Safety and Efficacy of Ophthalmic Phentolamine Mesylate to Reverse Pharmacologically Induced Mydriasis: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Safety and Efficacy of Ophthalmic Phentolamine Mesylate to Reverse Pharmacologically Induced Mydriasis (NCT04024891), a randomized phase 2 study. The primary outcome is Pupil Diameter (Change From Max).

2. Clinical Question

The study also set objectives concerning safety and the effect of Lumify® on conjunctival hyperemia potentially associated with Nyxol administration. The posted primary endpoint is narrower: it measures pupil diameter change at a specified time after treatment. The registry lists outcomes for pupil diameter, accommodation, eye redness, and visual acuity, but the posted numerical primary result concerns pupil diameter. The record identifies healthy subjects rather than people with a specified eye condition, so the result describes this study population and should not be treated as a finding in other populations.

3. Trial Design

The registry describes a randomized, crossover, double-masked, placebo-controlled study, with triple masking recorded in the design fields. The study is listed as Phase 2 and completed. It enrolled 32 participants. The registry lists Opus Genetics, Inc as sponsor and gives the study start as 2019-08-13 and primary completion as 2019-09-17.

The two interventions were phentolamine mesylate ophthalmic solution 1% and its vehicle, described as placebo. For both interventions, the arm description specifies one drop in each eye 1 hour after medically induced mydriasis. A crossover design means that treatment comparisons are made in a study where participants receive more than one intervention over the course of the trial. This general feature can allow comparisons within participants, but the exact treatment sequence, period structure, and washout procedures are not reported in the registry record.

Randomization indicates that assignment followed a randomized process; the record does not state the allocation sequence or how it was generated. The design fields describe the study as double-masked in the official title and triple-masked in the masking field. The identities of the masked parties and the procedures used to maintain masking are not reported in the registry record.

The primary endpoint was pupil diameter change from the pharmacologically induced maximum at 2 hours after treatment in the study eye. The registry labels the population for this outcome as a crossover design study. The posted results list 31 participants for each treatment arm in the primary outcome summary, while the adverse-event summaries list 31 at risk for phentolamine and 32 for vehicle. The record does not explain the difference between enrollment and these analysis counts or specify the analysis population in further detail.

The record lists 6 secondary outcomes and 7 outcome measures in total. It does not report the protocol’s sample-size justification, the original statistical design assumptions, treatment-period details, or whether interim analyses were planned or conducted.

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.

Before assignment: This is a crossover design study, so all 32 enrolled subjects were included in both treatment groups.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Crossover design 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.

Population: Subjects baseline values are included in the column to which they were randomized first in this crossover design trial. One subject in the PMOS Vehicle First, Then PMOS group was found to be pregnant after their first visit and was withdrawn from the trial and did not crossover to receive PMOS, resulting in an analytical sample of n = 31.

6. Primary Endpoint

The registry lists the primary outcome as Pupil Diameter (Change From Max), measured over 2 hours.

The primary endpoint is the change in the maximum pupil diameter induced by medication, measured 2 hours after treatment in the study eye. Its unit is millimeters. A change from the induced maximum expresses how pupil diameter differs from the maximum reached after pharmacologic dilation, rather than reporting only a single pupil measurement at the assessment time. The registry describes the reported endpoint as a least-squares mean and identifies standard error as its measure of dispersion.

In general, a pupil-diameter endpoint is a continuous measure: it can take values along a measurement scale rather than being limited to categories such as yes or no. A change endpoint is useful for comparing how much a measurement shifts from a defined reference state. Here, the reference is the pharmacologically induced maximum, and the post-treatment assessment is at 2 hours. The treatment contrast therefore addresses the difference in mean change between phentolamine and vehicle at that specified time.

The registry’s secondary outcomes include additional pupil-diameter assessments, return to baseline, accommodation, conjunctival hyperemia, and measures of distance and near visual acuity. Those outcomes provide other types of information, but the posted primary result is specifically about pupil diameter change. The registry record does not give further details about the measurement instrument, the timing of all secondary assessments, or how the study eye was selected.

7. Results Posted in the Registry

• Phentolamine Mesylate Ophthalmic Solution 1%: mean -1.69 versus -0.69 on control; difference -1.00 (95% CI -1.32 to -0.68), standardized effect d = -1.54; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry reports a mixed models analysis for the primary comparison and characterizes it as a superiority analysis. It gives a net mean difference, a 95% confidence interval, and a p-value. These are complementary summaries: the mean difference estimates the direction and size of the group contrast on the endpoint scale; the confidence interval indicates its precision; and the p-value describes how compatible the observed data are with a null hypothesis of no difference under the model’s assumptions.

What a mean difference represents

The endpoint is continuous and measured in millimeters. A mean difference compares the average change in pupil diameter for the two interventions. Because the endpoint is change from the pharmacologically induced maximum, negative arm values represent decreases relative to that maximum. The reported contrast is phentolamine minus vehicle in the registry’s result, with a net mean difference of -1.0 mm. The sign retains the direction of that subtraction; it is not a percentage or a count of participants.

The arm estimates are least-squares means, which are model-based means rather than necessarily simple arithmetic averages. In general, least-squares means are estimated from a statistical model and can account for terms included in that model. The registry does not report the full model specification or the terms included, so it is not possible to say which factors were adjusted for or how the crossover structure was represented in the model.

Why a mixed model may be used

General explanation: mixed models can represent both fixed effects, such as treatment, and random effects, such as variation associated with participants. They are often useful for data with repeated measurements or clustered observations because measurements from the same participant may be related rather than independent. In a crossover study, within-participant observations can be relevant to the treatment comparison. However, the record only names a mixed models analysis. Details such as participant-level terms, period effects, sequence effects, covariance structure, and treatment-by-period terms are not reported in the registry record and should not be assumed.

The observed arm summaries list 31 participants for each intervention. Those counts do not establish that every enrolled participant contributed a complete set of measurements, nor do they reveal the model’s handling of incomplete observations. Missing-data rules and the analysis population are not reported in the registry record.

How to read the p-value

The sponsor reports p < 0.001 for the primary comparison. In general, a p-value is calculated under a specified null hypothesis and model. It measures how unusual data at least as inconsistent with that null hypothesis would be if the assumptions held. It is not the probability that the null hypothesis is true, and it does not measure clinical importance. The p-value also does not describe the range of plausible effect sizes; the confidence interval provides information about estimate precision.

The record calls the analysis a superiority analysis. That label describes the direction of the statistical question, but it does not replace consideration of the estimated difference, confidence interval, study population, and limitations of the analysis. The registry does not report the prespecified significance threshold for the trial’s own analysis, although the separate planning illustration states a two-sided significance level of 0.05.

Recalculation and the sponsor analysis

A separate, simple unadjusted recalculation uses the posted arm summary statistics. It gives a mean difference of -1.0, a 95% confidence interval from -1.324 to -0.676, and p <0.001. This calculation relies on an approximate pooled standard deviation derived from the reported standard errors and sample sizes. It does not reproduce the crossover mixed model and should be read only as a basic check on the reported contrast. The sponsor’s own mixed models analysis takes precedence for the trial result; the registry record does not flag a discrepancy between the two results.

The standard error reported for each arm is 0.117. In general, a standard error reflects uncertainty in an estimated mean and tends to be smaller when estimates are more precise. It differs from a standard deviation, which describes variation among observations. The recalculation’s use of an approximate standard deviation is one reason it is not equivalent to the sponsor’s model-based analysis.

Multiplicity and secondary outcomes

The record lists 6 secondary outcomes in addition to the primary endpoint and lists 7 outcome measures overall. Multiple outcome tests can increase the chance of obtaining at least one small p-value by chance if many hypotheses are tested. General statistical practice may address this by prespecifying a testing hierarchy or adjusting significance thresholds, but the registry record does not report whether the trial used a multiplicity strategy. It also does not provide numerical secondary-outcome results in the registry record for this analysis. No conclusion about the secondary outcomes or any multiplicity-adjusted inference can therefore be drawn from the posted primary result alone.

Overall, the posted analysis is interpretable as a model-based estimate of the treatment contrast at the specified endpoint and time. Its full reproduction is not possible from the summary alone because model details, analysis-population definitions, and missing-data procedures are not reported in the registry record.

10. Confidence Intervals and Precision

The sponsor’s reported 95% confidence interval for the net mean difference is -1.3 to -0.7 mm, around an estimate of -1.0 mm. The interval summarizes statistical uncertainty in the estimated mean contrast under the sponsor’s model. Its limits are both negative, so the interval does not include a zero difference. The interval does not mean that 95% of individual participant changes lie between those limits; it concerns uncertainty about the estimated contrast.

The recalculated unadjusted interval is -1.324 to -0.676 mm. It is based on posted summary statistics and an approximate pooled standard deviation, rather than the full mixed models analysis. The recalculated interval is narrower in its printed precision, but that does not make it preferable to the sponsor’s result. The sponsor’s reported analysis is the relevant trial analysis, and its interval is reported to one decimal place.

In general, confidence intervals are affected by variability, sample size, and the analysis model. Greater precision corresponds to a narrower interval, while a wider interval reflects more uncertainty about the effect estimate. The arm-level standard error is 0.117 for each treatment, and each primary arm summary lists 31 participants. The record does not provide participant-level variability or the full model details, limiting independent assessment of how the interval was constructed.

Precision is not the same as importance. The interval describes the range of effect estimates compatible with the model and data at the stated confidence level; it does not establish whether a difference matters to patients or how the result applies to people outside this study’s healthy-subject population. The endpoint is measured at 2 hours, so the reported precision pertains to this time point, not to a broader course of response.

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 participants per arm, not total events. The sample-size assumptions state a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The planning calculation uses the observed effect as its starting point and considers detecting 100%, 75%, or 50% of that observed effect. These are planning illustrations, not the trial’s original design assumptions; the original sample-size justification and design assumptions are not reported in the registry record.

The 80% power column gives the illustrative number of participants per arm for a design with an 80% chance of detecting the stated effect under the calculation’s assumptions, if that effect is the true effect and the model assumptions hold. The 90% power column uses a higher target chance of detecting that effect, and therefore generally calls for more participants per arm. For example, planning for 100% of the observed effect gives 7 participants per arm for 80% power and 9 for 90% power. Planning for 75% gives 12 and 16; planning for 50% gives 27 and 36.

Smaller effects are harder to distinguish from random variation, so planning for a smaller fraction of the observed effect requires more participants per arm in these illustrations. These figures are not a retrospective measure of the trial’s probability of success. They are not observed power; they are planning calculations based on the observed effect and stated assumptions, and should not be read as evidence that the trial was designed with those sample sizes.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -1.000; pooled standard deviation σ = 0.651.
2. n = 2 × (1.96 + 0.842)² × 0.651² / -1.000² = 6.7, rounded up to 7 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -1                      # observed difference in means
sigma <- 0.651428430451113                     # 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(4024891)
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 (80% power), 9 (90% power)
 75% of observed effect: n per arm = 12 (80% power), 16 (90% power)
 50% of observed effect: n per arm = 27 (80% power), 36 (90% power)
power.t.test: 7.8 
Simulated power at n = 7 per arm: 0.746 (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. Analyses Reported by the Sponsor

The sponsor’s reported analysis is a mixed models analysis, with a net mean difference of -1.0, a 95% confidence interval from -1.3 to -0.7, and p < 0.001. This is the principal posted inferential result and takes precedence over a simple recalculation from summary statistics.

The unadjusted recalculation gives a mean difference of -1.0, a 95% confidence interval from -1.324 to -0.676, and p <0.001. It uses the arm means, standard errors, and sample sizes, with an approximate pooled standard deviation. It does not reproduce the mixed model’s handling of the crossover design or any model terms that may have been used. The registry record does not flag a discrepancy, and the estimated mean difference agrees at the reported one-decimal precision.

The recalculation is therefore a check on the broad numerical result, not an alternative analysis of equal standing. Differences in interval limits and p-value presentation can arise because the methods and rounding differ. The sponsor’s model-based estimate and uncertainty remain the appropriate reference for interpreting the posted trial analysis.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists 6 secondary outcomes and 7 outcome measures in total, alongside the primary endpoint. The secondary outcomes cover additional pupil-diameter measures, accommodation, conjunctival hyperemia, best corrected distance visual acuity, and distance-corrected near visual acuity. A group of related outcomes can raise multiplicity concerns because testing many hypotheses may increase the chance of at least one apparently strong result arising by chance.

General explanation: multiplicity can be handled through prespecified testing sequences, adjusted significance thresholds, or other methods that control the overall error rate. Whether a particular approach is needed depends on the study’s aims and analysis plan. The registry record does not report a multiplicity adjustment, a testing hierarchy, or whether secondary results were intended as confirmatory or exploratory. The numerical secondary-outcome results are not reported in the registry record for this analysis, so conclusions about those outcomes cannot be assessed.

The record lists one reported analysis for the primary comparison. It does not provide enough information to determine whether additional analyses were planned but not posted, or whether the posted analysis represents every analysis carried out. Interim analyses and any associated decision rules are not reported in the registry record.

The record does not describe the analysis populations, such as how participants were included or excluded from the primary analysis. It reports 32 enrolled participants and 31 participants in each primary arm summary, but does not explain the difference or state whether the 31 counts reflect complete data, a particular analysis set, or another rule.

Missing-data handling is also not reported in the registry record. The record does not state whether data were missing, how any missing observations were addressed, or whether sensitivity analyses assessed the effect of missingness. General explanation: missing-data methods matter because the validity of a treatment comparison can depend on why observations are missing and on the assumptions used to handle them. Without those details, the model-based result can be described as posted, but its sensitivity to missing data cannot be evaluated.

The crossover model specification is not reported beyond the label “Mixed Models Analysis.” Period, sequence, and participant terms, as well as the covariance assumptions, are not stated. These omissions limit assessment of the analysis implementation, but they do not change the numerical result reported by the registry.

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 serious adverse event summaries list 0 serious adverse events among 31 participants at risk for phentolamine and 0 among 32 participants at risk for vehicle. Deaths are listed as 0 in both groups. These are counts during the reported safety summaries; they do not establish that the risk of serious events is zero.

The numbers at risk differ between the two adverse-event groups, and they are not identical to the primary endpoint counts. The registry record does not explain the difference between the safety-group counts and the primary arm summaries. It also does not give the observation period for these safety counts or further details about event definitions and collection.

The record lists 11 other adverse events for phentolamine and 1 for vehicle. These are separate from the serious adverse-event counts. The totals alone do not convey event type, severity, duration, relatedness, or how many participants experienced more than one event. The registry’s safety figures should therefore be read as posted counts, not as a complete characterization of comparative safety.

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

The posted primary result is a mean difference in pupil diameter change at 2 hours after treatment in the study eye. The sponsor’s mixed models analysis estimates a net difference of -1.0 mm, with a 95% confidence interval from -1.3 to -0.7 and p < 0.001. The arm summaries are -1.69 mm for phentolamine and -0.69 mm for vehicle. Together, these results describe a greater mean decrease from the induced maximum in the phentolamine group than in the vehicle group at that assessment time.

The result does not show how individual participants responded. A group mean can coexist with a range of individual changes, and the registry does not provide the participant-level values or distribution needed to describe that range. It also does not establish the duration of the change beyond the reported endpoint time. The posted primary result is not a measure of every aspect of pupil function, vision, or redness.

The study population is described as normal healthy subjects. The registry record does not support generalizing the estimate to people with other characteristics or conditions. The primary result also does not answer the separate objectives concerning safety or the effect of Lumify® on conjunctival hyperemia. Numerical results for the listed secondary outcomes are not reported in the registry record for this analysis.

A confidence interval and p-value describe statistical evidence and precision under the analysis, not whether a measured difference is clinically important. The registry record does not specify a threshold for clinical importance. The reported safety counts include no serious adverse events in either group, but a zero count in a study of this size cannot establish absence of risk. The result should be understood as a specific statistical finding from a completed crossover study, rather than a general treatment recommendation.

17. Why This Trial Matters Statistically

This trial illustrates why an endpoint’s definition matters. The primary measure is not simply pupil diameter at one time; it is change from the pharmacologically induced maximum, assessed 2 hours after treatment in the study eye. The direction of a negative value is interpretable only with that reference in mind. Keeping the measurement scale and reference state explicit helps prevent confusion about what the group means represent.

The crossover design also makes the analysis context important. In general, crossover studies can compare treatments within the same participants, but interpretation depends on how the model accounts for repeated observations and study periods. The registry reports a mixed models analysis but does not report its specification. This makes it possible to describe the posted contrast while recognizing that the full analytical approach cannot be reconstructed from the record.

The result provides an example of how an estimate, confidence interval, and p-value answer different questions. The estimated mean difference describes the magnitude and direction of the contrast; the interval conveys uncertainty; and the p-value summarizes compatibility with a null hypothesis under model assumptions. None of these statistics alone describes individual variability or establishes clinical importance.

Finally, the record separates the primary efficacy measure from other objectives and safety observations. It lists several secondary outcome domains and reports serious adverse-event counts, but the posted primary finding cannot stand in for those results. Reading the primary endpoint narrowly, while recognizing what is unreported, is essential for a balanced statistical interpretation.

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 primary result is reported for normal healthy subjects, and the registry does not provide evidence for other populations. The endpoint is measured at 2 hours after treatment; the primary result alone does not describe the response at other times or its duration.

The record identifies the study as randomized and crossover, but does not report treatment sequence, period structure, washout procedures, or the full mixed-model specification. It is therefore not possible to assess from the registry summary how these design features were handled in the analysis. The record also does not describe the method of randomization or the parties included in masking.

Although 32 participants were enrolled, the primary arm summaries list 31 for each intervention. The registry does not explain the difference or define the analysis population. Missing-data procedures, sensitivity analyses, and the handling of incomplete crossover observations are not reported in the registry record. The original sample-size justification and trial-specific design assumptions are also not reported.

The registry lists 6 secondary outcomes, but numerical results for those outcomes are not available in the registry record for this analysis. Multiplicity procedures and the role of the secondary outcomes are not reported. Interim analyses are not reported either. These gaps limit assessment of the broader analysis plan and the completeness of outcome reporting.

The serious adverse-event summaries contain zero events in both groups, but the record does not give the safety observation period or detailed event definitions. Other adverse-event counts are posted without event-level detail. These limitations mean the safety summaries should not be interpreted as a full account of comparative safety.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Safety and Efficacy of Ophthalmic Phentolamine Mesylate to Reverse Pharmacologically Induced Mydriasis — NCT04024891.
• Registry record last updated 2026-10-30; status last verified 2022-08.
• Results first posted 2022-08-15.
• 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

The registry record describes a completed, randomized, crossover, placebo-controlled study of phentolamine mesylate ophthalmic solution 1% in normal healthy subjects with pharmacologically induced mydriasis. Enrollment was 32. The primary endpoint was pupil diameter change from the induced maximum in the study eye at 2 hours after treatment.

The mixed models analysis reports a net mean difference of -1.0 mm, with a 95% confidence interval from -1.3 to -0.7 and p < 0.001. The arm summaries report -1.69 mm for phentolamine and -0.69 mm for vehicle. Serious adverse events and deaths are listed as 0 in both groups.

The record does not report the full crossover model specification, missing-data procedures, multiplicity approach, or original sample-size justification. The primary result is specific to the stated endpoint, time, and study population.