A Study to Compare the Safety and Efficacy of a New Eye Drop Formulation With REFRESH PLUS® in Participants Following LASIK Refractive Surgery: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Study to Compare the Safety and Efficacy of a New Eye Drop Formulation With REFRESH PLUS® in Participants Following LASIK Refractive Surgery (NCT01886690), a randomized phase 3 study. The primary outcome is Ocular Surface Disease Index© (OSDI) Score Using a 5-Point Scale.

2. Clinical Question

3. Trial Design

The registry record describes a Phase 3, randomized, double-masked, parallel-group study of eye drops in participants following bilateral LASIK surgery. The study is listed as completed. Allergan is identified as the sponsor. Enrollment was 148. The recorded start date is 2013-08-20, and the primary completion date is 2014-08-18.

Participants were assigned to either the New Eye Drop Formulation or REFRESH PLUS®. Both arm descriptions specify carboxymethylcellulose sodium based eye drops, used as 1 to 2 drops in each eye as per protocol for 90 days. The record does not describe further details about how randomization was generated, how masking was maintained, or what steps were used to conceal treatment assignment; those details are not reported in the registry record.

The primary outcome was the Ocular Surface Disease Index© score at Day 90. Its stated analysis population is per protocol: randomized patients who had no significant protocol violations. The posted arm summaries contain 68 participants for the new formulation and 57 for REFRESH PLUS®. These outcome counts should not be treated as the full randomized enrollment. The registry record does not explain why the primary-outcome counts differ from enrollment or provide a full account of participants excluded from this population.

Four secondary outcomes are listed: change from baseline in corneal staining, tear break-up time, the Schirmer test, and uncorrected visual acuity, each in the worse eye. Results for these secondary outcomes are not reported in the registry record. The original sample-size justification and other details of the planned design are also 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: Per Protocol: all randomized patients who had no significant protocol violations

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 Surface Disease Index© (OSDI) Score Using a 5-Point Scale, measured over Day 90.

The primary endpoint is the Ocular Surface Disease Index© score at Day 90. The OSDI is described as a 12-question survey in which participants document dry-eye symptoms. Each question is rated on a 5-point scale, from 0 for none of the time to 4 for all of the time. Responses are totaled and normalized to a score from 0 to 100, where 0 represents no disability and 100 represents complete disability.

This measure is used to summarize participants’ reported symptom burden as a continuous score. Comparing average scores between groups provides one way to describe how symptom scores differed at the specified follow-up time. Because higher OSDI scores correspond to greater disability, the direction of a mean difference can be interpreted against that scale meaning. The outcome is a patient-reported survey measure; it is distinct from the listed clinical assessments of corneal staining, tear break-up time, the Schirmer test, and uncorrected visual acuity.

The registry record specifies the Day 90 time point and the per-protocol population for the primary endpoint. It does not report a clinically important difference threshold, a missing-data method, or additional details about how the score was handled in the analysis. Those omissions limit interpretation of what size of difference would matter and how incomplete measurements may have affected the posted result.

7. Results Posted in the Registry

• REFRESH PLUS®: mean 6.63 versus 6.99 on control; difference -0.36 (95% CI -3.09 to 2.37), standardized effect d = -0.05; z-test p = 0.796.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is a continuous measure, and the posted group summaries are means with standard deviations. A mean describes the average score in a group. A standard deviation describes the spread of individual scores around that group’s mean; it is not the uncertainty around the mean itself. Here, the New Eye Drop Formulation group has a mean of 6.99 and standard deviation of 8.511, while the REFRESH PLUS® group has a mean of 6.63 and standard deviation of 7.071.

What does a mean difference represent?

A mean difference places the group averages on the original OSDI score scale. The posted comparison is REFRESH PLUS® minus the New Eye Drop Formulation, giving an estimate of -0.36. The negative sign means the REFRESH PLUS® group’s posted mean was lower. Since higher scores indicate greater disability, that direction corresponds to a lower average score in the REFRESH PLUS® group. The estimate alone does not show whether the contrast is precise or important; the interval and scale context are also needed.

How should the confidence interval be read?

A confidence interval describes uncertainty around an estimated effect under the assumptions of the statistical procedure used. It gives a range of effect values compatible with the data and that procedure. The posted interval runs from -3.092 to 2.372. Because the range crosses zero, it includes both a negative and a positive mean difference, as well as a value of zero. The confidence level and the exact interval procedure are not reported in the registry record, so those details should not be inferred from the limits alone.

What does the p-value add?

The unadjusted p-value is 0.796. 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, nor a measure of clinical importance. A value of 0.796 does not indicate strong evidence against a null hypothesis of no mean difference. The registry record does not report the full analysis specification behind the p-value. The comparison is a recalculated, unadjusted summary from the posted statistics.

Why can spread and sample size affect precision?

In general, estimates of group means tend to be more precise when measurements are less variable and when more observations contribute, assuming other features of the analysis are comparable. The displayed standard deviations indicate that individual scores vary around the group means. The primary-outcome sample sizes are 68 and 57. The resulting interval remains broad enough to include differences in either direction. This is a statement about precision, not proof that the groups are the same.

What does a continuous-outcome model assume?

In general, methods for comparing means rely on assumptions about how measurements and errors behave, and their suitability can depend on the distribution of the outcome and the analysis design. OSDI is bounded between 0 and 100, while the posted group summaries are means and standard deviations. The registry record does not report diagnostic checks, transformations, covariate adjustment, or the exact model used for the primary comparison. It is therefore not possible to assess those modeling choices from this record.

What does the analysis population imply?

The primary population is specified as per protocol: all randomized patients who had no significant protocol violations. In general, excluding participants after randomization can affect how representative a comparison is of the randomized groups, particularly if reasons for exclusion relate to outcomes or assigned treatment. The registry record does not report the number or reasons for protocol violations, or how missing Day 90 scores were handled. The posted result should therefore be read as a comparison in the stated per-protocol population, not assumed to be an all-randomized analysis.

What is not established by these statistics?

The statistics describe the observed average score contrast and its uncertainty. They do not establish equivalence or non-inferiority without a prespecified margin and a corresponding design and analysis. They also do not show individual responses, explain why participants may have had different scores, or address the unreported secondary outcomes. The registry record does not report the original statistical analysis plan, multiplicity procedures, or a sample-size justification.

10. Confidence Intervals and Precision

The estimated mean difference in Day 90 OSDI score is -0.36 for REFRESH PLUS® compared with the New Eye Drop Formulation. Its confidence interval extends from -3.092 to 2.372. This interval is important because the point estimate alone can make the comparison appear more definite than the data support. The interval includes zero and covers values in both directions, so the posted summary is compatible with no average difference as well as with differences favoring either group numerically.

In general, a confidence interval expresses uncertainty around an estimate under a statistical method and its assumptions. It is not a range containing a specified proportion of individual participants’ scores, and it is not a guarantee that the true value lies within its limits. The confidence level and interval-construction method are not reported in the registry record. The interval therefore should be interpreted through its posted endpoints without assigning an unreported confidence level or method.

The posted group means are close on the 0-to-100 scale, but the interval is wider than the point estimate and includes potentially larger contrasts in either direction. The registry record does not provide a clinically important difference threshold. Consequently, the limits cannot be classified as clinically meaningful or unimportant based on a threshold in this record. The p-value of 0.796 is consistent with the interval’s inclusion of zero, but neither statistic proves that the two formulations have identical effects.

Precision also depends on the analysis population and measurement completeness. The primary summary includes 68 and 57 participants in the two groups, while the recorded enrollment is 148. The reasons for this difference and the handling of missing measurements are not reported in the registry record, limiting assessment of possible effects on precision and representativeness.

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 table and curve are planning illustrations based on fractions of the observed mean difference, not a record of the original trial’s design calculations. For this continuous outcome, the displayed sample sizes are participants per arm, not total events. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation; each row uses the stated fraction of the observed effect as the effect to detect. 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 that would, under those assumptions, yield an 80% chance of detecting the specified effect if that effect were the true one. The 90% power column applies the same idea with a higher chance of detection and therefore requires a larger planned sample size. These percentages describe the operating characteristics of a hypothetical future design under the assumptions, not the probability that a result is true.

The table considers planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. The corresponding figures are 7,537 and 10,090 participants per arm for 80% and 90% power at 100% of the observed effect; 13,399 and 17,937 at 75%; and 30,147 and 40,358 at 50%. Smaller effects require more participants to detect under the same planning assumptions. These very large illustrations reflect the small observed mean difference relative to the variability in the posted scores. This is not observed power.

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 = -0.360; pooled standard deviation σ = 7.888.
2. n = 2 × (1.96 + 0.842)² × 7.888² / -0.360² = 7,536.5, rounded up to 7,537 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 <- -0.36                      # observed difference in means
sigma <- 7.88805487940391                     # 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(1886690)
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 = 7,537 (80% power), 10,090 (90% power)
 75% of observed effect: n per arm = 13,399 (80% power), 17,937 (90% power)
 50% of observed effect: n per arm = 30,147 (80% power), 40,358 (90% power)
power.t.test: 7537.5 
Simulated power at n = 7,537 per arm: 0.799 (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 record lists the Day 90 OSDI score as the primary outcome and names four secondary outcomes: change from baseline in corneal staining, tear break-up time, the Schirmer test, and uncorrected visual acuity, each in the worse eye. The results for those secondary outcomes are not reported in the registry record. The record does not report how many comparisons were planned across all outcomes or time points, or whether any multiplicity adjustment was planned or used.

In general, when many outcomes or comparisons are tested, the chance of obtaining a small p-value by chance can increase. Multiplicity methods can address this issue, but the choice depends on the analysis plan and the role of each outcome. The posted primary comparison has an unadjusted p-value of 0.796. It should not be treated as a multiplicity-adjusted result, and no adjustment procedure should be inferred.

The primary-outcome population is defined as per protocol: randomized patients without significant protocol violations. The outcome summaries include 68 participants in the New Eye Drop Formulation arm and 57 in the REFRESH PLUS® arm, compared with recorded enrollment of 148. The registry record does not explain the difference in counts, report the number or reasons for exclusions, or state whether an intention-to-treat analysis was also conducted.

Missing Day 90 measurements, imputation, and sensitivity analyses are not reported in the registry record. In general, missing-data handling can affect estimates if the availability of measurements is related to participants’ outcomes or treatment assignment. Without details on completeness and the analysis of missing values, the influence of missing data cannot be assessed. The original statistical analysis plan, including planned contrasts and analysis populations beyond the stated per-protocol population, is not reported in the registry record.

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: abdominal pain (1.4%).

The serious adverse event figures list 75 participants at risk in the New Eye Drop Formulation group, with 0 affected by a serious adverse event, and 73 at risk in the REFRESH PLUS® group, with 1 affected. These counts describe the recorded safety groups and should be read separately from the primary-outcome sample sizes, which are based on the per-protocol population. The registry record also lists Abdominal Pain at 1.4% among the top serious adverse event terms.

The figures are descriptive counts, not a complete account of event timing, severity, duration, or causal attribution. The registry record does not provide further context about the listed serious event or identify which group the term listing represents. Death counts are not reported in the registry record. The other adverse event figures are 4 affected among 75 at risk in the New Eye Drop Formulation group and 18 affected among 73 at risk in the REFRESH PLUS® group. These counts alone do not establish why events occurred or whether differences are due to treatment.

In general, safety comparisons depend on how events were defined, collected, and classified, and on the amount of time participants were observed. Further details about these procedures are not reported in the registry record. The counts should not be interpreted as proof of safety or harm.

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

The posted primary-outcome comparison describes average Day 90 OSDI scores in the per-protocol groups. The means are 6.99 for the New Eye Drop Formulation and 6.63 for REFRESH PLUS®. The estimated mean difference, REFRESH PLUS® compared with the new formulation, is -0.36, with a confidence interval from -3.092 to 2.372 and an unadjusted p-value of 0.796. The interval includes zero and permits differences in either direction. The result therefore does not show a clear average separation in this posted summary.

That finding is not evidence that the formulations are identical. A study may fail to detect a difference even when some difference exists, especially when estimates are imprecise. Equivalence would require a prespecified margin that defines an acceptable range of differences and an analysis designed for that question. Neither is reported in the registry record. The clinical importance of the observed estimate also cannot be determined from the record because no important-difference threshold is given.

The primary outcome is a symptom questionnaire at Day 90. It does not encompass every possible outcome following LASIK. The listed secondary measures concern corneal staining, tear break-up time, Schirmer testing, and uncorrected visual acuity, but their results are not reported in the registry record. The posted primary comparison also does not establish individual-level response patterns or changes from baseline.

Interpretation is further bounded by the stated per-protocol population and the difference between recorded enrollment and the primary-outcome sample sizes. Reasons for exclusions and missing measurements are not reported. The result is best understood as an uncertain comparison of average Day 90 symptom scores among the participants included in the posted per-protocol summaries, rather than as a definitive conclusion about all randomized participants or every dimension of treatment effect.

16. Why This Trial Matters Statistically

This trial illustrates why a point estimate, its uncertainty, and the outcome scale need to be considered together. The estimated mean difference is -0.36, but the confidence interval extends from -3.092 to 2.372. The point estimate is close to zero, while the interval includes values on either side. Reporting only the group means or only the p-value would leave out important information about the range of effects compatible with the posted data.

The scale also matters. The OSDI score runs from 0, no disability, to 100, complete disability. That direction helps explain why a lower mean corresponds to a lower average symptom-disability score. But the registry record does not define a clinically important threshold. Statistical uncertainty and clinical importance are related but distinct questions, and the latter cannot be resolved by the p-value alone.

The analysis population is another important consideration. The registry identifies a per-protocol population and reports primary-outcome sample sizes of 68 and 57, while enrollment is 148. Without an explanation of the participant flow, readers cannot determine from the registry record how the exclusions or unavailable outcome measurements might affect the comparison. This is a reason to distinguish a result in the posted analysis population from a conclusion about all randomized participants.

Finally, the record names several secondary outcomes but does not report their results or a multiplicity plan. A primary-outcome comparison cannot stand in for a complete account across all outcomes. Together, these features show why transparent reporting of analysis populations, uncertainty, missing data, and planned comparisons is essential to interpreting clinical trial results.

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 gives a focused summary but leaves several trial-specific questions unanswered. Although the study is described as randomized and double-masked, details of sequence generation, allocation concealment, and masking procedures are not reported in the registry record. Further information about participant flow, reasons for protocol violations, and exclusions from the per-protocol population is also not reported.

The primary-outcome summaries include 68 participants in the New Eye Drop Formulation group and 57 in the REFRESH PLUS® group, while enrollment is 148. The registry record does not explain this difference or state how missing Day 90 scores were handled. It does not report whether an intention-to-treat analysis, imputation, or sensitivity analysis was performed. These gaps prevent assessment of how robust the posted per-protocol estimate is to missing outcomes or exclusions.

The record does not report the original sample-size justification, the complete statistical analysis plan, the confidence level or method for the interval, or the exact model behind the unadjusted p-value. It also does not provide a clinically important difference threshold. Results for the four listed secondary outcomes and details of any multiplicity adjustment are not reported in the registry record.

Safety reporting is limited to the posted counts and a serious-event term listing. Further details on event definitions, timing, attribution, and follow-up are not reported. These limitations do not change the posted numbers, but they constrain how broadly or causally the result can be interpreted.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: A Study to Compare the Safety and Efficacy of a New Eye Drop Formulation With REFRESH PLUS® in Participants Following LASIK Refractive Surgery — NCT01886690.
• Registry record last updated 2019-04-16; status last verified 2019-04.
• Results first posted 2015-10-05.
• 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 3 study sponsored by Allergan in participants following bilateral LASIK surgery. Enrollment was 148. The New Eye Drop Formulation was compared with REFRESH PLUS®, with both arm descriptions specifying 1 to 2 drops in each eye for 90 days.

The primary endpoint was the Ocular Surface Disease Index© score at Day 90 in the per-protocol population. Posted means were 6.99 for the new formulation and 6.63 for REFRESH PLUS®. The estimated mean difference was -0.36, with a confidence interval from -3.092 to 2.372 and an unadjusted p-value of 0.796. Four secondary outcomes are listed, but their results are not reported in the registry record.

The primary summaries are based on 68 and 57 participants, and the registry record does not explain how these counts relate to total enrollment. Details of missing-data handling, the original sample-size rationale, and the full analysis plan are not reported in the registry record.