A Study of the Response to AG-86893 in Patients With Pterygium Hyperemia: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Study of the Response to AG-86893 in Patients With Pterygium Hyperemia (NCT03533244), a randomized phase 2 study. The primary outcome is Change From Baseline in Overall Conjunctival Hyperemia Score.

2. Clinical Question

The study also assessed safety and tolerability. Its stated hypothesis was that at least one AG-86893 concentration would show an acceptable safety profile compared with vehicle and that at least one concentration would improve mean change in hyperemia score compared with vehicle. The posted primary outcome concerns the score change, while the registry’s separate safety results report adverse events.

3. Trial Design

This was a randomized, parallel-group phase 2 study with three groups: vehicle, 0.1% AG-86893, and 0.3% AG-86893. The registry record reports enrollment of 64 participants and a completed study. The start date was 2018-10-11, and primary completion was 2019-09-05. The intervention schedule was one drop in the study eye three times daily for 28 days for each group.

The registry’s masking field says quadruple masking, while the official title describes the study as double-masked. The record therefore contains different masking descriptions; it does not explain how those labels were applied. Details about allocation concealment, the randomization procedure, or who was included among the masked parties are not reported in the registry record.

The primary outcome was assessed at Baseline and Day 28 in the modified intent-to-treat population. The posted arm sizes for that outcome were 18 for vehicle, 22 for 0.1% AG-86893, and 22 for 0.3% AG-86893. These are outcome-specific counts and should not be treated as a substitute for the overall enrollment figure. The record does not report the protocol’s planned sample size, its original sample-size assumptions, or a detailed account of participant flow and missing outcome data.

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 (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 Change From Baseline in Overall Conjunctival Hyperemia Score, measured over Baseline and Day 28.

The primary endpoint was change from Baseline in the overall conjunctival hyperemia score at Day 28. Digital ocular photographs were used to assess four eye quadrants: superior, inferior, nasal, and temporal. Each quadrant was scored on a 5-point scale from 0, none, through 4, very severe. The overall score was the average of the four quadrant scores. Change was calculated by subtracting the Baseline score from the Day 28 score.

The direction of the measure matters: an increase indicates worsening hyperemia, while a decrease indicates improvement. The reported arm summaries are least-squares means with standard errors. A least-squares mean is a model-based estimate of an arm’s mean outcome; its standard error describes the estimated uncertainty in that mean. The registry record does not give the model specification or the covariates used to obtain these estimates.

Using a standardized photographic score provides a way to compare the recorded degree of redness across treatment groups over the study period. The outcome is a score, not a direct measure of vision, pterygium growth, or a patient’s overall experience. The registry record does not report a threshold for a clinically important change in this score, so the size of a score change cannot be translated into a clinical-importance category from these results alone.

7. Results Posted in the Registry

• 0.1% AG-86893 Eye Drops: mean -0.33 versus -0.06 on control; difference -0.27 (95% CI -0.59 to 0.04), standardized effect d = -0.54; z-test p = 0.091.
• 0.3% AG-86893 Eye Drops: mean -0.35 versus -0.06 on control; difference -0.30 (95% CI -0.61 to 0.02), standardized effect d = -0.58; z-test p = 0.068.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Change From Baseline in Conjunctival Hyperemia Score in the Quadrant With the Pterygium

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
• Result:
  • 0.1% AG-86893 Eye Drops: mean -0.43 versus -0.11 on control; difference -0.32 (95% CI -0.73 to 0.09), standardized effect d = -0.49; z-test p = 0.128.
  • 0.3% AG-86893 Eye Drops: mean -0.50 versus -0.11 on control; difference -0.39 (95% CI -0.79 to 0.01), standardized effect d = -0.60; z-test p = 0.059.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 0.1% AG-86893 Eye Drops and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 0.3% AG-86893 Eye Drops and the control. The interval gives the range of effects that remain compatible with the data.

The registry posts one secondary outcome: change from Baseline in the conjunctival hyperemia score in the quadrant containing the pterygium. Its arm-level estimates follow the same broad directional pattern as the primary outcome: average change is negative in all groups, and the AG-86893 group estimates are more negative than the vehicle estimate. This is broadly consistent with the direction of the primary endpoint, but the secondary outcome concerns one quadrant rather than the average across all four.

The registry reports mixed-model p-values for the secondary comparisons, as well as recalculated unadjusted comparisons. These are separate analyses and should not be combined as if they were independent confirmation of the primary result. The primary and secondary outcomes are related measures of hyperemia, so their results may reflect overlapping information. The registry record does not report a strategy for controlling multiplicity across outcomes or comparisons.

Unadjusted secondary results carry less weight as confirmatory evidence when several outcomes or contrasts are examined without a reported multiplicity plan. A nominal result can arise by chance among multiple tests, and a secondary outcome may be less central to the original question than the primary endpoint. The registry record does not describe whether this secondary analysis was prespecified in a detailed statistical analysis plan or how it was intended to inform conclusions. It is therefore best interpreted as supportive descriptive context rather than as a stand-alone basis for a definitive claim.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Change From Baseline in Conjunctival Hyperemia Score in the Quadrant With the Pterygium

9. Statistical Interpretation

10. Statistical Methods Explained

What does a mean change represent?

The primary outcome is continuous: it is a numeric score, and the registry reports a mean change for each group. The mean summarizes the group’s average change from Baseline to Day 28. In this study, negative values indicate that the score fell, which the outcome description identifies as improvement in hyperemia. A group mean does not show how much individual participants varied or whether every participant changed in the same direction.

The registry reports least-squares means and standard errors. Least-squares means are model-based group estimates rather than necessarily simple arithmetic averages. Standard error describes uncertainty in an estimated mean, not the spread of individual scores. Standard deviation, by contrast, describes variation among individual observations. Confusing these measures can make a group estimate appear more or less variable than it is.

What is the role of the confidence interval?

A confidence interval gives a range of values reasonably compatible with the observed data under the analysis assumptions. For a difference in means, zero represents no difference between groups. When an interval includes zero, the data do not exclude no difference at the interval’s stated confidence level. The interval also indicates the range of differences that remain compatible with the data; it is not a guarantee that the true difference falls inside that range in every particular study.

The recalculated intervals are unadjusted and derived from posted summary statistics. Their interpretation is limited by that method. In particular, they are not the confidence intervals from the sponsor’s mixed-model analysis, and the registry record does not post such intervals for the sponsor analyses.

Why are the recalculated comparisons approximate?

The recalculations use the posted arm means, sample sizes, and standard errors to construct simple unadjusted comparisons. The pooled variability used in those calculations is approximate, because the posted summaries report standard errors rather than individual-level observations or standard deviations. A simple summary-statistic comparison also does not reproduce the structure or assumptions of a mixed model. It cannot account for model features that are not described in the registry record.

These recalculations are therefore best read as a transparent reference analysis of the posted summaries. They can help readers see how the group means compare and how broad the uncertainty is under a simple approach. They should not be interpreted as a reconstruction of the sponsor’s analysis plan or as a substitute for individual-level data.

What does a p-value tell the reader?

A p-value describes how unusual results at least as incompatible with a specified null hypothesis would be if that hypothesis and the analysis assumptions were true. It is not the probability that the null hypothesis is true, nor is it a measure of the size or clinical importance of a difference. The recalculated p-values are unadjusted. The registry’s p-values come from mixed-model superiority analyses, but the model specification is not reported in the registry record.

Because more than one active concentration was compared with vehicle, the set of comparisons raises a multiplicity question. Testing several hypotheses can increase the chance of obtaining at least one apparently notable result by chance if no adjustment or other control is used. Whether and how the trial’s analyses addressed this issue is not reported in the registry record. The unadjusted recalculated p-values should not be treated as multiplicity-adjusted evidence.

How should the analysis population be understood?

The primary outcome identifies the analysis population as modified intent-to-treat. This label indicates that the analysis population was not described simply as every randomized participant, but the registry record does not define the modifications or list the inclusion rules. The exact handling of participants without Day 28 measurements, protocol deviations, or treatment discontinuation is also not reported in the registry record.

For general interpretation, missing outcome data can affect a comparison if the probability or reason for missingness differs across groups or is related to the outcome. Methods such as imputation or model-based handling can make assumptions about those unobserved values. The registry record does not report which missing-data procedures were used, so the impact of missing data cannot be evaluated from the posted summary alone.

Finally, the posted mean changes describe the outcome over the specified Baseline-to-Day-28 period. They do not establish what happened beyond that timeframe. The registry record does not report a longer-term assessment for this primary endpoint in the registry record for this analysis.

11. Confidence Intervals and Precision

Precision is reflected in the uncertainty around an estimated difference, not just in the direction of the group means. For the recalculated comparison of 0.1% AG-86893 with vehicle, the estimated mean difference was -0.274 and the 95% confidence interval ranged from -0.592 to 0.044. For 0.3% AG-86893 versus vehicle, the estimated mean difference was -0.296 and the 95% confidence interval ranged from -0.614 to 0.022. Each interval includes zero, and each also includes negative values of greater magnitude than the point estimate.

This breadth means the recalculated results do not identify a narrowly determined treatment difference. The interval endpoints reflect uncertainty under the simple unadjusted calculation; they are not the confidence limits from the registry’s mixed-model analysis. The registry record does not report confidence intervals for those sponsor analyses, limiting direct assessment of their precision.

The arm-level standard errors were 0.12 for vehicle and 0.109 for each AG-86893 group in the primary outcome. These describe uncertainty in the reported arm means, not individual participant variation. The outcome-specific groups were modest in size, with 18 participants in the vehicle arm and 22 in each AG-86893 arm. Estimates from groups of this size can be sensitive to the observed data and assumptions used in the analysis.

Confidence intervals do not show whether a difference is important to patients or clinically meaningful. The registry record does not provide a threshold for meaningful change in the hyperemia score. The intervals therefore communicate statistical uncertainty about the score difference, not a clinical judgment about the value of that difference.

12. 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. They are illustrations based on the observed effect rather than a reconstruction of the trial’s original design. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set at the stated fraction of the observed effect. The original design assumptions and the trial’s own sample-size justification are not reported in the registry record.

The 80% power column gives the estimated number of participants per arm for a planning scenario in which a study has an 80% chance of detecting the specified effect under the stated assumptions, if that effect is the true effect and the assumptions hold. The 90% power column describes the corresponding planning target for a 90% chance. These are prospective planning concepts; neither column describes the probability that this completed study found a real effect.

Rows planning for 100%, 75%, and 50% of the observed effect illustrate how the assumed target affects the required group size. A smaller effect is harder to distinguish from random variation, so planning for a smaller effect requires more participants per arm. The figures are not observed power: observed power is not a useful substitute for interpreting the estimated effects and their uncertainty after the study. The planning values also do not account for unreported design features or analysis choices in the original trial.

13. 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 = -0.274; pooled standard deviation σ = 0.510.
2. n = 2 × (1.96 + 0.842)² × 0.510² / -0.274² = 54.4, rounded up to 55 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 <- -0.274                      # observed difference in means
sigma <- 0.510299757108764                     # 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(3533244)
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 = 55 (80% power), 73 (90% power)
 75% of observed effect: n per arm = 97 (80% power), 130 (90% power)
 50% of observed effect: n per arm = 218 (80% power), 292 (90% power)
power.t.test: 55.4 
Simulated power at n = 55 per arm: 0.795 (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.

14. Analyses Reported by the Sponsor

The registry reports the sponsor’s primary-outcome comparisons as mixed-model superiority analyses. The p-value was 0.290 for 0.1% AG-86893 versus vehicle and 0.218 for 0.3% AG-86893 versus vehicle. The model-based effect estimates and confidence intervals are not reported in the registry record, so the direction and precision of those particular contrasts cannot be fully assessed from the sponsor results alone.

The recalculated comparisons are simple, unadjusted analyses from the posted arm means and standard errors. Their estimated differences and p-values are not the sponsor’s model outputs. The numerical differences between the recalculated and sponsor p-values are not, by themselves, evidence of an error: the approaches use different statistical methods, and the registry does not provide enough model detail to reproduce the sponsor analyses.

The record does not identify a discrepancy between the posted summary statistics and the sponsor analysis. The sponsor’s mixed-model results should therefore be read as the registry’s reported inferential analyses, while the recalculations offer a separate, approximate view based on arm-level summaries. Neither set of p-values establishes the magnitude or clinical relevance of a difference on its own.

15. Multiplicity, Missing Data and Analysis Populations

The trial has two active concentrations compared with one vehicle group for the primary endpoint, and the registry also posts a secondary hyperemia outcome with corresponding comparisons. That creates more than one statistical comparison. When multiple hypotheses are tested, the chance of at least one apparently notable finding can rise unless the analysis plan accounts for the multiplicity or uses a clearly defined hierarchy.

The registry record does not report whether the sponsor adjusted p-values or confidence intervals for multiple comparisons, designated a testing hierarchy, or used another multiplicity-control procedure. The recalculated p-values are explicitly unadjusted. They should not be interpreted as if they controlled the overall chance of a false-positive conclusion across the set of comparisons.

The primary outcome names the modified intent-to-treat population, but the registry record does not define that population. It does not state how many participants were excluded from it or why, nor does it report the missing-data rules, imputation method, or sensitivity analyses. The primary outcome arm counts are posted, but these counts alone do not explain what happened to participants without an evaluable outcome.

In general, missing data can affect an estimated treatment difference if missingness is related to treatment assignment, participant characteristics, or the unobserved outcome. Different handling methods rely on different assumptions. Without the details of missingness and its treatment, readers cannot determine whether the model or the recalculated summaries adequately address this issue.

The registry record also does not report the detailed statistical analysis plan, including the prespecified model terms, covariates, or any interim analyses. Their absence from the record is not evidence that they were or were not part of the trial conduct; it means those details cannot be evaluated from the registry information.

16. 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

For serious adverse events, the registry reports zero affected participants in each group: vehicle had 0 of 20 at risk, 0.1% AG-86893 had 0 of 22 at risk, and 0.3% AG-86893 had 0 of 22 at risk. No deaths were reported in any of these groups. These counts describe the safety results recorded during the study; they do not establish that a serious event is impossible or that the groups have identical safety profiles.

The registry also reports other adverse events affecting 5 participants in the vehicle group, 5 in the 0.1% group, and 15 in the 0.3% group. The event terms and severity breakdown for these other adverse events are not reported in the registry record in the registry record for this analysis. The serious-event counts should be read separately from these other adverse-event counts.

The group sizes and study duration limit how much can be inferred about uncommon or later-occurring harms. The registry record reports the study’s 28-day dosing schedule but does not provide additional follow-up detail in the registry entries. These results describe observed reports, not a complete characterization of longer-term safety.

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

The results show that the mean overall hyperemia score decreased from Baseline to Day 28 in all three groups. The decreases were more pronounced in the posted arm estimates for both AG-86893 concentrations than in the vehicle estimate. In the simple recalculations, the estimated differences versus vehicle were negative, but their confidence intervals included zero. The registry’s mixed-model analyses report p-values without corresponding effect estimates or confidence intervals.

These findings do not establish that either concentration produced a difference from vehicle. Nor do they establish that the groups were equivalent: an interval that includes zero can also be compatible with differences in either direction, within the range it spans. The uncertainty and the absence of the sponsor’s model-based estimates limit how specifically the comparative results can be described.

The endpoint measures a photographic score for conjunctival redness over the study period. It is not a direct measure of visual function, pterygium growth, or long-term disease course. The registry record does not report a clinically important threshold for the score, so statistical estimates cannot be translated into a statement about clinical importance from these registry entries alone.

The study’s safety results report no serious adverse events or deaths in the posted groups, alongside other adverse-event counts. These observations are limited to the study record and do not establish the absence of risk. The record also does not describe longer-term follow-up or provide the event terms for the other adverse events in the registry record for this analysis.

In short, the data support a descriptive account of score changes and their uncertainty. They do not, on their own, justify a medical recommendation or a broad conclusion about treatment efficacy, safety, or longer-term effects.

18. Why This Trial Matters Statistically

This study is statistically informative because it illustrates the distinction between an observed direction of change and a precise comparison between groups. The arm means move downward, but the recalculated intervals extend across zero. Looking at the mean estimates alone would omit important uncertainty; looking only at p-values would omit the size and range of plausible differences.

It also demonstrates why readers need to distinguish a sponsor’s model-based analysis from a simple recalculation using summary statistics. The registry reports mixed-model p-values, while the independent summary-statistic comparisons use approximate variability and do not reproduce the model. Both can be described, but they answer the inferential question through different methods and should not be blended together.

The record additionally highlights the importance of complete reporting. Without model estimates and confidence intervals for the sponsor analyses, a detailed multiplicity plan, and information about missing data and the modified intent-to-treat population, readers have less ability to assess robustness and precision. These limitations do not negate the posted results; they define what can be concluded from them.

Finally, the planning illustrations show how sample-size needs depend on the effect a future study aims to detect. Smaller target effects require more participants per arm under the stated planning assumptions. Those illustrations are not a retrospective judgment of whether this trial was adequately designed, because the original sample-size assumptions are not reported in the registry record.

19. 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 sponsor’s mixed-model results are reported as p-values alone. The model-based contrasts, their confidence intervals, the model specification, and the covariates are not reported in the registry record. This limits assessment of the size and precision of the sponsor’s primary analysis and prevents its direct reproduction from the registry entries.

The recalculated comparisons are unadjusted and approximate. They use posted group summaries rather than participant-level data, and the pooled variability is inferred approximately from standard errors. The registry’s masking descriptions also differ: the masking field says quadruple masking, whereas the official title says double-masked. The record does not explain the difference.

The primary outcome identifies a modified intent-to-treat population but does not define its membership. Participant flow, reasons for missing outcome data, missing-data methods, and sensitivity analyses are not reported in the registry record. The original sample-size justification, detailed analysis plan, and multiplicity strategy are also not reported. Thus, the planning calculations cannot be used to assess the trial’s original design assumptions.

The posted primary endpoint concerns change over Baseline to Day 28, and the record does not establish longer-term effects. The score’s clinical-importance threshold is not reported. Safety reporting includes counts of participants with other adverse events, but the corresponding terms are not reported in the registry record for this analysis. These gaps limit interpretation without changing the descriptive results that are posted.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: A Study of the Response to AG-86893 in Patients With Pterygium Hyperemia — NCT03533244.
• Registry record last updated 2020-11-06; status last verified 2020-01.
• Results first posted 2020-11-06.
• 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.

23. Record Summary

This completed randomized phase 2 study enrolled 64 participants with pterygium and compared vehicle with 0.1% and 0.3% AG-86893 eye drops. All groups used one drop in the study eye three times daily for 28 days. The primary endpoint was change in the overall conjunctival hyperemia score from Baseline to Day 28 in the modified intent-to-treat population.

Posted arm means decreased in all groups, with more negative estimates for both AG-86893 concentrations than for vehicle. The simple unadjusted recalculated comparisons have confidence intervals that include zero. The registry’s mixed-model analyses report p-values but not model-based effect estimates or confidence intervals.

No serious adverse events or deaths were reported in the posted safety groups. The registry record does not report the original sample-size assumptions, detailed multiplicity and missing-data procedures, or the model specification.