Safety and Efficacy of Nyxol Eye Drops as a Single Agent and With Adjunctive Low-Dose Pilocarpine Eye Drops in Subjects With Presbyopia: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Safety and Efficacy of Nyxol Eye Drops as a Single Agent and With Adjunctive Low-Dose Pilocarpine Eye Drops in Subjects With Presbyopia (NCT05646719), a randomized phase 3 study. The primary outcome is Percent of Subjects With ≥ 15 Letters of Improvement in Photopic Binocular DCNVA and With < 5 Letters of Loss in Photopic Binocular BCDVA in Nyxol-treated Subjects.

2. Clinical Question

3. Trial Design

The registry describes NCT05646719 as a randomized, quadruple-masked, parallel-group phase 3 study. It is listed as completed, with enrollment of 333. The recorded start date is 2022-12-22 and the primary completion date is 2023-10-11. The sponsor is Opus Genetics, Inc.

The study concerns presbyopia and evaluates Nyxol, phentolamine ophthalmic solution 0.75%, as a single agent and with adjunctive low-dose pilocarpine. The listed low-dose pilocarpine concentration is 0.4%. The interventions also include placebo and low-dose pilocarpine vehicle. The outcome data list Nyxol plus low-dose pilocarpine, Nyxol plus low-dose pilocarpine vehicle, placebo plus low-dose pilocarpine, and placebo plus low-dose pilocarpine vehicle.

Randomization assigns participants to study groups by chance, while masking is intended to limit the influence of treatment knowledge on study conduct or assessment. The registry identifies quadruple masking but does not report the roles included in that masking designation. Parallel-group design means the listed groups are compared over the study rather than participants being described as crossing between treatments.

The primary endpoint is assessed at Visit 5 (Stage 2 Day 8), with the measurement described as baseline to 30 min post-LDP/vehicle. The registry identifies the endpoint analysis population as Modified Intent to treat. Further details on the definition of that population, allocation procedures, treatment duration, and the trial’s original statistical plan are not reported in the registry record.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Analysis population for the primary outcome, as defined in the registry: Modified Intent to treat

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.

Population: Modified intent to treat population

6. Primary Endpoint

The registry lists the primary outcome as Percent of Subjects With ≥ 15 Letters of Improvement in Photopic Binocular DCNVA and With < 5 Letters of Loss in Photopic Binocular BCDVA in Nyxol-treated Subjects, measured over Baseline at 30 min post-LDP/vehicle comparing subjects treated with Nyxol + LDP to subjects treated with placebo + LDP vehicle at Visit 5 (Stage 2 Day 8).

The primary endpoint classifies whether a participant met a combined visual-acuity response definition. A participant must have at least 15 letters of improvement in photopic binocular distance-corrected near visual acuity (DCNVA) and fewer than 5 letters of loss in photopic binocular best-corrected distance visual acuity (BCDVA), relative to baseline. The measure is recorded at 30 min post-LDP/vehicle at Visit 5 (Stage 2 Day 8).

This is a binary endpoint: each participant either meets the combined response definition or does not. The registry reports counts of participants meeting the definition in each group. The endpoint combines a near-vision improvement condition with a limit on distance-vision loss, so it captures both requirements in a single response measure. A count alone does not describe the size of a participant’s visual-acuity change beyond whether the threshold was met.

The registry describes the primary endpoint as a percent of subjects, but the posted group results give counts and group denominators. The reported endpoint population is Modified Intent to treat. Why this endpoint and its particular thresholds were selected, and how missing measurements were handled, are not reported in the registry record.

7. Results Posted in the Registry

• Nyxol + Low Dose Pilocarpine: 34.6% (27/78) versus 38.8% (31/80) on control; risk difference -4.1 percentage points (95% CI -19.1 to 10.9), risk ratio 0.89 (0.59–1.35); unadjusted two-proportion z-test p = 0.590.
• Placebo + Low Dose Pilocarpine: 20.3% (16/79) versus 38.8% (31/80) on control; risk difference -18.5 percentage points (95% CI -32.4 to -4.6), risk ratio 0.52 (0.31–0.88); unadjusted two-proportion z-test p = 0.011.
• Placebo + Low Dose Pilocarpine Vehicle: 26.8% (22/82) versus 38.8% (31/80) on control; risk difference -11.9 percentage points (95% CI -26.3 to 2.4), risk ratio 0.69 (0.44–1.09); unadjusted two-proportion z-test p = 0.106.

8. Statistical Interpretation

9. Statistical Methods Explained

The outcome is binary because it records whether each participant meets the combined visual-acuity response definition. For a binary outcome, results can be expressed as event counts and denominators, or as contrasts between groups. The posted counts are 27 of 78 for Nyxol plus low-dose pilocarpine, 31 of 80 for Nyxol plus low-dose pilocarpine vehicle, 16 of 79 for placebo plus low-dose pilocarpine, and 22 of 82 for placebo plus low-dose pilocarpine vehicle.

What does a risk difference describe?

A risk difference compares the proportion meeting the response definition in one group with the proportion in a reference group. It is expressed on the same scale as the outcome proportion. A value of zero represents no difference in the response proportions; a negative value means the named comparison group has a lower response proportion than its reference, given the subtraction direction used in these recalculations. The recalculated risk differences use Nyxol plus low-dose pilocarpine vehicle as the reference group.

The listed recalculated risk differences are -0.041 for Nyxol plus low-dose pilocarpine, -0.185 for placebo plus low-dose pilocarpine, and -0.119 for placebo plus low-dose pilocarpine vehicle. Their confidence intervals and unadjusted p-values are reported alongside those estimates. These are simple unadjusted recalculations from the posted summary statistics, not the sponsor’s reported primary analysis.

How do odds ratios differ?

An odds ratio compares the odds of meeting the response definition between groups. It is a different effect measure from a risk difference, so the numerical values are not directly interchangeable. The sponsor reports an odds ratio of 2.27 for Nyxol plus low-dose pilocarpine versus placebo plus low-dose pilocarpine vehicle, with a 95% confidence interval from 1.23 to 4.20 and p < 0.01. A second result for those groups is an odds ratio of 1.44, without a method, confidence interval, or p-value. The registry does not explain the relationship between these results.

Effect direction depends on which group is in the numerator or reference position. The sponsor entry is labelled as a superiority analysis, but its reported odds ratio should be interpreted using the sponsor analysis’ group ordering and method. The recalculated risk differences use a different group comparison, so their signs cannot be used to contradict the sponsor’s odds ratio without aligning the contrasts and analysis details.

What do confidence intervals and p-values contribute?

A confidence interval describes uncertainty around an estimated effect under the analysis assumptions. A narrow interval indicates greater precision than a wide interval, while an interval spanning the null value is compatible with no difference as well as effects in either direction. For risk differences, the null value is zero. For odds ratios, the null value is one. A p-value describes how incompatible the observed data are with a specified null hypothesis under the statistical model; it does not measure the probability that a treatment effect is real.

The recalculated p-values are unadjusted. The registry record does not report whether or how the sponsor adjusted for multiple comparisons. Nor does it report the statistical model behind the sponsor odds ratio analysis beyond the first entry’s method, described as a two-sided t-test. The registry’s analysis details are therefore insufficient to reconstruct the sponsor analysis fully.

Why might over-dispersion matter?

Over-dispersion is a general concern when data vary more than a statistical model expects. It is particularly relevant to models for counts or clustered observations, where assuming less variability than is present can make uncertainty appear too small. This endpoint is posted as participant counts for a binary response, and the registry does not report an over-dispersion assessment or identify a count-model analysis. No conclusion about over-dispersion can be drawn from the posted information.

What is known about analysis populations?

The primary endpoint population is identified as Modified Intent to treat. The registry does not define this population, explain how participants entered it, or report whether the analyses used an additional per-protocol or safety population. Randomization and masking are documented, but allocation concealment, covariate adjustment, handling of missing outcome observations, and interim analyses are not reported in the registry record.

The study lists one outcome measure and two sponsor analyses. That does not by itself establish the complete statistical analysis plan or whether additional outcomes were assessed but not posted. The registry record does not report a multiplicity strategy. Accordingly, the unadjusted recalculations should not be treated as a complete account of confirmatory inference, and the sponsor’s own analysis takes precedence where a discrepancy is flagged.

10. Confidence Intervals and Precision

Precision is conveyed by the confidence interval around an estimate. A confidence interval gives a range of effects that are compatible with the observed data and the analysis assumptions; it is not a guarantee that the true effect lies within that range. Wider intervals reflect more uncertainty about the estimate than narrower intervals.

For the recalculated comparison of Nyxol plus low-dose pilocarpine with Nyxol plus low-dose pilocarpine vehicle, the risk difference is -0.041 and the confidence interval runs from -0.192 to 0.109. This interval includes zero, so the recalculation is compatible with no difference as well as with differences in either direction. Its unadjusted p-value is 0.59.

For placebo plus low-dose pilocarpine versus Nyxol plus low-dose pilocarpine vehicle, the recalculated risk difference is -0.185, with a confidence interval from -0.324 to -0.046 and an unadjusted p-value of 0.011. For placebo plus low-dose pilocarpine vehicle versus the same recalculation reference, the estimate is -0.119, with a confidence interval from -0.263 to 0.024 and an unadjusted p-value of 0.106. The latter interval includes zero.

The sponsor’s primary comparison has a different reported measure: an odds ratio of 2.27 with a 95% confidence interval from 1.23 to 4.20 and p < 0.01. The interval excludes one, the null value for an odds ratio. However, the recalculated risk differences do not directly estimate this same contrast. The registry flags a discrepancy, and the sponsor’s own analysis takes precedence. The second sponsor odds ratio, 1.44, has no posted confidence interval, so its precision cannot be assessed from that entry.

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 figures are illustrations based on the observed effect, not the trial’s original design assumptions. For these binary-outcome comparisons, the figures are participants per arm, not total events. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The trial’s own original sample-size assumptions are not reported in the registry record.

The 80% power column gives the participants per arm that the illustration estimates would be needed to have an 80% chance of detecting the specified effect under those assumptions, if that effect and model assumptions were correct. The 90% power column gives the corresponding planning count for a 90% chance. These are design-planning quantities, not descriptions of what occurred in the trial.

Each comparison has its own observed effect and therefore its own planning figures. For example, the recalculation for Nyxol plus low-dose pilocarpine versus Nyxol plus low-dose pilocarpine vehicle uses the observed risk difference of -0.041. Its planning figures range from 2,132 participants per arm for 80% power and 2,854 for 90% power when planning for 100% of the observed effect, to 8,628 and 11,549 when planning for 50% of that effect. The other contrasts have different observed effects and different planning illustrations.

Planning for a smaller effect requires more participants because a smaller separation between groups is harder to distinguish from random variation. The 75% and 50% rows therefore represent increasingly smaller target effects than the 100% row. These figures are 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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.388; treatment proportion p₁ = 0.346; average p̄ = 0.367.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6816 = 1.3358.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6809 = 0.5731.
4. n = (1.3358 + 0.5731)² / (-0.0413)² = 2,131.6, rounded up to 2,132 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 <- 0.3875                          # control proportion
p1 <- 0.346153846153846                          # 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(5646719)
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 = 2,132 (80% power), 2,854 (90% power)
 75% of observed effect: n per arm = 3,813 (80% power), 5,104 (90% power)
 50% of observed effect: n per arm = 8,628 (80% power), 11,549 (90% power)
power.prop.test: 2131.6 
Simulated power at n = 2,132 per arm: 0.801 (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. Analyses Reported by the Sponsor

The sponsor’s reported primary comparison is Nyxol plus low-dose pilocarpine versus placebo plus low-dose pilocarpine vehicle. For that comparison, the registry lists an odds ratio of 2.27, a 95% confidence interval from 1.23 to 4.20, and p < 0.01, labelled as a superiority analysis. It also lists an odds ratio of 1.44 for the same groups, but that entry has no reported method, confidence interval, or p-value.

The simple recalculations do not reproduce this primary contrast. They use Nyxol plus low-dose pilocarpine vehicle as the reference group, and report risk differences rather than odds ratios. The recalculated risk difference for placebo plus low-dose pilocarpine vehicle versus that reference is -0.119, with a confidence interval from -0.263 to 0.024 and an unadjusted p-value of 0.106. That result is not a direct recalculation of the sponsor’s comparison between Nyxol plus pilocarpine and placebo plus vehicle.

The registry flags a discrepancy. The sponsor’s own analysis takes precedence over the unadjusted recalculations, but the available record does not explain why the entries differ or how the second odds ratio was produced. The two effect measures and their group contrasts should be kept distinct rather than treated as interchangeable results.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists one outcome measure and two analyses, but it does not report a multiplicity plan. Multiplicity arises when several outcomes, treatment contrasts, or analysis choices are examined: interpreting each result without accounting for the full set can make evidence appear stronger than it would under a prespecified testing strategy. The available record does not establish which analyses were prespecified, whether the listed comparisons were all intended as confirmatory, or whether any adjustment was used.

The primary endpoint is identified as belonging to the Modified Intent to treat population. The registry does not define that population or explain which participants were included in the endpoint analysis. The outcome counts have denominators of 78, 80, 79, and 82 for the four listed groups. The safety counts have different at-risk denominators for some groups. The record does not explain these differences, so no reason should be inferred from the counts alone.

Missing data handling is not reported in the registry record. It is not stated whether missing visual-acuity measurements were excluded, imputed, treated as nonresponses, or handled in another way. The record also does not describe sensitivity analyses for missing data. These details matter because the endpoint is based on whether a participant met a combined threshold at a specific assessment.

The sponsor analysis method is only partly described. The first reported analysis is identified as a two-sided t-test, with an odds ratio, confidence interval, and p-value. The second entry gives an odds ratio but no method or uncertainty measures. The record does not provide enough information to reconstruct either analysis in full or reconcile the reported odds ratios with the unadjusted recalculations.

The registry does not report interim analyses, stopping boundaries, a full statistical analysis plan, covariate adjustment, or allocation-concealment details. Their absence from the record is not evidence that such procedures were or were not used. The registry’s stated Modified Intent to treat population and the sponsor’s posted analyses are the available basis for describing the reported results.

15. 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 each listed safety group. The serious-event counts are zero in all groups: Nyxol plus low-dose pilocarpine, zero of 79 at risk; Nyxol plus low-dose pilocarpine vehicle, zero of 80; placebo plus low-dose pilocarpine, zero of 81; and placebo plus low-dose pilocarpine vehicle, zero of 82. Deaths are also reported as zero in each group. No top serious-event terms are listed.

The record separately gives counts for other adverse events: 13 of 79, 12 of 80, 18 of 81, and 13 of 82 in the respective groups. These are not serious adverse-event counts and should not be conflated with them.

Zero reported serious events in these groups describes the posted safety record, but does not establish that no serious event could occur or that groups have identical safety profiles. The registry entry does not provide event descriptions for the other adverse events, their timing, severity, or relatedness to treatment. Safety interpretation is therefore limited to the categories and counts recorded.

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

The primary endpoint asks whether participants met a combined near-vision improvement and distance-vision loss threshold at the specified assessment. The sponsor reports an odds ratio of 2.27 for Nyxol plus low-dose pilocarpine versus placebo plus low-dose pilocarpine vehicle, with a 95% confidence interval from 1.23 to 4.20 and p < 0.01. The record labels this analysis as superiority. A separate sponsor entry reports an odds ratio of 1.44 for the same groups without accompanying method or uncertainty information.

These entries describe the sponsor’s posted analysis; they do not show how every participant’s visual acuity changed, nor do they establish the durability of a response beyond the recorded assessment. The outcome is a threshold-based classification, and the registry does not report results for continuous changes in acuity or other secondary outcomes. It lists no secondary posted outcomes.

The unadjusted recalculations concern different contrasts, with Nyxol plus low-dose pilocarpine vehicle as their reference. They include both intervals that span the risk-difference null value of zero and one interval that does not. They should not be substituted for the sponsor’s primary comparison. Because the registry flags a discrepancy, the sponsor’s own analysis takes precedence, while the precise source of the difference remains unreported.

The results also do not, by themselves, establish the reason for any observed group difference. The registry record does not give detailed information on missing measurements, analysis adjustments, or the relationship between the two sponsor entries. The safety data report no serious adverse events or deaths in the listed groups, alongside separate counts of other adverse events. These recorded counts do not answer questions about event type, severity, or treatment relationship that are not detailed in the record.

Overall, the posted result is evidence about a defined binary visual-acuity endpoint at a defined visit in the stated analysis population. It is not a complete account of every potential benefit, harm, or longer-term outcome, and it should not be read as medical advice.

17. Why This Trial Matters Statistically

This trial is statistically notable because its primary endpoint combines two conditions into a binary response: a minimum near-vision improvement and a limit on distance-vision loss. That construction makes the endpoint easy to interpret as a participant-level response, but it also means the count does not show how far participants were above or below either threshold.

The posted analyses illustrate why comparison choice matters. The sponsor’s primary contrast is Nyxol plus low-dose pilocarpine versus placebo plus low-dose pilocarpine vehicle. The simple recalculations instead use Nyxol plus low-dose pilocarpine vehicle as their reference. An estimate from one contrast cannot be treated as an estimate from another, even when the groups overlap. Similarly, an odds ratio and a risk difference describe effects on different scales.

The registry also flags a discrepancy between the sponsor analysis and the recalculations. The sponsor’s own analysis takes precedence, but the record does not explain the discrepancy or fully describe the second sponsor entry. That makes transparent reporting of analysis populations, group ordering, methods, and missing-data handling especially important for readers assessing a binary endpoint.

The planning illustrations show how sample-size requirements depend on the target effect: smaller target effects require more participants under the stated assumptions. They are not a retrospective measure of the trial’s success or power. Keeping planning calculations separate from observed results helps prevent an illustrative design calculation from being mistaken for evidence about what the study detected.

18. 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 important details unresolved for interpreting this trial’s posted results. It does not define the Modified Intent to treat population or explain the inclusion of participants in each endpoint analysis. Missing visual-acuity data and their handling are not reported. The posted endpoint denominators differ from the safety at-risk denominators in some groups, but the record does not explain why.

The sponsor reports two odds ratios for the same primary groups. One has a 95% confidence interval and p-value and is identified as a two-sided t-test; the other has no method, confidence interval, or p-value. The registry flags a discrepancy with the simple recalculations, whose contrasts use a different reference group and whose effect measure is risk difference. The information available does not allow the discrepancy to be reconciled.

The registry does not report a multiplicity strategy, interim analyses, covariate adjustment, the trial’s original sample-size assumptions, or detailed outcome-assessment procedures. It also does not provide secondary outcome results. These omissions limit assessment of the full analysis plan and the robustness of the reported findings; they do not establish that any particular method was or was not used.

Safety information is presented as counts of serious events, deaths, and other adverse events. Detailed descriptions of the other events, their severity, timing, and treatment relationship are not reported in the information summarized in the registry record. Follow-up beyond the stated endpoint assessment and the persistence of response are likewise not described in the posted results.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Safety and Efficacy of Nyxol Eye Drops as a Single Agent and With Adjunctive Low-Dose Pilocarpine Eye Drops in Subjects With Presbyopia — NCT05646719.
• Registry record last updated 2026-10-30; status last verified 2026-06.
• Results first posted 2025-06-03.
• 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.

22. Record Summary

NCT05646719 is a completed randomized, quadruple-masked, parallel-group phase 3 study in presbyopia, sponsored by Opus Genetics, Inc. The registry reports enrollment of 333, a start date of 2022-12-22, and a primary completion date of 2023-10-11. The study evaluates Nyxol alone and with low-dose pilocarpine.

The primary endpoint is a combined threshold response in photopic binocular near and distance visual acuity, assessed at Visit 5 (Stage 2 Day 8). The stated primary comparison is Nyxol plus low-dose pilocarpine versus placebo plus low-dose pilocarpine vehicle. The sponsor reports an odds ratio of 2.27, with a 95% confidence interval from 1.23 to 4.20 and p < 0.01, plus a second odds ratio of 1.44 without accompanying uncertainty measures. A discrepancy with unadjusted recalculations is flagged; the sponsor’s own analysis takes precedence.

The registry reports zero serious adverse events and zero deaths in each listed safety group. Further details on missing data, multiplicity, and the full analysis plan are not reported in the registry record.