Safety and Efficacy Study BRIMOCHOL™ PF and Carbachol PF in Subjects With Emmetropic Phakic or Pseudophakic Presbyopia: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Safety and Efficacy Study BRIMOCHOL™ PF and Carbachol PF in Subjects With Emmetropic Phakic or Pseudophakic Presbyopia (NCT05270863), a randomized phase 3 study. The primary outcome is Proportion of Subjects With >=15 Letter Gain Without >=5 Letter Loss in Near Visual Acuity.

2. Clinical Question

3. Trial Design

This was a Phase 3, randomized, double-masked, crossover study sponsored by Visus Therapeutics. The registry record lists an enrollment of 182 and a completed status. The recorded start date was 2022-03-30, and primary completion was 2023-03-17. The study title identifies participants with emmetropic phakic or pseudophakic presbyopia.

The three treatment groups were BRIMOCHOL™ PF, Carbachol PF, and brimonidine tartrate. Each treatment description specifies a single drop in each eye at a visit. In a crossover design, participants receive treatments in a sequence rather than remaining in only one treatment group throughout the study. This design can allow within-participant comparisons, but interpretation depends on details such as treatment order, period effects, and any interval between treatments. Those details are not reported in the registry record.

Double masking means that masking was intended for two study roles, but the registry record summarized for this analysis does not identify those roles or explain how masking was maintained. The outcome population was mITT: participants who received at least one dose of study treatment. The reported endpoint was assessed at Day 1 Hour 1, described as one hour post-dose at a study visit.

The registry record reports one outcome measure and one analysis. It does not report the trial’s original sample-size justification, the planned sequence structure, a detailed protocol for the crossover periods, or a full statistical analysis plan. The enrollment figure should not be treated as the denominator for each treatment result: treatment-specific denominators are reported separately, and crossover observations may involve the same participant under different treatments.

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.

Visit 2 First Intervention

Reasons for not completing this period:

First Washout

Reasons for not completing this period:

Visit 3 Second Intervention

Reasons for not completing this period:

Second Washout

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: All participants who received at least one dose of study treatment (mITT)

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 Proportion of Subjects With >=15 Letter Gain Without >=5 Letter Loss in Near Visual Acuity, measured over Day 1 Hour 1.

The primary endpoint was the proportion of participants with a gain of at least 15 letters in near visual acuity without a loss of at least 5 letters. The registry identifies the assessment time as Day 1 Hour 1, or one hour post-dose at a study visit. The endpoint population was the mITT group, defined in the record as participants who received at least one dose of study treatment.

This is a binary, threshold-based outcome: each participant either met both parts of the definition or did not. The proportion therefore describes how often the specified combination of near-vision improvement and avoidance of the specified loss occurred in each treatment group. It does not describe the average change in letters, the full distribution of visual-acuity changes, or how long an outcome persisted beyond the stated assessment time.

In general, a threshold endpoint can make a result easier to interpret as the share of participants reaching a prespecified response criterion. It also discards information about how far a participant’s result was from the threshold. Participants with different amounts of improvement can be grouped together if they meet the criterion, while a small difference around the threshold can place otherwise similar results in different categories. The registry record does not report additional endpoint details such as the baseline assessment method or how missing measurements were handled.

7. Results Posted in the Registry

• Carbachol PF: 35.0% (62/177) versus 49.4% (88/178) on control; risk difference -14.4 percentage points (95% CI -24.6 to -4.2), risk ratio 0.71 (0.55–0.91); unadjusted two-proportion z-test p = 0.006.
• Brimonidine Tartrate: 22.7% (40/176) versus 49.4% (88/178) on control; risk difference -26.7 percentage points (95% CI -36.3 to -17.1), risk ratio 0.46 (0.34–0.63); unadjusted two-proportion z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry reports a binary endpoint expressed as a percentage of participants with an event, where the event is meeting the specified near-visual-acuity response criterion. The primary outcome includes a 95% confidence interval for each treatment group. The registry also reports a sponsor analysis using logistic regression, described as a superiority analysis. Separate pairwise p-values in the posted comparisons are unadjusted recalculations from summary statistics.

What does a percentage represent?

In general, a percentage for a binary endpoint is the proportion of participants who meet the outcome definition among those included in that treatment group’s analysis. Here, the outcome is not simply any improvement: it requires a gain of at least 15 letters without a loss of at least 5 letters. The reported values are 49.4% for BRIMOCHOL™ PF, 35.0% for Carbachol PF, and 22.7% for brimonidine tartrate. The denominators are treatment-specific, and the crossover design means the same person may contribute observations under more than one treatment. The group counts should not be combined as if they necessarily represented separate people.

What does logistic regression do?

In general, logistic regression models the probability of a binary outcome as a function of one or more explanatory variables. It can be used to compare outcome odds between treatment conditions and, depending on its specification, to adjust for other variables or design features. The registry identifies logistic regression but does not report the model formula, covariates, treatment sequence terms, period terms, or the estimate and confidence interval from the model. The reported p-value alone cannot reveal those details.

The registry labels the sponsor’s analysis as a superiority analysis and reports p <.001 across the three treatment groups. This is distinct from the pairwise unadjusted recalculations. The reported overall test does not, by itself, state the size or precision of each individual treatment contrast. It also does not show how the model handled the repeated treatment observations characteristic of a crossover study.

Why does the crossover structure matter?

In general, crossover studies can compare treatment responses within the same participant. Outcomes from one participant are often related, so methods that treat every treatment observation as independent may not represent that relationship. The sequence of treatments and the time period in which an outcome is measured can also matter. A crossover analysis may therefore account for participant-level correlation and period or sequence effects. Whether and how those features were handled in the sponsor’s regression is not reported in the registry record.

The recalculated pairwise results are described as simple, unadjusted recalculations from posted summary statistics. They are useful as descriptive checks, but they are not a reconstruction of the sponsor’s crossover model. The registry record does not report a sponsor model estimate or a pairwise confidence interval for these comparisons in the analysis information available for this outcome.

What does an unadjusted p-value mean?

In general, a p-value is calculated under a null hypothesis and a statistical model. It describes how unusual data at least as incompatible with that null would be under the model’s assumptions. A smaller p-value can indicate stronger statistical evidence against the null, but it does not give the probability that the null hypothesis is true. It does not tell readers the probability that a result will repeat, the size of an effect, or whether an effect is important in practice.

The recalculated p-values are unadjusted. When several hypotheses are tested, multiplicity can increase the chance of at least one false-positive result across the set of tests. A prespecified testing strategy can address that issue, but the registry record does not report such a strategy or any adjustment for the pairwise comparisons. The sponsor’s overall test is reported separately; the record does not explain its relationship to any planned sequence of pairwise tests.

How should the endpoint and analysis population be read?

The mITT population is defined in the registry as all participants who received at least one dose of study treatment. That definition does not specify how participants with missing endpoint assessments were handled, whether all randomized participants were included in a particular analysis, or whether any additional exclusions occurred. Those details are not reported in the registry record. The outcome is assessed at Day 1 Hour 1, so it should not be generalized to another time point without results for that time point.

In general, threshold-based outcomes can be straightforward to communicate but may conceal variation within the group that meets the criterion and the group that does not. A participant just meeting the criterion and one with a larger gain are both counted as responders, while a participant narrowly missing it is counted as a nonresponder. The registry reports this endpoint and not a fuller distribution of near-visual-acuity changes in the posted primary result.

10. Confidence Intervals and Precision

The 95% confidence intervals quantify uncertainty around each treatment-specific proportion. BRIMOCHOL™ PF has a reported proportion of 49.4%, with an interval from 41.9% to 57.0%. Carbachol PF has a proportion of 35.0%, with an interval from 28.0% to 42.5%. Brimonidine tartrate has a proportion of 22.7%, with an interval from 16.8% to 29.6%.

In general, a confidence interval gives a range of values compatible with the data and the method used to calculate the interval. It reflects sampling uncertainty under that method’s assumptions. It is not a guarantee that the underlying value lies within the specific reported interval, nor does it capture every possible source of bias or uncertainty. The registry labels the intervals as 95% confidence intervals but does not give further calculation details.

The intervals are for the individual group proportions, not for differences between treatment groups. Comparing the overlap or non-overlap of separate group intervals is not a substitute for a confidence interval for a treatment contrast. The posted recalculated pairwise comparisons include contrast intervals internally, but their reported endpoints have more than three decimal places and are not reproduced. The registry record does not provide a sponsor-reported confidence interval for the logistic-regression analysis.

The estimates are tied to the mITT population and Day 1 Hour 1 endpoint. Their precision does not establish how well results generalize to people outside the study population or to outcomes at other times. In a crossover trial, precision of treatment contrasts also depends on how within-participant relationships and the study design are handled; the detailed sponsor model is not reported in the registry record.

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 justification. The original design assumptions are not reported in the registry record. The illustrations assume a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. They consider detecting the stated fraction of the observed effect.

These figures are participants per arm, not total participants across both arms and not total events. The 80% power column means the planning calculation targets an 80% chance of detecting the stated effect under the listed assumptions if that effect is the true one. The 90% power column uses a higher target chance of detection under the same general planning framework. Neither column describes the power actually achieved by this trial.

The table gives separate planning scenarios for BRIMOCHOL™ PF versus Carbachol PF and BRIMOCHOL™ PF versus brimonidine tartrate. For the comparison with Carbachol PF, planning for 100% of the observed effect gives 184 participants per arm for 80% power and 245 for 90% power; planning for 75% gives 331 and 442, and planning for 50% gives 750 and 1,003. For the comparison with brimonidine tartrate, the corresponding figures are 50 and 66 for 100% of the observed effect, 93 and 123 for 75%, and 215 and 287 for 50%.

In general, a smaller effect is harder to distinguish from random variation, so planning for a smaller effect requires more participants under the same assumptions. The figures are planning illustrations, not observed power. They also do not account for design features not included in the stated assumptions, such as the crossover structure, or for any multiplicity strategy.

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 = 0.494; treatment proportion p₁ = 0.350; average p̄ = 0.422.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6985 = 1.3691.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.6911 = 0.5816.
4. n = (1.3691 + 0.5816)² / (-0.1441)² = 183.3, rounded up to 184 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 <- 0.49438202247191                          # control proportion
p1 <- 0.350282485875706                          # 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(5270863)
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 = 184 (80% power), 245 (90% power)
 75% of observed effect: n per arm = 331 (80% power), 442 (90% power)
 50% of observed effect: n per arm = 750 (80% power), 1,003 (90% power)
power.prop.test: 183.3 
Simulated power at n = 184 per arm: 0.803 (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-reported analysis is a logistic regression superiority analysis across the three treatment groups, with p <.001. The registry record does not provide the model’s treatment-effect estimate, confidence interval, detailed specification, or a pairwise sponsor result. That overall analysis should be distinguished from the pairwise unadjusted recalculations based on the posted summary statistics.

The recalculated pairwise unadjusted p-value is 0.006 for BRIMOCHOL™ PF versus Carbachol PF, and <0.001 for BRIMOCHOL™ PF versus brimonidine tartrate. These simple recalculations do not reproduce a crossover-model analysis and do not include a reported multiplicity adjustment. The sponsor analysis and the recalculations answer related but not identical statistical questions.

No discrepancy is flagged between the posted outcome information and the calculations. Still, the sponsor’s analysis is the registry’s reported analysis; the recalculated comparisons are supplementary descriptive checks and should not be presented as the sponsor’s model results. The statistical analysis plan and details needed to verify the sponsor model are not reported in the registry record.

14. Multiplicity, Missing Data and Analysis Populations

The registry reports one primary outcome measure and one analysis. It gives a sponsor-reported logistic-regression superiority test across the three treatment groups and the posted results also include two pairwise unadjusted recalculations comparing BRIMOCHOL™ PF with the other treatments. The pairwise p-values are not reported as multiplicity-adjusted.

In general, multiplicity arises when several hypotheses or outcomes are tested. The more tests conducted, the greater the chance that at least one test may appear statistically significant by chance if all null hypotheses are true. Trial protocols can specify a testing sequence or adjustment to control this risk. The registry record does not report a multiplicity strategy, whether the pairwise comparisons were prespecified, or whether any adjustment was applied to the sponsor’s analysis.

The analysis population is described as mITT, comprising participants who received at least one dose of study treatment. The record does not report how missing primary endpoint measurements were handled, whether participants with incomplete crossover data were included, or whether an imputation method was used. It also does not report a sensitivity analysis for missing data or deviations from the treatment schedule.

The crossover design makes analysis details particularly relevant. In general, a crossover analysis may need to address the relationship between repeated observations from the same participant, treatment sequence, and study period. The registry identifies logistic regression but does not report whether or how the model accounted for those features. It does not report the treatment sequences, period-specific results, or a washout interval.

Accordingly, the posted information supports a description of the endpoint proportions and the stated tests, but not a full audit of the analysis plan. Missing details should not be filled in by assumption: the planned handling of multiplicity, incomplete observations, and crossover-specific effects is not reported in the registry record.

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 2% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: nephrolithiasis (0.6%).

The registry lists serious adverse events for each treatment group. One serious adverse event is reported for BRIMOCHOL™ PF, and zero are reported for Carbachol PF and brimonidine tartrate. The corresponding treatment-group counts at risk are 178, 177, and 176, respectively. No deaths are reported in any of the three groups.

The registry also lists nephrolithiasis as a top serious adverse-event term, with 0.6% reported. The record does not identify which treatment group that term belongs to. The figures describe events recorded in the study; they do not establish whether an event was caused by a treatment. The registry does not report further details about the serious event or its timing in the information available for this outcome.

In general, small counts can provide limited precision for comparing uncommon safety outcomes. A count of zero in a group does not prove that the risk is absent, and a count in one group does not by itself show a treatment-related difference. These figures should be read as descriptive registry safety information, not as a complete assessment of safety across all possible outcomes or periods.

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

The posted primary results show that the proportions meeting the defined near-visual-acuity response criterion at Day 1 Hour 1 were 49.4% with BRIMOCHOL™ PF, 35.0% with Carbachol PF, and 22.7% with brimonidine tartrate. The corresponding 95% confidence intervals describe the precision of each group estimate. The sponsor reported a logistic-regression superiority analysis across the three groups with p <.001. The pairwise recalculated p-values are unadjusted and are not the sponsor’s crossover-model results.

These findings concern a specific threshold endpoint, population, and assessment time. They do not describe the size of average letter change, the full distribution of visual-acuity results, or persistence at later times. The registry record lists no secondary outcomes in the posted results. It therefore does not establish results for other efficacy measures or longer-term outcomes.

Statistical evidence is not the same as a complete judgment of clinical importance. In general, a p-value does not measure how large or meaningful a difference is, and a confidence interval for a group percentage does not by itself quantify a treatment contrast. The registry record does not report the sponsor model’s treatment estimates and confidence intervals or enough detail to assess its crossover-specific assumptions.

The safety figures report one serious adverse event with BRIMOCHOL™ PF and none with either comparator, with no deaths listed. These counts alone cannot establish causation or rule out risks. Overall, the registry supports a description of the observed endpoint proportions, their reported uncertainty, the sponsor’s overall statistical test, and the listed serious-event counts. It does not settle questions that require unreported design, analysis, or outcome information.

17. Why This Trial Matters Statistically

This study illustrates why the design and the statistical summary both matter when interpreting clinical trial results. The randomized, double-masked crossover structure differs from a parallel-group design because participants may contribute observations under more than one treatment. That can make within-participant analysis important. The registry reports logistic regression but does not provide enough detail to determine how the sponsor’s model represented the crossover structure.

The primary endpoint is a binary threshold measure: participants are counted according to whether they gained at least 15 letters without losing at least 5 letters in near visual acuity. That makes the outcome expressible as a proportion, but it does not retain all information about the magnitude of a participant’s change. The distinction between a threshold response and a continuous measure is important for understanding what the estimates mean.

The posted group proportions are accompanied by confidence intervals, while the sponsor analysis is reported as an overall superiority test. These answer different statistical questions: group intervals describe uncertainty around each proportion, whereas the overall test evaluates a treatment-group comparison under the sponsor’s model. The separate pairwise recalculations are unadjusted and do not replace a model that accounts for the trial design.

Finally, the record demonstrates the value of distinguishing statistical evidence from clinical interpretation. The reported p-values do not express effect size or clinical importance, and the serious-event counts do not establish causation. Missing information about multiplicity, missing data, the crossover model, and the original sample-size rationale limits how fully the analysis can be audited. Transparent reporting of those details would help readers assess the strength and scope of the evidence.

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.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

The registry record provides limited detail about the crossover implementation. It does not report treatment sequences, period-specific results, or an interval between treatments. Those details matter because treatment order, period effects, and within-participant correlation can affect interpretation of crossover results. The sponsor analysis is identified as logistic regression, but its formula and handling of crossover features are not reported.

The record does not report the original sample-size justification or the trial’s planned design assumptions. The sample-size figures associated with the posted comparison are planning illustrations based on observed effects and specified assumptions; they cannot establish what the study was originally designed to detect.

The primary outcome is reported at Day 1 Hour 1 only in the posted endpoint information. The registry lists one outcome measure and no secondary outcomes in the posted results. The record does not provide a fuller distribution of letter changes, other assessment times, or results for additional visual-acuity outcomes. As a threshold measure, the endpoint also does not distinguish different magnitudes of change among participants on the same side of the response criterion.

The mITT population is defined as participants who received at least one dose, but the registry record does not describe missing endpoint handling, exclusions, or sensitivity analyses. It also does not report a multiplicity plan for the overall and pairwise comparisons. The recalculated pairwise p-values are unadjusted and should not be treated as a full analysis of the crossover data.

Safety information is limited to the listed adverse-event counts and the top serious-event term. The record does not establish causality, and the group attribution for nephrolithiasis is not reported in the information. These limitations constrain conclusions to the reported endpoint and registry entries.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Safety and Efficacy Study BRIMOCHOL™ PF and Carbachol PF in Subjects With Emmetropic Phakic or Pseudophakic Presbyopia — NCT05270863.
• Registry record last updated 2024-10-15; status last verified 2024-10.
• Results first posted 2024-09-05.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

NCT05270863 is a completed Phase 3 randomized, double-masked crossover study sponsored by Visus Therapeutics. It enrolled 182 participants and evaluated BRIMOCHOL™ PF, Carbachol PF, and brimonidine tartrate in people with emmetropic phakic or pseudophakic presbyopia. Each treatment was described as a single drop in each eye at a visit.

The primary endpoint was the proportion meeting the defined near-visual-acuity response criterion at Day 1 Hour 1 in the mITT population. Posted proportions were 49.4% for BRIMOCHOL™ PF, 35.0% for Carbachol PF, and 22.7% for brimonidine tartrate, each with a 95% confidence interval. The sponsor reported a logistic-regression superiority analysis with p <.001; recalculated pairwise p-values are unadjusted.

The record lists one serious adverse event with BRIMOCHOL™ PF, none with either comparator, and no deaths. Details about the original sample-size rationale, crossover model, multiplicity, and missing-data handling are not reported in the registry record.