Study Evaluating the Safety of KetoNaph Ophthalmic Solution in Healthy Volunteers: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Study Evaluating the Safety of KetoNaph Ophthalmic Solution in Healthy Volunteers (NCT01159015), a randomized phase 3 study. The primary outcome is Percentage of Participants With at Least One Adverse Event..

2. Clinical Question

The primary adverse-event definition covers an unfavorable and unintended sign, symptom, or disease temporally associated with use of a test article, whether or not it was considered related to the test article. This is a broad safety outcome: an event can contribute to the endpoint even when the record does not classify it as caused by treatment.

The registry lists allergic conjunctivitis as a condition, but its title and summary describe a safety study in healthy volunteers or subjects. The record does not explain how the condition listing relates to the enrolled population. It also does not report the primary outcome population. These details limit how specifically the result can be applied to a particular age group or clinical population.

3. Trial Design

The registry describes a completed phase 3 study with randomized allocation and a parallel-group model. The official title calls it multi-center, double-masked, randomized, placebo-controlled, and parallel-group. The registry's masking field says triple masking; the record does not explain the difference between that label and the title's double-masked description.

The two groups received KetoNaph ophthalmic solution or its vehicle. The registry records an enrollment of 534. The posted group sizes are 357 for KetoNaph and 177 for Vehicle. The groups therefore have different recorded sizes; the registry record does not explain the allocation process or why the sizes differ. No further details of treatment administration, visit schedule, or adherence are reported in the registry record.

The registry records the study start as 2010-07 and primary completion as 2010-09, with status completed. The primary outcome timeframe is 42 days. The brief summary says the study evaluated safety in healthy adult subjects and pediatric subjects with a history or family history of ocular allergy. However, the trial title refers to healthy, normal volunteers, and the primary outcome population field is blank. The record does not clarify which groups of participants were included in the primary analysis.

The registry record does not report the trial's original sample-size justification, the planned statistical analysis, or the procedures used to maintain masking. It also contains no posted secondary outcomes and no listed analyses beyond the primary comparison. These omissions mean that the observed group sizes and posted primary result can be described, but the original design choices cannot be reconstructed from the 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

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 at Least One Adverse Event., measured over 42 days.

The primary endpoint is the percentage of participants with at least one adverse event over 42 days. The outcome data are presented as participant counts: 113 of 357 in the KetoNaph group and 34 of 177 in the Vehicle group. Each participant is counted once for this endpoint, regardless of whether they experienced one event or more than one.

The registry defines an adverse event as an unfavorable and unintended sign, symptom, or disease temporally associated with use of a test article, whether or not considered related to that test article. The definition is intentionally broad in the sense that it does not require a judgment that the study product caused the event. An event count under this definition is therefore not, by itself, a count of reactions established to be caused by treatment.

Counting participants with any event is a common way to summarize the overall frequency of events during a specified period. It gives a straightforward group-level measure, but it does not describe the number of events per participant, their duration, severity, timing, or clinical importance. The record does not provide those details for all events as part of the primary endpoint. The primary outcome population field is not reported in the registry record, which also leaves the analysis population unclear.

7. Results Posted in the Registry

• KetoNaph: 31.7% (113/357) versus 19.2% (34/177) on control; risk difference 12.4 percentage points (95% CI 4.9 to 20.0), risk ratio 1.65 (1.17–2.31); unadjusted two-proportion z-test p = 0.002.

8. Statistical Interpretation

9. Statistical Methods Explained

The principal comparison is a difference between the proportion of participants with at least one adverse event in each group. For each arm, the outcome is binary at the participant level: a participant either had at least one event during the stated timeframe or did not. The posted counts are 113 of 357 for KetoNaph and 34 of 177 for Vehicle. The registry reports the risk difference as 0.124, with a confidence interval from 0.049 to 0.200.

What does a risk difference describe?

A risk difference subtracts one group's event proportion from the other group's event proportion. It is an absolute measure, rather than a ratio. Its sign indicates the direction of the comparison, and its magnitude reflects the distance between the two proportions on the proportion scale. Here, the positive estimate means the event proportion was higher in the KetoNaph group in the posted data. The estimate is not a causal conclusion: randomization supports a comparative design, but the registry record does not report enough detail about outcome assessment, missing observations, or analysis populations to assess all possible sources of uncertainty.

How should the p-value be read?

The unadjusted p-value is 0.002. In general, a p-value measures the compatibility of observed data with a null hypothesis under a statistical model. Smaller values indicate that the observed data would be less typical if the null model and its assumptions held. A p-value does not state the probability that a treatment has no effect, and it does not show whether a difference is clinically important. The registry does not report the exact test or model used to obtain this p-value, so the method behind the posted result is not reported in the registry record.

Why are risk ratios and odds ratios also listed?

The risk ratio compares the event proportions using a ratio scale. Its posted estimate is 1.648, with limits 1.175 and 2.311. The odds ratio compares the odds of an event between groups; its posted estimate is 1.948, with limits 1.26 and 3.011. These are alternative ways to express the group contrast, not separate outcomes. Ratio measures can appear larger or smaller than an absolute difference because they use a different scale. The risk difference is often easier to interpret as a contrast in proportions, whereas ratios describe relative contrasts.

The confidence intervals attached to these estimates convey uncertainty in the comparison. In general, a confidence interval gives a range of values compatible with the data under a particular method and its assumptions. Its width reflects precision: a narrower interval indicates less sampling uncertainty than a wider interval, all else equal. The registry record does not identify the interval calculation method or state whether the posted estimates were adjusted for any covariates.

What does randomization contribute?

Random allocation is intended to make the treatment groups comparable, on average, with respect to factors present before assignment. In a randomized study, a between-group outcome contrast can therefore be informative about the assigned interventions when allocation is implemented as intended and follow-up and analysis are appropriately handled. Randomization does not guarantee that the groups are identical, does not eliminate chance variation, and cannot correct for missing data or outcome measurement problems by itself. The registry record does not provide enough detail to assess those implementation and analysis issues.

The registry labels the study triple-masked, while the official title describes it as double-masked. Masking can reduce the influence of participants' or study personnel's knowledge of treatment assignment on behavior, reporting, or assessment. The record does not clarify which roles were masked or reconcile the differing labels. The parallel-group model means participants are assigned to a group for comparison rather than crossing between study groups; the specific treatment schedule is not reported in the registry record.

The primary outcome counts participants with one or more adverse events, not the total number of events. This participant-level summary avoids letting a participant with repeated events contribute repeatedly to the primary count. However, it discards information about repeated events and event characteristics. The registry record does not report the statistical analysis plan, covariate adjustment, handling of missing outcomes, or population definitions. As a result, the methods behind the posted comparison cannot be fully reconstructed from the record.

10. Confidence Intervals and Precision

The posted risk-difference estimate is 0.124, with a confidence interval from 0.049 to 0.200. The interval lies on the positive side of zero, so the values within it indicate a higher event proportion in the KetoNaph group than in the Vehicle group on the risk-difference scale. The interval also shows that the data are compatible with a range of possible differences, not just the point estimate.

In general, a confidence interval is a measure of statistical precision under a specified method and its assumptions. It is not a guarantee that the true value lies within the interval, nor does it describe the range of individual participants' outcomes. A narrower interval would indicate a more precise estimate; a wider interval would indicate greater uncertainty. The registry record does not report the method used to calculate this interval, so its precise coverage properties cannot be assessed from the record alone.

The posted relative estimates give additional views of the contrast. The risk ratio is 1.648, with limits 1.175 and 2.311; the odds ratio is 1.948, with limits 1.26 and 3.011. These intervals also indicate uncertainty, but their scales differ from the risk-difference scale. The risk difference is an absolute contrast, while the risk ratio and odds ratio are relative contrasts.

The interval and p-value address sampling uncertainty within the statistical comparison; they do not account automatically for unreported design or analysis details. The primary outcome population, missing-data handling, and interval method are not reported in the registry record. Precision should therefore be understood as precision of the posted estimate under its unstated calculation method, not as a complete account of uncertainty about generalizability, causation, or event classification.

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 figures are planning illustrations based on the observed effect, not the trial's original design calculation. For this binary outcome, the entries refer to participants per arm, not total events. The figures assume a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning row considers an effect to detect set at the stated fraction of the observed effect.

The 80% power column gives the number of participants per arm that the illustration estimates would be needed for an 80% chance of detecting the assumed effect under those planning assumptions. The 90% power column gives the corresponding number per arm for a 90% chance. These are planning probabilities under the assumed effect and method, not guarantees for a future study. This is not observed power.

For 100% of the observed effect, the illustration lists 192 participants per arm for 80% power and 256 participants per arm for 90% power. For 75% of the observed effect, the corresponding figures are 327 and 437 participants per arm. For 50% of the observed effect, they are 702 and 940 participants per arm. A smaller effect is harder to distinguish from random variation, so more participants are needed to maintain the stated power under the same assumptions. The original trial's sample-size assumptions and justification are not reported in the registry record. Any curve associated with the planning display should be read as representing these assumptions and effect scenarios, not as evidence about the trial's observed probability of success.

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 = 0.192; treatment proportion p₁ = 0.317; average p̄ = 0.254.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6159 = 1.2070.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6095 = 0.5130.
4. n = (1.2070 + 0.5130)² / (0.1244)² = 191.1, rounded up to 192 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 <- 0.192090395480226                          # control proportion
p1 <- 0.316526610644258                          # 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(1159015)
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 = 192 (80% power), 256 (90% power)
 75% of observed effect: n per arm = 327 (80% power), 437 (90% power)
 50% of observed effect: n per arm = 702 (80% power), 940 (90% power)
power.prop.test: 191.1 
Simulated power at n = 192 per arm: 0.809 (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 reports one primary outcome measure and no posted secondary outcomes. It lists one primary group comparison and an unadjusted p-value of 0.002. The registry record does not report whether additional outcomes or comparisons were planned in the protocol, whether any interim analyses were conducted, or whether a multiplicity adjustment was planned or performed. The absence of posted secondary outcomes is not evidence that none were considered in the original study.

Multiplicity matters when several statistical tests are conducted. In general, testing multiple hypotheses can increase the chance of obtaining at least one apparently unusual result by chance. Adjustment methods can account for a family of tests, but the appropriate approach depends on the study's prespecified questions and analysis plan. Because those details are not reported in the registry record, the posted p-value should be described as unadjusted and should not be treated as evidence that all possible testing has been accounted for.

The record does not state how missing primary outcome data were handled, whether every randomized participant was included in the analysis, or whether the comparison followed an intention-to-treat approach. It also does not identify a per-protocol or safety population. The population field for the primary endpoint is blank. These analysis-population and missing-data details are important because exclusions or incomplete follow-up can affect the estimated group proportions.

In general, missing outcomes can reduce precision and may introduce bias if the likelihood of missingness is related to treatment assignment or outcome status. The registry record does not report the amount, reasons, or handling of missing data, so their influence cannot be evaluated. It likewise does not report the original statistical analysis plan, covariate adjustment, or any sensitivity analyses. These omissions limit independent assessment of how the primary estimate was produced and how robust it is to alternative 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 serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: drug abuse (0.6%), alcohol abuse (0.6%), small intestinal obstruction (0.3%), cholecystitis (0.3%), septic shock (0.3%).

The serious adverse-event summary lists 3 affected participants among 357 at risk in the KetoNaph group and 1 among 177 at risk in the Vehicle group. The separate other-adverse-event summary lists 20 among 357 at risk for KetoNaph and 1 among 177 at risk for Vehicle. These are group-level counts; they should not be combined with the primary endpoint counts or treated as a complete description of each participant's event history.

The registry lists serious-event terms including Drug abuse and Alcohol abuse, each reported as 0.6%, and Small intestinal obstruction, Cholecystitis, Septic shock, and Road traffic accident, each reported as 0.3%. These terms and percentages describe the listed serious-event entries; the record does not provide an explanatory narrative linking them to treatment or clarifying their clinical circumstances.

Deaths are not reported in the registry record. The serious-event and other-event summaries do not establish whether an event was caused by study treatment. They also do not provide the timing, duration, resolution, or complete severity profile for each event. The primary endpoint uses a broader adverse-event definition and counts participants with at least one event, whereas the serious-event figures are a separate safety summary.

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

The registry result describes a difference in the proportion of participants with at least one recorded adverse event during 42 days. The event counts were 113 of 357 in the KetoNaph group and 34 of 177 in the Vehicle group, and the posted risk difference was 0.124. The confidence interval, from 0.049 to 0.200, communicates uncertainty around that group contrast under the interval method used. The posted unadjusted p-value is 0.002.

This finding does not by itself establish that KetoNaph caused the recorded events. The registry definition includes events temporally associated with use of a test article whether or not considered related. A group comparison is informative about the recorded outcome, but causal interpretation also depends on how the trial was conducted, how outcomes were assessed, how missing information was handled, and how participants were analyzed. Several of those details are not reported in the registry record.

The primary endpoint is a broad, participant-level measure. It indicates whether a participant had at least one event, but not the total number of events, their severity, duration, or importance. The separate serious-event summary adds some safety information, yet it does not supply a full narrative or establish attribution. Nor does the endpoint answer questions about effectiveness, symptom relief, or other clinical outcomes; no secondary outcomes are posted.

The record's population descriptions require caution. The title describes healthy, normal volunteers, while the brief summary mentions healthy adult subjects and pediatric subjects with a history or family history of ocular allergy. Allergic conjunctivitis is listed as a condition, but the primary outcome population is not reported in the registry record. The result should therefore be understood in the context of a registry-reported safety study, without assuming a more specific population or broader applicability than the record documents.

16. Why This Trial Matters Statistically

This study illustrates why a safety endpoint needs to be interpreted with attention to its definition. The primary outcome counts participants with at least one adverse event, including events not considered related to the test article. That broad definition can support a descriptive comparison of events observed during follow-up, but it is not equivalent to a count of treatment-caused reactions.

It also shows the value of reading absolute and relative measures together. The risk difference describes the separation between group proportions on an absolute scale; the risk ratio and odds ratio describe relative contrasts. Each measure answers a different descriptive question. The confidence intervals add information about precision, while the unadjusted p-value addresses compatibility with a null comparison under a statistical model. No single statistic captures event seriousness, causal attribution, or clinical importance.

The record also demonstrates how reporting detail shapes statistical interpretation. It includes a primary result, arm counts, and safety summaries, but does not report the analysis population, missing-data handling, exact comparison method, or original sample-size rationale. The masking labels differ between the official title and the registry field, without an explanation. These gaps do not erase the posted data, but they limit how fully readers can evaluate the analysis and its assumptions.

Finally, the planning illustrations distinguish design sensitivity from observed results. They show how the participant requirements change under specified assumptions and effect scenarios; they do not provide evidence that the completed study had a particular probability of finding a result. Keeping observed comparisons, uncertainty, and planning calculations separate is central to sound biostatistical reading.

17. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The registry record leaves the primary analysis population blank. Its title refers to healthy, normal volunteers, while the brief summary describes healthy adult subjects and pediatric subjects with a history or family history of ocular allergy. Allergic conjunctivitis is listed as a condition, but the record does not explain how that listing relates to the study population. The reported group contrast cannot therefore be assigned confidently to a more specific population than the record documents.

There is also an unresolved difference in masking descriptions: the official title says double-masked and the registry field says triple. The record does not identify which roles were masked or explain the discrepancy. The statistical analysis plan, comparison method, covariate adjustment, missing-data procedures, and analysis-population definitions are not reported in the registry record.

The primary endpoint is limited to whether each participant had at least one adverse event. It does not summarize repeated events or provide complete details on severity, timing, duration, or attribution. The separate safety summaries list serious and other adverse events, but offer limited context about individual events. Deaths are not reported in the registry record.

The record reports an unadjusted p-value and does not describe multiplicity procedures or interim analyses. No secondary outcomes are posted, and the original sample-size justification is not reported. These limitations make it difficult to assess the complete analysis strategy, the role of missing information, and the scope of inference beyond the reported primary comparison and safety counts.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Study Evaluating the Safety of KetoNaph Ophthalmic Solution in Healthy Volunteers — NCT01159015.
• Registry record last updated 2020-10-05; status last verified 2020-10.
• Results first posted 2020-09-14.
• 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 phase 3, randomized, parallel-group study comparing KetoNaph ophthalmic solution with its vehicle. It records enrollment of 534 and a primary outcome of participants with at least one adverse event during 42 days. The posted counts are 113 of 357 for KetoNaph and 34 of 177 for Vehicle.

The risk difference is 0.124, with a confidence interval from 0.049 to 0.200; the unadjusted p-value is 0.002. The record also lists risk-ratio and odds-ratio estimates and separate serious and other adverse-event summaries. Population and analysis details, missing-data handling, and the original statistical plan are not reported in the registry record.