Effect of Topical Naltrexone Ophthalmic Solution on the Signs and Symptoms of Dry Eye in Diabetic Subjects: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effect of Topical Naltrexone Ophthalmic Solution on the Signs and Symptoms of Dry Eye in Diabetic Subjects (NCT03660475), a randomized phase 2 study. The primary outcome is Total Ocular Surface Disease Index.

2. Clinical Question

This is a question about the observed group means and the uncertainty around their difference, not a question that can be settled by comparing the means alone. The registry record reports a mean of 21.17 in the naltrexone group and 21.36 in the placebo group. The reported sponsor analysis gives p = 0.967. These figures describe the posted Day 29 comparison; they do not establish that the treatments are equivalent or that a difference of any particular size is impossible.

3. Trial Design

The registry identifies NCT03660475 as a completed, randomized Phase 2 study of topical naltrexone ophthalmic solution for dry eye in diabetic subjects. It lists a parallel-group model and a single-center setting. The enrollment entry is 60. The primary outcome results are reported for 30 participants in each arm.

The intervention was Naltrexone Ophthalmic Solution 0.002%, and the comparator was Placebo Ophthalmic Solution. The study objective in the registry was to determine the safety and efficacy of the naltrexone solution compared with placebo for signs and symptoms of dry eye in diabetic subjects. The primary outcome was Total Ocular Surface Disease Index at Day 29. Secondary outcomes included measures of staining, tear-film break-up time, conjunctival redness, tear production, corneal sensitivity, tear osmolarity, inflammation, and ocular discomfort.

The registry's masking entry is QUADRUPLE, while the official title describes the study as double masked. The record does not explain this difference, so the masking arrangement cannot be characterized more specifically from the registry information. It lists the study as starting on 2018-07-31, with primary completion on 2018-11-01, and status COMPLETED.

The registry record does not report the original sample-size rationale, detailed allocation procedures, the analysis population, or how missing observations were handled. The study's phase and exploratory objective provide context for interpreting its estimates, but do not substitute for those unreported design and analysis details.

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

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 Total Ocular Surface Disease Index, measured over Day 29.

The primary endpoint was the Total Ocular Surface Disease Index (OSDI) score at Day 29. The OSDI is a 12-item questionnaire intended to assess symptoms of ocular irritation consistent with dry eye disease and their impact on vision-related functioning. Each question uses a 0-to-4 scale; the total score ranges from 0 to 48. A higher score indicates a worse outcome.

A continuous score preserves more information about the measured symptom burden than a simple classification into categories would. Reporting a group mean gives a summary of the scores, while the standard deviation describes how much individual scores varied around that mean. Neither statistic describes every participant's experience, and a group average should not be read as an individual-level prediction.

The comparison concerns the mean score in the naltrexone group relative to the placebo group at the stated assessment time. It is a comparison at Day 29, not a reported estimate of change from baseline: baseline values and a baseline-adjusted primary analysis are not reported in the registry record. The endpoint therefore answers the posted between-group question at that time point, subject to the uncertainty and reporting limitations.

7. Results Posted in the Registry

• Naltrexone: mean 21.17 versus 21.36 on control; difference -0.19 (95% CI -9.02 to 8.64), standardized effect d = -0.01; z-test p = 0.966.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Lissamine Green Staining

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Naltrexone: mean 2.65 versus 2.59 on control; difference 0.06 (95% CI -0.54 to 0.66), standardized effect d = 0.05; z-test p = 0.844.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Naltrexone and the control. The interval gives the range of effects that remain compatible with the data.

Tear Film Break-up Time

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Naltrexone: mean 2.76 versus 3.48 on control; difference -0.72 (95% CI -1.68 to 0.24), standardized effect d = -0.38; z-test p = 0.141.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Naltrexone and the control. The interval gives the range of effects that remain compatible with the data.

Conjunctival Redness

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Naltrexone: mean 1.00 versus 1.00 on control; difference 0.00 (95% CI -0.22 to 0.22), standardized effect d = 0.00; z-test p = 1.000.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Naltrexone and the control. The interval gives the range of effects that remain compatible with the data.

The registry lists 12 posted secondary outcomes, with measures covering ocular surface staining, tear-film stability, redness, tear production, corneal sensitivity, tear osmolarity, inflammation, and ocular discomfort. Detailed group summaries and comparisons are included for some of these measures. Across the three secondary comparisons described in detail, the estimated differences point in different directions, including one at zero; their recalculated intervals include zero. This is a mixed pattern rather than a consistent separation favoring one group across the described measures.

The secondary outcomes provide additional views of dry-eye signs and symptoms, but they do not replace the primary OSDI comparison. Their relationship to the primary result is therefore contextual: they do not form a single combined measure, and variation across measures is possible because they assess different features. The registry record does not report a prespecified hierarchy or a multiplicity-adjusted analysis that would establish how these outcomes should be ranked or combined.

Unadjusted secondary results generally carry less weight when many outcomes are examined. In general, testing more outcomes creates more opportunities for apparently notable results to arise by chance, even when each individual test uses a conventional threshold. Adjustment methods or a prespecified testing strategy can address this issue, but neither is reported in the registry record. The listed secondary findings are best treated as exploratory signals, not as independent confirmation of the primary result.

The record also lists 17 outcome measures and 11 analyses. It does not explain the relationship between these counts, which measures were included in each analysis, or whether every listed measure had a reported result. The secondary record should therefore be read with attention to what is actually reported, without assuming that unreported measures had no findings.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Lissamine Green Staining
• Tear Film Break-up Time
• Conjunctival Redness
• Schirmer's Test
• Cochet-Bonnet Corneal Sensitivity Test
• Tear Osmolarity
• Matrix Metalloprotienase-9 (MMP-9) is a Marker of Inflammation.
• Ocular Discomfort (Scale 1)

9. Statistical Interpretation

10. Statistical Methods Explained

The primary outcome is continuous: each participant has an OSDI score, and the registry reports the group mean and standard deviation. A mean describes the central location of the observed scores. A standard deviation describes their spread around the mean; it is not the uncertainty in the mean and is not a range containing every participant's score.

What does the mean difference represent?

The comparison is expressed as the naltrexone mean minus the placebo mean. The recalculated estimate is -0.19, using the posted group means. Because lower OSDI scores indicate a better outcome on the stated scale, a negative estimate points toward a lower observed average in the naltrexone group. The estimate is small in relation to the reported variability, so the direction and size should be interpreted together with the uncertainty interval rather than in isolation.

What does the t-test assess?

The registry reports a two-sided t-test for the primary comparison. In general, a two-sided test assesses evidence for a difference in either direction, rather than testing only whether one named group has a higher mean. A t-test evaluates the observed difference relative to its estimated sampling variability under the test's assumptions. The resulting p-value is not the probability that the null hypothesis is true, and it is not a measure of the size or importance of a difference.

The sponsor's reported p-value is 0.967. The unadjusted recalculation from the posted summary statistics gives p = 0.966. These are closely aligned descriptions of the comparison, but the sponsor's analysis is the registry's reported inferential result. The record does not provide the sponsor's underlying test statistic, degrees of freedom, or analysis details beyond identifying a two-sided t-test.

Why does variability matter?

In general, a mean difference is estimated less precisely when individual measurements vary widely or when there is limited information. The primary outcome standard deviations are 17.72 for naltrexone and 17.16 for placebo, while the reported group means are close. The spread indicates substantial variation in scores within each group relative to the estimated difference between their means. This helps explain why a small point estimate does not, by itself, establish that the true group difference is close to zero.

General statistical tests also rely on assumptions about the data and the analysis. For a t-test, relevant considerations include whether the observations are independent and whether the method adequately handles the score distributions and variance structure. The registry record does not report diagnostic checks or alternative analyses, so it is not possible to assess those details from the record.

What is recalculated?

The recalculated comparison is an unadjusted estimate based on the posted group means, standard deviations, and group sizes. It is not a participant-level reanalysis and cannot account for covariates, missing outcomes, protocol deviations, or other adjustments that may have been used by the sponsor. The registry's reported analysis remains the direct record of the sponsor's result.

The confidence interval attached to the recalculated mean difference describes a range of values compatible with the estimate under the calculation's assumptions. In general, such an interval conveys both the estimate's direction and its precision. The confidence level for the recalculated interval is not stated in the registry record, and the sponsor's analysis does not include a reported confidence interval. Interpretation should not assign an unstated confidence level to the posted interval.

Why are planning figures not evidence of achieved power?

Sample-size planning figures use an assumed effect and design conditions to illustrate how many participants might be needed for a specified target power. They depend on the effect chosen for planning and on statistical assumptions. Here the planning illustrations use fractions of the observed effect and specified assumptions described in the sample-size discussion. They are not a measurement of the study's ability to detect an effect after the results have been observed, and they do not replace the estimate and its uncertainty.

General power calculations are especially sensitive when the observed difference is very small: planning to detect a smaller effect requires more participants, all else being equal. That relationship explains why the planning illustrations can be much larger than the enrolled groups without implying that those figures were the original design target. The original sample-size assumptions are not reported in the registry record.

11. Confidence Intervals and Precision

The recalculated mean difference for the primary outcome is -0.19, with an interval from -9.017 to 8.637. The interval includes zero, so the summary statistics are compatible with no mean difference as well as with values in either direction. Its width indicates that the estimate is not precise enough to tightly locate the underlying difference. The confidence level for this recalculated interval is not reported in the registry record.

The interval should be interpreted in the context of the OSDI scale, which ranges from 0 to 48 and is oriented so that higher scores are worse. Its lower and upper limits span meaningfully different possible group differences, rather than concentrating near the point estimate. The interval does not mean that every value inside it is equally likely, nor does it establish that values outside it are impossible.

The reported group means are 21.17 for naltrexone and 21.36 for placebo, with standard deviations of 17.72 and 17.16, respectively. Those standard deviations describe variability among observed scores, whereas the interval describes uncertainty around the estimated difference. Confusing these two quantities can make results seem more precise than they are.

The sponsor's reported analysis gives p = 0.967 but does not report a confidence interval in the registry record. The recalculated interval comes from the posted summary statistics and should not be mistaken for a sponsor-reported interval. Taken together, the point estimate, interval, and p-value indicate that the observed comparison is close to zero but do not establish equivalence or rule out potentially relevant differences. A threshold for clinical importance is not reported, so the clinical meaning of the interval's limits cannot be determined from the record alone.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm, not total participants across the study. They are planning illustrations calculated from the observed effect, not the original design rationale for this trial. The record'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 the stated fraction of the observed effect.

The 80% power column describes the number of participants per arm that the illustration estimates would be needed to have an 80% chance of detecting the specified effect under those assumptions. The 90% power column gives the corresponding planning target for a 90% chance. These are prospective planning concepts: power depends on the assumed effect, variability, design, and test conditions.

For the primary outcome, the figures are 132,293 participants per arm for 80% power and 177,103 participants per arm for 90% power when planning for 100% of the observed effect. For 75% of the observed effect, the figures are 235,187 and 314,849 participants per arm. For 50% of the observed effect, they are 529,171 and 708,409 participants per arm. Smaller effects require more participants to detect under otherwise unchanged assumptions.

These figures are not observed power. They are highly dependent on the observed effect used as their starting point, and the registry does not report the original sample-size justification. They should not be treated as a recommendation for a future trial without a separately justified target effect and design.

13. 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 = -0.190; pooled standard deviation σ = 17.442.
2. n = 2 × (1.96 + 0.842)² × 17.442² / -0.190² = 132,292.5, rounded up to 132,293 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 <- -0.189999999999998                      # observed difference in means
sigma <- 17.442247561596                     # 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(3660475)
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 = 132,293 (80% power), 177,103 (90% power)
 75% of observed effect: n per arm = 235,187 (80% power), 314,849 (90% power)
 50% of observed effect: n per arm = 529,171 (80% power), 708,409 (90% power)
power.t.test: 132293.5 
Simulated power at n = 132,293 per arm: 0.800 (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.

14. Analyses Reported by the Sponsor

The registry reports the sponsor's primary analysis as a two-sided t-test with p = 0.967. The unadjusted recalculation from the posted summary statistics gives a mean difference of -0.19 and p = 0.966. These p-values are closely aligned, so the recalculation does not point to a material disagreement in the primary comparison's test result.

The recalculation is derived from the reported group means, standard deviations, and sample sizes. It cannot reproduce any participant-level adjustments or analysis choices that are not documented in the registry record. The sponsor's analysis is therefore the direct reported result; the recalculation is a transparent, unadjusted check based on the posted summary data.

The registry record does not include a sponsor-reported confidence interval for the primary comparison. The interval from -9.017 to 8.637 is the recalculated interval, and its confidence level is not stated in the record. The sponsor p-value and recalculated interval answer related but not identical reporting needs: the p-value summarizes a test against a null difference, while an interval expresses uncertainty about a range of possible differences under its calculation assumptions.

No discrepancy is flagged between the reported and recalculated primary analysis. The small difference between their p-values should not be overinterpreted, and neither result establishes equivalence or rules out effects that could matter.

15. Multiplicity, Missing Data and Analysis Populations

The registry record lists multiple outcomes and analyses: 17 outcome measures and 11 analyses, alongside 12 posted secondary outcomes. It does not describe a multiplicity strategy, such as a prespecified testing hierarchy or adjustment across multiple comparisons. Without that information, individual unadjusted secondary p-values would not account for the possibility of chance findings across a collection of tests. The primary endpoint has a stated role in the record, but the broader confirmatory status of secondary outcomes is not reported.

Missing-data handling is not reported in the registry record. The primary results give 30 participants in each group, but those figures alone do not explain whether all randomized participants contributed data, whether any outcome values were missing, or how missing observations were treated. The analysis population is also not reported. It is not possible to determine from the summary whether the analysis followed assignment regardless of treatment received or used another population definition.

The registry record does not report a detailed statistical analysis plan, the handling of protocol deviations, baseline adjustment, or model diagnostics. These omissions limit assessment of how the sponsor selected and implemented the analysis, and whether alternative analysis choices might affect the estimate. They also mean that the recalculation from summary statistics should be understood as unadjusted, rather than as a substitute for a documented participant-level analysis.

These reporting gaps do not show that the analyses were inappropriate or that data were missing. They mean that the registry record does not provide enough information to assess those matters. A careful interpretation distinguishes the posted results from questions that require an analysis plan, participant flow information, or additional methods reporting.

16. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

Most frequent non-serious adverse event terms

The registry reports serious adverse events for 0 of 30 participants in the naltrexone group and 0 of 30 in the placebo group. It reports 0 deaths in each group. No serious adverse event terms are listed.

For other adverse events, the record reports 0 of 30 participants affected in the naltrexone group and 1 of 30 in the placebo group. These are counts of participants reported as affected, not rates calculated from additional follow-up information. The registry does not provide event descriptions for the non-serious event in this summary.

Zero reported serious events in these groups does not establish that serious events cannot occur, and the small study does not characterize uncommon risks precisely. The record also does not provide enough detail to assess severity, timing, relatedness to study treatment, or the method used to collect adverse events. These figures describe the safety information posted in the registry record and should not be interpreted as a complete safety profile.

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

The primary result describes a Day 29 comparison of OSDI group means in a randomized, placebo-controlled study of diabetic subjects with dry eye disease. The reported means were 21.17 with naltrexone and 21.36 with placebo. The sponsor's two-sided test yielded p = 0.967, and the recalculated difference was -0.19 with an interval from -9.017 to 8.637.

These results do not show a clear statistical difference between the groups in the posted primary comparison. They also do not prove that the treatments are equivalent, establish that there is no effect, or rule out differences that could be important. Equivalence or non-inferiority requires a defined margin and an analysis designed for that question; such a margin and analysis are not reported in the registry record.

The OSDI is a symptom and functioning measure, and the higher-is-worse direction gives the score a clear orientation. Still, the record does not specify a threshold for a clinically important difference. A small numerical difference cannot therefore be labeled clinically unimportant solely from the reported means, and a broad interval cannot be translated into a clinical conclusion without additional context.

The study's single-center setting, Phase 2 designation, exploratory objective, and assessment at Day 29 constrain what can be inferred. The record does not establish whether the observed pattern applies to other populations or settings, or how outcomes might differ at other time points. The appropriate conclusion is limited to the posted comparison and the uncertainty represented by its estimate and interval.

18. Why This Trial Matters Statistically

This trial illustrates why a point estimate, a test result, and an uncertainty interval answer different statistical questions. The mean difference describes the observed separation between group averages. The p-value summarizes the test against a null difference under its assumptions. The recalculated interval conveys the range of values compatible with the estimate under the interval calculation. None should be read alone as a complete verdict.

The primary estimate is close to zero, while the interval is broad enough to include differences in both directions. This is an important distinction: a result that does not show a clear statistical separation is not the same as precise evidence that the groups are alike. For clinical researchers, the scale's interpretation and a prespecified threshold for meaningful change are important alongside statistical uncertainty; the latter threshold is not reported in the registry record.

The record also demonstrates why exploratory secondary findings need careful handling. Multiple signs and symptoms can be measured, and they need not move together. Without a reported multiplicity strategy, a pattern across secondary tests should be treated cautiously rather than used as an independent confirmatory claim.

Finally, planning calculations based on the observed effect can become very large when that effect is small. Such illustrations show the dependence of sample size on the effect one intends to detect, but they do not reveal the trial's original design assumptions or imply that the trial had a particular observed power. The registry record does not report the original sample-size rationale. These distinctions help separate what the posted data quantify from what remains uncertain.

19. 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 study was single-center and enrolled diabetic subjects with dry eye disease. That setting and population define the scope of the posted results; the registry record does not establish how well the findings apply to other populations or care settings. The study was identified as Phase 2 and exploratory, and the primary assessment was at Day 29. Results at other time points are not described in the primary outcome record.

The registry gives primary group means, standard deviations, and sample sizes, but does not report baseline OSDI values or a baseline-adjusted primary estimate. It also does not report the analysis population, missing-data procedures, protocol deviations, or diagnostic checks for the statistical test. These omissions constrain evaluation of the analysis and of whether the summary comparison represents all randomized participants.

The registry's masking entry says QUADRUPLE, while the official title says double masked. The record does not reconcile those descriptions. It also does not provide enough detail to characterize how masking was implemented. The treatment description identifies the solution concentration but does not report a fuller dosing schedule in the registry record recorded for this analysis.

The sponsor reports a p-value but no primary confidence interval in the registry record. The recalculated interval is based on summary statistics, and its confidence level is not stated. A clinical-importance threshold is also not reported, making it difficult to interpret the range of possible differences clinically. Finally, multiplicity handling for the several outcomes is not reported. These are limitations of the available registry information and do not by themselves establish that the study methods were deficient.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Effect of Topical Naltrexone Ophthalmic Solution on the Signs and Symptoms of Dry Eye in Diabetic Subjects — NCT03660475.
• Registry record last updated 2022-12-02; status last verified 2022-10.
• Results first posted 2022-12-02.
• 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.

23. Record Summary

NCT03660475 is a completed, randomized, parallel-group Phase 2 study of Naltrexone Ophthalmic Solution 0.002% versus Placebo Ophthalmic Solution in diabetic subjects with dry eye disease. The registry lists enrollment of 60 and a single-center setting. The official title calls the study double masked, while the registry masking entry is QUADRUPLE; the record does not explain the difference.

The primary outcome was Total Ocular Surface Disease Index at Day 29. The reported means were 21.17 for naltrexone and 21.36 for placebo. The sponsor's two-sided t-test result was p = 0.967. The unadjusted recalculation gives a mean difference of -0.19 and an interval from -9.017 to 8.637; the confidence level for that interval is not reported.

The posted primary comparison does not show a clear statistical separation, but it does not establish equivalence or rule out potentially relevant differences. The registry record does not report the original sample-size rationale, multiplicity strategy, missing-data handling, or analysis population.