Design Validation of Toric Contact Lenses in Senofilcon A With a Blue-Blocking Chromophore: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Design Validation of Toric Contact Lenses in Senofilcon A With a Blue-Blocking Chromophore (NCT05778786), a randomized na study. The primary outcome is Distance Monocular logMAR Visual Acuity.

2. Clinical Question

3. Trial Design

The registry describes a completed, randomized, controlled, single-masked, bilateral-wear crossover study. Its brief summary specifies four visits, two treatments, two sequences, and two wear periods. Participants were assigned to Test/Control or Control/Test, so the order of lens use differed between sequences. Each participant was to wear each lens bilaterally for a minimum of 8 hours per day for at least 5 days during its wear period. The registry does not report further details about any interval between wear periods.

The lenses compared were the TRA100/TRA200 series toric contact lens with an HEVL-blocking chromophore and Acuvue Oasys 1 Day for Astigmatism. The results label these as Test-senofilcon A (C3) and Control-senofilcon A (C3). Enrollment was 188. The reported primary endpoint population included dispensed subjects with 1-week follow-up data regardless of protocol deviation; the results give 180 for the test arm and 181 for the control arm.

The registry lists the study as completed, with a start date of 2023-03-13 and a primary completion date of 2023-05-24. It lists the phase as NA. The registry record does not report the original sample-size justification, detailed eligibility criteria, the masking procedure, or the planned statistical model for the primary comparison. The crossover structure is important when interpreting the results: participants received both lenses, but the posted summary statistics alone do not convey all the information that may be used in a model of within-participant comparisons.

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.

Period 1

Reasons for not completing this period:

Period 2

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: All dispensed subjects regardless of deviation from protocol with data collected at the 1-week follow-up.

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: All subjects dispensed at least one study lens.

6. Primary Endpoint

The registry lists the primary outcome as Distance Monocular logMAR Visual Acuity, measured over 1-Week Follow-up.

The primary endpoint was distance monocular visual acuity measured at the 1-week follow-up under high-luminance, high-contrast conditions. Visual acuity was assessed using ETDRS charts, and letter-by-letter results were used to calculate a performance score for each chart read. The endpoint is reported as a mean on the logMAR scale, with standard deviations describing variability among participants.

As a general interpretation of this scale, scores closer to zero or below zero indicate better visual acuity; a score of 0.0 is equivalent to Snellen visual acuity of 20/20. This makes the direction of the measure relevant: a lower logMAR value is a more favorable acuity score according to the registry description. The primary comparison is a difference in group means, test minus control, rather than a proportion of participants meeting a threshold.

The endpoint captures measured visual performance under the stated chart and lighting conditions at the specified follow-up. It does not by itself describe visual performance in every setting or at other times. The registry record does not report a clinically meaningful difference threshold for this endpoint, so the size of the observed mean contrast should be read alongside its uncertainty rather than treated as a threshold-based judgment.

7. Results Posted in the Registry

• Test-senofilcon A (C3): mean -0.11 versus -0.10 on control; difference -0.00 (95% CI -0.02 to 0.01), standardized effect d = -0.04; z-test p = 0.693.

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.

CLUE Comfort Score

• 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 deviations.
• Result:
  • Test-senofilcon A (C3): mean 66.20 versus 67.04 on control; difference -0.84 (95% CI -5.63 to 3.95), standardized effect d = -0.04; z-test p = 0.731.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Test-senofilcon A (C3) and the control. The interval gives the range of effects that remain compatible with the data.

CLUE Handling Score

• 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 deviations.
• Result:
  • Test-senofilcon A (C3): mean 70.30 versus 70.87 on control; difference -0.57 (95% CI -5.09 to 3.95), standardized effect d = -0.03; z-test p = 0.805.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Test-senofilcon A (C3) and the control. The interval gives the range of effects that remain compatible with the data.

The two posted secondary outcomes are CLUE Comfort Score and CLUE Handling Score, both measured at the 1-week follow-up. For each, the re-calculated mean contrast is small and negative for test minus control, and each confidence interval includes zero. The unadjusted p-values likewise do not provide strong evidence against a zero mean difference. This broad pattern is consistent with the primary endpoint in the limited sense that none of the posted re-calculated comparisons clearly separates the test and control means.

These outcomes complement the visual-acuity result by describing comfort and handling scores rather than chart-based visual performance. They are not substitutes for the primary endpoint, and a similar direction across measures does not independently confirm a treatment effect. Their interpretation depends on the measurement scales and the uncertainty in each estimate. The registry record does not report clinically meaningful thresholds for these scores.

Unadjusted secondary results carry less weight when several outcomes are examined. As a general statistical principle, looking across multiple outcomes increases the opportunity to find an apparently notable result by chance, especially if no multiplicity approach is applied. The registry record does not report a multiplicity adjustment or a prespecified hierarchy for interpreting the secondary outcomes. The posted secondary comparisons should therefore be treated as supportive and exploratory rather than as stand-alone confirmatory findings. This is a caution about interpretation, not a claim that a particular adjustment was or was not performed outside what the registry records.

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

• CLUE Comfort Score
• CLUE Handling Score

9. Statistical Interpretation

10. Statistical Methods Explained

What is being compared? The primary measure is continuous: distance monocular visual acuity expressed as a logMAR mean. The unadjusted comparison is the test-arm mean minus the control-arm mean. A negative difference points toward a lower mean for the test lens, and the endpoint description says lower logMAR indicates better acuity. The estimated difference is -0.003, with a 95% confidence interval from -0.018 to 0.012.

What does a mean represent? A mean is a measure of the central value of a set of observations. It provides a concise way to compare average scores, but it does not show the full distribution or how individual participants' results varied. The standard deviations in the registry describe variability around the arm means. As a general statistical concept, a standard deviation describes spread among observations; it is different from a standard error, which describes uncertainty in an estimated quantity.

What does the confidence interval add? A confidence interval gives a range of values compatible with the data and the method used to construct it. As a general explanation, a confidence interval reflects both the estimated effect and its precision; a wider interval indicates less precision than a narrower interval on the same scale. The interval for this mean difference includes zero and extends in both directions. It therefore does not distinguish a small test-favoring difference from a small control-favoring difference at the stated confidence level. It is not a range containing a known fixed proportion of individual participant scores.

How should the p-value be read? The unadjusted p-value is 0.693. In general, a p-value measures the compatibility of the observed data with a null hypothesis under a statistical model. It is not the probability that the null hypothesis is true, and it does not quantify the probability that a result will replicate. The registry record does not report a p-value from the sponsor's direct primary comparison, so the posted unadjusted value should not be attributed to the sponsor's model.

Why does the crossover design matter? In a crossover study, each participant receives both treatments in an assigned order. As a general statistical principle, the comparison can use information about how measurements from the same participant are related. The registry reports the design as crossover, but it does not provide participant-level paired results, a detailed statistical model for the primary endpoint, or details about period and sequence terms. The simple re-calculation from posted summary statistics is not a reproduction of a model-based crossover analysis. The registry record does not report whether the sponsor's model accounted for particular period, sequence, or carryover effects.

What does over-dispersion mean in general? For count outcomes, over-dispersion means that observed variability is greater than a model assumes, which can make standard errors and intervals too optimistic if not addressed. The primary endpoint is continuous rather than a count, so over-dispersion is not the central issue in interpreting this mean comparison. The registry record does not report a variance-structure assessment for the primary model.

What can be inferred from the posted analysis? The re-calculation gives an unadjusted summary-statistic contrast, not an adjusted causal estimate. It does not account for unreported participant-level information or resolve how the sponsor handled the crossover design. The registry record lists a Linear Mixed Model for a sponsor-reported least-square mean for the test group, but does not report the corresponding control estimate or a direct treatment contrast in the posted primary analysis. Those limits mean the re-calculation is informative as a descriptive comparison, while it should not be mistaken for a full reconstruction of the sponsor's analysis.

General statistical concepts in this explanation describe how means, standard deviations, confidence intervals, and p-values are commonly interpreted. The trial-specific statements are limited to the endpoint definition, design, posted estimates, and analysis details recorded for this study.

11. Confidence Intervals and Precision

The primary estimate is a mean difference of -0.003 logMAR, with a 95% confidence interval from -0.018 to 0.012. The interval includes zero and crosses from negative to positive values. Thus the posted estimate is not precise enough to determine the direction of a mean difference with confidence. The p-value of 0.693 is consistent with that uncertainty, but it should not be read as proof that the means are equal.

As a general statistical explanation, a confidence interval expresses uncertainty around an estimate under the method used to calculate it. It is not a description of the range of individual participant scores. The primary arm standard deviations, 0.074 and 0.070, describe participant-level spread, whereas the confidence interval describes uncertainty about the between-arm mean difference. These quantities answer different questions.

The interval's interpretation is also limited by the information available for the re-calculation. It is based on posted summary statistics and does not reproduce a model-based analysis of the crossover design. The registry record does not report a prespecified clinically meaningful difference, equivalence margin, or noninferiority margin for the primary endpoint. Without such a threshold, the interval cannot be classified as excluding or including a clinically important difference.

The sponsor-reported primary analysis gives a test-group least-square mean of -0.13 and reports a 95% interval with an upper endpoint of -0.10; the other endpoint is not reported in the registry record. That result is not a complete interval for the direct test-versus-control contrast. It therefore does not provide a second direct estimate of the comparative effect with which to judge precision.

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 sample-size table gives planning illustrations in participants per arm, not total events. The assumptions listed for these illustrations are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each row considers an effect to detect equal to the stated fraction of the observed effect. These are planning assumptions for the illustrations; the registry record does not report the original trial's sample-size assumptions or justification.

The 80% power column describes the number of participants per arm that the illustration estimates would be needed for an 80% chance of detecting the specified effect under those assumptions. The 90% power column describes the corresponding number for a 90% chance. These are hypothetical design calculations, not a statement about the chance that this completed study detected an effect. This is not observed power.

The rows consider planning for 100%, 75%, and 50% of the observed effect. Smaller effects require more participants to detect under the same assumptions, which is why the illustrated sample sizes rise as the target fraction decreases. Because the observed effect is small, the resulting illustrations are large. They are not a retrospective judgment about the trial's adequacy and should not be mistaken for the study's planned enrollment target.

The sample-size curve should be read as a visual representation of how the planning requirement changes with the effect size under the stated assumptions. The registry identifies the trial as a crossover study, whereas these illustrations use equal allocation between two arms and a normal approximation. The record does not report a planning method tailored to its crossover structure, so the figures should be understood as general illustrations rather than as a reconstruction of the original design.

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 = -0.003; pooled standard deviation σ = 0.072.
2. n = 2 × (1.96 + 0.842)² × 0.072² / -0.003² = 9,108.9, rounded up to 9,109 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 <- -0.003                      # observed difference in means
sigma <- 0.0722663172772307                     # 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(5778786)
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 = 9,109 (80% power), 12,195 (90% power)
 75% of observed effect: n per arm = 16,194 (80% power), 21,679 (90% power)
 50% of observed effect: n per arm = 36,436 (80% power), 48,778 (90% power)
power.t.test: 9109.9 
Simulated power at n = 9,109 per arm: 0.801 (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 a sponsor analysis using a Linear Mixed Model and a least-square mean for the test group. That analysis gives a value of -0.13 and a 95% interval whose reported upper endpoint is -0.10; the other interval endpoint and a p-value are not reported in the registry record. A corresponding control-group least-square mean and a direct model-based treatment contrast are also not reported in the primary analysis information.

The re-calculation is different in purpose and method. It uses the posted arm means and standard deviations to produce an unadjusted mean difference of -0.003, with a 95% confidence interval from -0.018 to 0.012 and an unadjusted p-value of 0.693. It is not a reproduction of the sponsor's Linear Mixed Model and does not provide a like-for-like comparison with the sponsor's test-group least-square mean.

The registry marks no discrepancy between the posted summary statistics and the simple re-calculation. That does not make the two analyses interchangeable: one is a reported model-based result for a group, while the other is an unadjusted comparison derived from arm summaries. The sponsor's analysis should take precedence if a discrepancy is identified; no such discrepancy is indicated in the registry record.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists eight outcome measures and eight analyses, while the posted results include the primary visual-acuity endpoint and two secondary outcomes, CLUE Comfort Score and CLUE Handling Score. The record does not report a complete account of how all outcome measures were prioritized or how the analyses were linked to a prespecified testing hierarchy. It also does not report whether any multiplicity adjustment was used.

As a general statistical principle, testing several outcomes or contrasts can increase the chance that at least one result appears notable by chance. Adjustment methods or a prespecified hierarchy can address that issue, but the registry record does not identify such a method for these results. The secondary p-values are unadjusted, so they should be interpreted cautiously and should not be treated as independent confirmation of the primary result.

The primary population is described as all dispensed subjects regardless of protocol deviation with data collected at the 1-week follow-up. The reported sample sizes are 180 for the test lens and 181 for the control lens, while enrollment is 188. These counts do not establish why a participant may not appear in an endpoint summary. Reasons for missing follow-up data, the amount and pattern of missingness, and any imputation or sensitivity analyses are not reported in the registry record.

The record does not describe how protocol deviations were handled beyond the primary population definition, nor does it provide a separate per-protocol analysis in the registry record recorded for these results. The detailed analysis population for each secondary measure is not separately described. These omissions limit assessment of whether missing data or analysis-population choices could affect the estimates; they do not establish that either did affect them.

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.

The safety figures are reported separately for each lens. For the test lens, 185 participants were listed as at risk for serious adverse events and zero were reported as affected; 185 were listed for other adverse events and zero were affected. For the control lens, the corresponding at-risk counts were 184, with zero affected for serious adverse events and zero affected for other adverse events. Deaths were recorded as zero in both groups, and no serious adverse event terms are listed.

These figures describe what the registry reports for the recorded safety categories; they do not establish that no other symptoms or events occurred outside the categories or reporting period represented. The registry record does not report detailed event definitions, a fuller safety follow-up description, or how events were assigned in relation to the crossover periods. The at-risk counts should be read as reported group counts, not as proof that the two sets of participants were independent, since participants received both lenses in the crossover design.

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

The posted results show mean distance monocular logMAR scores of -0.107 for the test lens and -0.104 for the control lens at the 1-week follow-up. The unadjusted test-minus-control difference is -0.003, with a 95% confidence interval from -0.018 to 0.012 and an unadjusted p-value of 0.693. The estimate is close to zero, and the interval includes zero while allowing differences in either direction.

This result does not establish that the lenses have identical mean visual-acuity scores. It also does not establish a difference between them. A failure to distinguish a difference statistically is not the same as demonstrating equivalence. The registry record does not report an equivalence or noninferiority margin, or a clinically meaningful threshold for interpreting the logMAR contrast.

The endpoint is limited to chart-based distance monocular acuity assessed under high-luminance, high-contrast conditions at the specified follow-up. It does not directly describe comfort, handling, visual performance under other conditions, or outcomes at other times. Comfort and handling were also listed as secondary outcomes, but those measures answer different questions from visual acuity.

The comparison is an unadjusted re-calculation from posted summary statistics, not a replacement for the sponsor's model-based analysis of the crossover study. The sponsor's reported primary analysis does not include a direct treatment contrast in the recorded results. The posted information therefore supports a cautious description of the observed means and uncertainty, rather than a broad conclusion about performance beyond these outcomes and conditions.

18. Why This Trial Matters Statistically

This trial is statistically instructive because it combines a crossover design with continuous outcomes and registry-posted summary results. In a crossover study, participants receive both treatments in a randomized order, making within-participant information potentially relevant to the comparison. The available means and standard deviations allow a simple unadjusted contrast, but they do not provide all the information needed to reconstruct a model-based analysis of the design.

The primary contrast is close to zero, while its confidence interval spans values on either side of zero. This illustrates why an estimate and its precision should be read together. A p-value alone does not show the range of effects compatible with the data, and a result that does not distinguish the groups is not evidence of equivalence without an appropriate design and margin.

The registry also distinguishes a sponsor-reported least-square mean from an unadjusted between-group re-calculation. They answer different statistical questions and cannot be treated as interchangeable results. This distinction matters when interpreting registry analyses: a group mean is not itself a treatment contrast, and a summary-statistic re-calculation does not reproduce a mixed model.

Finally, secondary outcomes and safety summaries provide additional context but have reporting limits. The record does not report a multiplicity approach, missing-data methods, or full details of the crossover model. Recognizing those limits helps readers separate what the posted statistics quantify from what remains unspecified.

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 registry record does not report the original sample-size justification or detailed assumptions for the trial's design. The sample-size illustrations are based on separate planning assumptions and should not be taken as the study's intended calculation. The record also does not report a clinically meaningful difference threshold for the primary endpoint, making it difficult to relate the observed contrast to a prespecified practical benchmark.

The sponsor's primary analysis is reported as a Linear Mixed Model least-square mean for the test group, but the control estimate, direct treatment contrast, other confidence-interval endpoint, and p-value are not reported. The unadjusted re-calculation is therefore not a direct replication of the sponsor's comparison. The registry record does not specify model terms for period, sequence, or carryover in the crossover analysis, and participant-level paired data are not reported.

The primary population is described as dispensed participants with 1-week follow-up data regardless of protocol deviation. The record does not report reasons for missing data, missing-data handling, or sensitivity analyses. It also does not provide a reported multiplicity strategy for the listed outcomes. These gaps limit assessment of the robustness of the estimates and of the secondary findings.

Safety reporting is limited to counts for serious and other adverse events and deaths. The record does not provide event definitions or further detail on timing and attribution within the crossover periods. The study summary describes habitual soft contact lens wearers, but detailed eligibility criteria are not reported. These reporting limits constrain interpretation and generalization beyond the recorded measures, participants, and follow-up.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Design Validation of Toric Contact Lenses in Senofilcon A With a Blue-Blocking Chromophore — NCT05778786.
• Registry record last updated 2024-07-17; status last verified 2024-06.
• Results first posted 2024-07-17.
• 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

NCT05778786 is a completed, randomized, single-masked crossover study of toric contact lenses. Participants were assigned to test/control or control/test sequences and wore both lenses bilaterally across two wear periods. Enrollment was 188.

The primary endpoint was distance monocular logMAR visual acuity at the 1-week follow-up. The posted unadjusted test-minus-control mean difference was -0.003, with a 95% confidence interval from -0.018 to 0.012 and an unadjusted p-value of 0.693. The interval includes zero and does not establish equivalence or a difference.

The registry reports a sponsor Linear Mixed Model least-square mean for the test group but no direct comparative estimate in the recorded primary analysis. Two secondary outcomes and safety counts are also posted. Details of the original sample-size justification, multiplicity handling, missing-data methods, and the sponsor's full crossover model are not reported in the registry record.