A Safety, Efficacy and Pharmacokinetic Study of AGN-199201 and AGN-190584 in Patients With Presbyopia: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Safety, Efficacy and Pharmacokinetic Study of AGN-199201 and AGN-190584 in Patients With Presbyopia (NCT02780115), a randomized phase 2 study. The primary outcome is Weighted Average Change From Baseline in Uncorrected Near Visual Acuity (UNVA) Letters in the Nondominant Eye.

2. Clinical Question

3. Trial Design

This was a Phase 2, randomized, double-masked, vehicle-controlled, parallel-group study of a fixed combination of AGN-199201 and AGN-190584 in patients with presbyopia. The registry lists an enrollment of 151 and a completed status. The recorded start date is 2016-05-26 and the primary completion date is 2017-10-31. Allergan is listed as the sponsor.

Five cohorts were described. One was a vehicle control, with vehicle given in both eyes. Three cohorts received lower-, medium-, or higher-dose fixed combinations in both eyes. In the remaining cohort, the dominant eye received vehicle and the nondominant eye received the higher-dose combination. Dosing was once daily during office visits 1 through 5. The posted primary outcome is analyzed for the nondominant eye, so the different-eye treatment arrangement in the fifth cohort is relevant when interpreting that cohort’s comparison.

The primary outcome was assessed at baseline and Day 28. Its stated analysis population was the modified Intent-to-Treat population, defined as all randomized patients with a baseline and at least one post-baseline assessment of mesopic, high-contrast uncorrected near visual acuity. The registry lists one secondary outcome: the number of participants experiencing one or more treatment-emergent adverse events.

The registry record does not report further details about the randomization procedure, allocation concealment, the exact dose levels, or the reasons for using the five cohort arrangements. The original sample-size justification and the trial’s planned statistical assumptions are not reported in the registry record. The planning illustrations associated with the posted summary statistics are separate from the original trial design.

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: Randomization and treatment assignment were based on a randomization scheme prepared by Allergan Biostatistics prior to the start of the study.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Modified Intent-to-Treat (mITT) population: all randomized patients who were randomized with a baseline and at least 1 post baseline assessment of mesopic, high contrast, UNVA.

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: Safety population: All patients who received ≥ 1 administration of study treatment

6. Primary Endpoint

The registry lists the primary outcome as Weighted Average Change From Baseline in Uncorrected Near Visual Acuity (UNVA) Letters in the Nondominant Eye, measured over Baseline, Day 28.

The primary endpoint is weighted average change from baseline in uncorrected near visual acuity letters in the nondominant eye, assessed at baseline and Day 28. Uncorrected means that the near-vision assessment is made without corrective lenses. The registry describes use of an eye chart and counts the number of lines read correctly, reporting the measure in letters correctly read. It states that a higher number of correctly read lines means better visual acuity.

This endpoint targets near vision, which is directly relevant to the condition described in the registry record: difficulty focusing on close-up items. Measuring change from baseline relates the Day 28 result to each participant’s starting assessment rather than describing only an endpoint value. The weighted average is the named summary measure in the posted outcome; the registry record does not explain the weighting procedure.

The outcome is continuous, so the reported group summaries are means rather than event counts. The arm-level posted results are least-squares means with standard errors. The registry’s primary analysis population includes randomized patients who have the required baseline and post-baseline assessments. The record does not report how missing Day 28 assessments were handled, or whether the weighted average combines additional visits or assessments beyond the stated timeframe.

Visual-acuity letters describe performance on the specified chart assessment. They do not, by themselves, describe every aspect of near vision, everyday functioning, or a participant’s overall experience. Interpretation should therefore remain tied to this particular eye-chart outcome, eye, population, and assessment time.

7. Results Posted in the Registry

• Cohort 2: AGN-199201 Lower Dose and AGN-190584 Lower Dose: mean 4.96 versus 3.00 on control; difference 1.96 (95% CI -0.85 to 4.77), standardized effect d = 0.36; z-test p = 0.172.
• Cohort 3: AGN-199201 Medium Dose and AGN-190584 Medium Dose: mean 7.77 versus 3.00 on control; difference 4.77 (95% CI 1.96 to 7.58), standardized effect d = 0.87; z-test p = <0.001.
• Cohort 4: AGN-199201 Higher Dose and AGN-190584 Higher Dose: mean 7.54 versus 3.00 on control; difference 4.54 (95% CI 1.77 to 7.31), standardized effect d = 0.83; z-test p = 0.001.
• Cohort 5: Vehicle, AGN-199201 Higher Dose and AGN-190584 Higher Dose: mean 7.81 versus 3.00 on control; difference 4.81 (95% CI 1.97 to 7.65), standardized effect d = 0.86; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

What does an ANCOVA comparison represent?

The sponsor reports the primary comparisons using ANCOVA and labels the reported quantity as a least-squares mean difference. In general, analysis of covariance estimates a group contrast while accounting for specified covariates in a statistical model. The resulting least-squares means are model-based group means, and their difference is the estimated contrast between a treatment cohort and the vehicle-control cohort. The registry record does not identify the covariates, model details, or handling of assumptions used in the ANCOVA, so those details cannot be inferred from the method name alone.

The arm-level results also give least-squares means and standard errors. A standard error describes the estimated sampling uncertainty of a mean: a smaller standard error indicates a more precisely estimated mean, given the model and data. It is not the same as the spread of individual participant measurements. The posted comparison is the contrast between two arms, while the arm-level values are separate group summaries.

What do the confidence intervals tell the reader?

A confidence interval describes a range of values reasonably compatible with the observed data and the statistical model, under the interval’s stated procedure. The sponsor reports 95% confidence intervals for the between-cohort mean differences. An interval that includes zero is compatible with no mean difference under that analysis; an interval entirely on one side of zero indicates that the data are less compatible with a zero contrast under the same assumptions. The interval does not give the probability that a particular value is true, and it does not capture every possible source of uncertainty, such as limitations in study conduct or applicability.

For the lower-dose cohort, the sponsor’s interval extends from -0.83 to 4.74 and includes zero. For the medium-dose, higher-dose, and fifth-cohort comparisons, the reported intervals are above zero. The size of an interval matters alongside its position: a range can indicate both the direction of the estimated contrast and how much uncertainty remains about its magnitude.

How should the recalculations be understood?

The recalculated comparisons use the posted arm-level summary statistics to form simple, unadjusted mean differences. Their pooled standard deviations are approximate, as indicated in the analysis information, because they are derived from the reported standard errors. This calculation is not the same as reproducing the sponsor’s ANCOVA, which may use model information not recoverable from arm-level summaries. The reported recalculated mean differences are 1.96, 4.77, 4.54, and 4.81 letters for the four respective comparisons. Their estimates are close to the sponsor’s reported estimates, but the recalculated interval limits and p values differ. Since the discrepancy flag is true, the sponsor’s own analysis takes precedence.

An unadjusted p value evaluates how compatible the observed contrast is with a specified null hypothesis under its analysis assumptions. It is not the probability that the null hypothesis is true, nor does it measure the size or practical importance of a difference. The recalculated p values do not account for any adjustment unless such an adjustment is explicitly stated; the registry record does not report a multiplicity adjustment for these comparisons. The sponsor’s reported p values come from its ANCOVA analyses and should be read as those model-based results.

Why can over-dispersion matter?

In general, over-dispersion occurs when observed variation is greater than a statistical model assumes. It can make standard errors too small and confidence intervals too narrow if it is not addressed. This is a general statistical consideration, not a reported feature of this trial. The primary outcome is a continuous letter measure, and the registry record does not report an over-dispersion assessment or a special adjustment for it. The term should not be taken to imply that over-dispersion was present in these data.

What are the analysis population and endpoint summary?

The stated modified Intent-to-Treat population includes all randomized patients who had a baseline and at least one post-baseline assessment of mesopic, high-contrast uncorrected near visual acuity. This definition preserves randomization for patients meeting the assessment requirement, but it is narrower than a population consisting of every randomized patient if some randomized patients lack the required measurements. The record does not report the number excluded by this definition or the reasons for missing assessments.

The endpoint is a weighted average change from baseline at the stated baseline and Day 28 timeframe. The registry record does not describe how the weighting was done or whether the weights relate to multiple assessments. Readers should therefore interpret the measure as the posted weighted average without assuming a specific formula. The arm results are continuous-measure means, and the primary comparison is a mean difference, not a risk difference or event-rate comparison.

10. Confidence Intervals and Precision

The sponsor’s 95% confidence intervals quantify uncertainty around the estimated mean differences under its reported ANCOVA analyses. The lower-dose cohort estimate is 1.96 letters, with an interval from -0.83 to 4.74. Because this interval includes zero, the posted result leaves open both a small negative contrast and a positive contrast, as well as no difference under the model. The interval is relatively broad compared with the point estimate, so the exact size of the contrast is uncertain.

For the medium-dose cohort, the estimated difference is 4.77 letters, with a 95% interval from 1.98 to 7.56. The higher-dose cohort estimate is 4.54 letters, with an interval from 1.79 to 7.29. For the cohort receiving vehicle in the dominant eye and the higher-dose combination in the nondominant eye, the estimate is 4.81 letters, with an interval from 2.03 to 7.58. These intervals lie above zero, but their widths still indicate uncertainty about the magnitude of each contrast.

Intervals are not guarantees that the true effect lies inside a particular range, and they reflect sampling and model uncertainty rather than every limitation of the trial. In particular, they do not resolve uncertainty about multiplicity, missing data, the undisclosed ANCOVA covariates, or whether the findings apply beyond the studied population and assessment. The recalculated intervals differ somewhat from the sponsor’s intervals; because the discrepancy flag is true, the sponsor’s analysis should be used as the primary inferential result.

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 illustrations give participants per arm, not a total across both arms and not total events. Each comparison is framed as a two-arm planning exercise. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The target effect is set at the stated fraction of the observed effect for that comparison. These are planning illustrations based on observed estimates, not the original trial’s design assumptions, which are not reported in the registry record.

The 80% power column gives the planned participants per arm for a hypothetical study with an 80% chance of detecting the specified effect if that effect were the true effect and the planning assumptions held. The 90% power column gives the corresponding participants per arm for a higher target chance of detecting that effect. Power is a property of a proposed study under assumptions; it is not a measure of whether the observed result is true or important.

For each comparison, the illustrations include planning for 100%, 75%, and 50% of the observed effect. The participant requirements increase as the assumed target effect becomes smaller. For example, for the medium-dose comparison, planning for 100% of the observed effect gives 21 participants per arm for 80% power and 28 participants per arm for 90% power; planning for 50% gives 83 and 111 participants per arm, respectively. The rows are scenarios rather than predictions about the effect in a future study. These figures are not observed power.

The registry record does not report the trial’s original sample-size calculation, its planned target effect, or its original power assumptions. The illustrations should not be used to infer that the trial was prospectively sized to detect the observed differences.

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 = 1.960; pooled standard deviation σ = 5.464.
2. n = 2 × (1.96 + 0.842)² × 5.464² / 1.960² = 122.0, rounded up to 123 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 <- 1.96                      # observed difference in means
sigma <- 5.46423501377039                     # 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(2780115)
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 = 123 (80% power), 164 (90% power)
 75% of observed effect: n per arm = 217 (80% power), 291 (90% power)
 50% of observed effect: n per arm = 489 (80% power), 654 (90% power)
power.t.test: 123 
Simulated power at n = 123 per arm: 0.799 (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 primary comparisons are ANCOVA estimates. The posted unadjusted recalculations are simpler contrasts derived from summary statistics and are not a substitute for the sponsor’s model-based analysis. Their mean-difference estimates closely match the sponsor’s reported estimates: 1.96, 4.77, 4.54, and 4.81 letters. However, the recalculated confidence limits and p values differ from the sponsor’s results.

The discrepancy flag is true. Accordingly, the sponsor’s own analysis takes precedence for interpretation. The sponsor reports 95% confidence intervals of -0.83 to 4.74 for the lower-dose comparison, 1.98 to 7.56 for the medium-dose comparison, 1.79 to 7.29 for the higher-dose comparison, and 2.03 to 7.58 for the cohort with vehicle in the dominant eye. Its p value for the lower-dose comparison is above 0.05; the other reported p values are below 0.01.

The registry record does not explain the numerical discrepancy or provide enough model detail to reproduce the ANCOVA from the summary statistics. The simple recalculation is therefore a descriptive cross-check, while the sponsor’s reported analysis is the relevant inferential result. Neither analysis by itself establishes the clinical importance of the estimated differences.

14. Multiplicity, Missing Data and Analysis Populations

Four primary comparisons are posted, each contrasting a different cohort with the same vehicle-control cohort. The registry record does not report whether the sponsor adjusted for multiple comparisons, used a pre-specified hierarchy, or controlled a family-wise error rate. This omission matters because evaluating several contrasts can increase the chance of at least one apparently unusual result when all null hypotheses are true. The posted p values should therefore be read as reported, without assuming an adjustment or a particular testing sequence.

The registry record lists the primary endpoint timeframe as baseline and Day 28 and defines the modified Intent-to-Treat population as randomized patients with a baseline and at least one post-baseline assessment of mesopic, high-contrast UNVA. That definition says which participants enter the stated analysis, but does not explain how missing outcome values were handled after entry. The record does not report the number of randomized participants without qualifying assessments, reasons for missing data, imputation methods, or sensitivity analyses. No particular missing-data procedure should be inferred.

The analysis population is not described as every randomized patient without qualification: it is restricted by the requirement for baseline and post-baseline assessments. The registry record does not report the numbers analyzed in each primary-outcome group separately as an explicit analysis-population flow, though posted arm summaries give cohort sample sizes. Nor does it report whether exclusions or missingness differed across cohorts.

The record reports ANCOVA for the sponsor’s primary comparisons, but does not identify the covariates, model specification, diagnostics, or whether model assumptions were assessed. It also does not report a protocol-level analysis plan or interim analyses. These absences limit independent reconstruction of the sponsor’s analysis and assessment of how robust the results are to alternative choices.

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 5% reporting threshold.

Most frequent non-serious adverse event terms

The serious adverse event figures show zero participants with serious adverse events in each of the five cohorts. The numbers at risk were 28 in vehicle control, 30 in the lower-dose cohort, 30 in the medium-dose cohort, 32 in the higher-dose cohort, and 31 in the cohort receiving vehicle in the dominant eye. No deaths were reported in any cohort.

These are participant counts in the posted safety summary. A zero count means no serious adverse event was recorded for the participants represented in that cohort during the reported collection period; it does not establish that the risk is absent. The registry record does not provide the duration of safety follow-up or further detail about event ascertainment in the information summarized for these results.

The posted counts for other adverse events are 7, 8, 10, 11, and 7 across the cohorts in the same order. They are distinct from the serious adverse event counts. The record lists a secondary outcome concerning participants who experienced one or more treatment-emergent adverse events, but the summary does not provide event terms or severity details. The available counts therefore support a limited descriptive reading, not a full comparison of safety profiles.

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

The posted results describe average change in a specific near-vision eye-chart measure in the nondominant eye at Day 28. The sponsor’s ANCOVA results estimate positive mean differences versus vehicle for all four non-control cohorts. The lower-dose comparison has a 95% confidence interval that includes zero; the other three reported intervals lie above zero. These statements summarize the statistical results in the registry record, not a recommendation about treatment.

The values do not establish how an individual participant’s vision changed. Group means can coexist with substantial variation among participants, and the posted summary does not give individual response distributions. The measured outcome is uncorrected near visual acuity as assessed by the specified chart, not a comprehensive measure of vision, daily function, or satisfaction. The trial also does not, from these results alone, answer questions about outcomes beyond the stated timeframe.

The comparisons are against a vehicle-control cohort, and one treatment cohort used vehicle in the dominant eye with the higher-dose combination in the nondominant eye. That cohort is not identical in treatment arrangement to the cohorts dosed in both eyes. Its contrast should be interpreted with that design detail in mind.

The findings do not resolve the consequences of multiple comparisons, because adjustment is not reported. Nor do they settle the effect of missing assessments, since the missing-data approach and the number of participants excluded under the analysis-population definition are not reported. Confidence intervals describe precision under the sponsor’s model, not uncertainty arising from unreported design or analysis details. The serious adverse event summary records no events, but this limited count does not establish that no safety risks exist.

17. Why This Trial Matters Statistically

This trial illustrates how a continuous clinical outcome can be analyzed as a change from baseline and compared across randomized cohorts. The eye-chart result is summarized as a mean number of correctly read letters, and the sponsor reports model-based mean differences with confidence intervals. Reading both the estimate and its interval gives more information than treating a p value as a complete description of a result.

It also demonstrates why the distinction between model-based and summary-statistic analyses matters. The sponsor reports ANCOVA, while the recalculated contrasts are unadjusted estimates based on posted summaries. Their point estimates are close, but their intervals and p values differ. Because the discrepancy flag is true, the sponsor analysis takes precedence; the simpler recalculation is a check, not a reproduction of the full model.

The five-cohort arrangement makes comparison structure important. Four contrasts use the same vehicle-control cohort, and one of those treatment cohorts applies vehicle and combination to different eyes. The registry record does not report a multiplicity approach, so readers should not assume that the comparisons were adjusted or interpreted under a particular testing hierarchy.

Finally, the sample-size illustrations show the sensitivity of planning requirements to the effect chosen for detection. Smaller assumed effects require more participants per arm under the stated planning assumptions. They are illustrations based on observed effects and do not reveal the trial’s original design rationale or observed power. Together, these points show why estimates, uncertainty, analysis choices, and reporting gaps need to be considered alongside the headline result.

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 several trial-specific details unreported. It does not give the dose levels, the randomization method, allocation concealment procedures, or further information about how masking was maintained. It also does not identify the ANCOVA covariates or provide enough detail to reconstruct the sponsor’s model from the posted results.

The primary outcome is described as a weighted average, but the registry record does not specify the weighting formula. The analysis population requires a baseline and at least one post-baseline assessment, while the missing-data method, number of participants omitted under that requirement, and sensitivity analyses are not reported. This leaves uncertainty about the effects of missing measurements on the estimates.

Four comparisons are reported against a shared control, but the registry record does not report a multiplicity adjustment or testing hierarchy. The recalculated confidence intervals and p values differ from the sponsor’s ANCOVA results; the discrepancy flag is true, and the sponsor analysis takes precedence. The record does not explain why the calculations differ.

The reported endpoint is limited to uncorrected near visual acuity in the nondominant eye at the stated timeframe. The registry entries do not establish effects on other visual measures or later outcomes. Safety information is also limited: serious adverse event and death counts are posted, as are counts for other adverse events, but detailed terms, severity, relatedness, and follow-up duration are not reported in the registry record. These limitations constrain interpretation without establishing that any particular bias or problem occurred.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: A Safety, Efficacy and Pharmacokinetic Study of AGN-199201 and AGN-190584 in Patients With Presbyopia — NCT02780115.
• Registry record last updated 2020-12-22; status last verified 2020-11.
• Results first posted 2020-12-22.
• 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

NCT02780115 is a completed, randomized, double-masked, parallel-group Phase 2 study of fixed combinations of AGN-199201 and AGN-190584 in patients with presbyopia. The registry lists enrollment of 151 and five cohorts: vehicle control, three dose combinations given in both eyes, and a cohort receiving vehicle in the dominant eye with the higher-dose combination in the nondominant eye.

The primary outcome was weighted average change from baseline in uncorrected near visual acuity letters in the nondominant eye at Day 28. The sponsor used ANCOVA for four comparisons against vehicle control. The lower-dose comparison’s 95% confidence interval includes zero; the other three sponsor-reported intervals lie above zero. The registry also reports zero serious adverse events and zero deaths in each cohort.

The record does not report multiplicity handling, missing-data methods, original sample-size assumptions, or detailed ANCOVA specifications. Because the recalculated results differ from the sponsor’s results, the sponsor’s own analysis takes precedence.