance are different questions. The reported p-values are unadjusted and both are p < 0.001, but a small p-value does not indicate how important a difference is to patients. The registry does not report a clinically important difference threshold for the itching scale. The interpretation should therefore focus on the observed scale differences and their uncertainty, without assigning an unreported clinical meaning.

The findings are specific to this completed randomized, double-masked, parallel-group Phase 4 study and its Day 0 post-challenge endpoint. The record does not provide enough information to assess longer-term outcomes, the full missing-data process, or how all secondary comparisons were handled. No treatment recommendation follows from these statistical summaries.

16. Why This Trial Matters Statistically

This trial offers an example of how a continuous, subject-reported symptom can be summarized and compared across randomized groups. The endpoint is a numeric itching score, and the registry reports both group means and standard deviations. That pairing matters: the means describe the average score, while the standard deviations show the variability among subjects.

The posted results also illustrate why an effect estimate should be read alongside an interval and a p-value. The mean differences retain the units of the itching scale and convey direction and magnitude. The reported intervals express uncertainty around those estimates, while the unadjusted p-values address compatibility with a null comparison under the calculation used. None of these measures alone establishes clinical importance.

The record also makes the distinction between an outcome population and overall enrollment visible. The primary outcome is defined for randomized subjects with data at the time point, and the displayed group summaries report 52 subjects per arm, while enrollment is 157. Since the record does not explain missingness or analysis-set differences, readers need to avoid treating the outcome summaries as if they automatically represented every enrolled participant.

Finally, the registry lists multiple outcomes but provides primary comparison results for a specific endpoint and time. The absence of reported details about multiplicity, the analysis plan, and a direct active-treatment comparison limits what can be concluded beyond these posted summaries. These are central issues in interpreting trial evidence, even when the numerical differences themselves are straightforward to read.

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 primary endpoint is a single subject-rated itching assessment at 3 minutes post challenge on Day 0. It therefore gives a focused view of itching at one time point rather than a longer-term pattern. The record does not report the challenge procedure in detail, so the exact context of the post-challenge assessment cannot be evaluated from the registry information alone.

The score averages the ratings for both eyes into one subject-level value. This approach avoids treating each eye as a separate subject in the stated endpoint, but it also means the posted mean does not show eye-specific outcomes. The registry lists secondary eye-category and investigator-rated outcomes, but their numerical results are not included in these primary comparisons.

The primary outcome summaries include 52 subjects per group, while the registry reports enrollment of 157. The record does not explain why the outcome sample differs from enrollment, how missing outcome data were handled, or whether exclusions occurred. The population definition limits the result to randomized subjects with available data at the specified time point.

The registry does not report the original statistical analysis plan, sample-size justification, confidence interval method, multiplicity strategy, or a direct comparison between the active treatments. The posted comparisons are unadjusted recalculations from summary statistics. The safety record reports no serious or other adverse events in the listed groups, but does not state the observation period or provide death counts. These omissions constrain interpretation of the primary result and the broader study record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: A Study to Evaluate the Efficacy of Lastacaft® Compared to Pataday™ and Placebo in Patients With Acute Allergic Conjunctivitis — NCT01732757.
• Registry record last updated 2014-01-14; status last verified 2013-11.
• Results first posted 2014-01-14.
• 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, double-masked, parallel-group Phase 4 study sponsored by Allergan, with enrollment of 157. It compared Lastacaft® (alcaftadine 0.25%) and Pataday™ (olopatadine 0.2%) with placebo for ocular itching associated with allergic conjunctivitis.

The primary outcome was subject-rated ocular itching at 3 minutes post challenge on Day 0, with lower scores indicating less itching. Posted group means were 0.4 for Lastacaft®, 0.76 for Pataday™, and 2.0 for placebo. The recalculated unadjusted mean differences versus placebo were -1.6 and -1.24, respectively, with p < 0.001 for both comparisons. The registry does not report a direct Lastacaft®-versus-Pataday™ comparison or the trial’s original analysis plan.