Clinical Performance Evaluation of Two Frequent Replacement Silicone Hydrogel Multifocal Toric Contact Lenses: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Clinical Performance Evaluation of Two Frequent Replacement Silicone Hydrogel Multifocal Toric Contact Lenses (NCT06461455), a randomized na study. The primary outcome is Mean Binocular Visual Acuity at Distance (4 Meters) at Day 30 With Study Lenses.

2. Clinical Question

3. Trial Design

This is a completed, randomized, double-masked, crossover study sponsored by Alcon Research. The registry lists an enrollment of 95 and identifies presbyopia and astigmatism as the conditions under study. The purpose stated in the record is to evaluate on-eye clinical performance of the investigational contact lenses following 30 days of wear in the intended population. The study is listed as phase NA.

The two lens products were lehfilcon A multifocal for astigmatism contact lenses, labeled LID230451, and samfilcon A multifocal for astigmatism contact lenses, labeled ULTRA MFfA. Participants were assigned to one of two sequences: LID230451 followed by ULTRA MFfA, or ULTRA MFfA followed by LID230451. The lenses were worn bilaterally during typical contact lens wearing hours for at least 8 hours per day. A wear period was defined as 30 days (-2/+1).

The crossover design allows measurements from the same participant under both study lenses at different periods. That structure can help make a within-participant comparison, but interpreting it depends on how period, sequence, and potential carryover effects are handled in the analysis. The specific statistical handling of those features is not reported in the registry record. The record identifies the study as double-masked but does not describe who was masked or how masking was maintained.

The primary outcome was mean binocular visual acuity at distance at Day 30 (-2/+1) of each wear period. The posted outcome groups include 82 for LID230451 and 81 for ULTRA MFfA. These groups reflect the reported outcome data; they are not a basis for deriving the number of unique participants contributing across both periods. The registry lists the study as completed, with primary completion on 2024-12-31.

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: Of the 95 enrolled, 6 subjects were discontinued as screen failures prior to randomization, and 4 subjects were discontinued post randomization and prior to exposure to the study lenses. This reporting group includes all subjects exposed to any study lenses evaluated in this study.

First Wear Period (Approx 30 Days)

Reasons for not completing this period:

Washout Period (Approx 2-4 Days)

Reasons for not completing this period:

Second Wear Period (Approx 30 Days)

Analysis population for the primary outcome, as defined in the registry: Full Analysis Set with data at visit

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: This analysis population includes all subjects exposed to any study lenses evaluated in this study.

6. Primary Endpoint

The registry lists the primary outcome as Mean Binocular Visual Acuity at Distance (4 Meters) at Day 30 With Study Lenses, measured over Day 30 (-2/+1) of each wear period. A wear period was 30 days (-2/+1) according to randomization assignment..

The primary endpoint is mean binocular visual acuity at distance, measured at 4 meters with study lenses in place at Day 30 (-2/+1) of each wear period. Binocular means that the measurement was made with both eyes together. The assessment used letter charts under high-contrast, high-illumination lighting, and the result was recorded on the logMAR scale.

Visual acuity is relevant to the stated aim because it directly measures distance vision while the study lenses are being worn. The record describes a logMAR value of 0 as equivalent to 20/20 Snellen visual acuity, and says negative logMAR values represent better than 20/20 acuity. The scale ranges from -0.30 (20/10 Snellen) to 1.00 (20/200 Snellen). Thus, interpretation requires attention to the direction of the scale: a more negative value represents better measured acuity, not worse acuity.

The posted endpoint is a mean, a summary of a continuous measurement, and its accompanying standard deviation describes variability within the reported group. The primary population is the Full Analysis Set with data at visit. The record does not report how missing Day 30 measurements were handled, nor does it give more detail about the definition of the Full Analysis Set.

7. Results Posted in the Registry

• ULTRA MFfA: mean -0.08 versus -0.50 on control; difference 0.42 (95% CI 0.39 to 0.45), standardized effect d = 4.41; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: visual acuity is recorded numerically on the logMAR scale, and the registry reports means and standard deviations. General statistical explanation: a mean describes the central value of measurements, while a standard deviation describes how dispersed the measurements are around that mean. Neither summary alone describes the full distribution of measurements or the participant-level pairing in a crossover study.

What does the unadjusted comparison represent?

The posted re-calculation compares the two group means without adjustment, using the group summaries in the outcome record. It reports a mean difference of 0.42, a 95% confidence interval from 0.391 to 0.449, and p < 0.001. These quantities describe the unadjusted comparison, not the sponsor's least squares mean analysis. The comparison uses the posted group summaries and does not account for participant-level pairing, sequence, period, or other covariates. The registry does not report enough detail to establish whether or how the sponsor's model accounted for those features.

General statistical explanation: an unadjusted comparison is useful as a transparent description of group summaries, but it may not match the primary analysis in a crossover trial. In a crossover design, each participant can contribute outcome data under both study lenses. Analysis may need to reflect the within-participant relationship and the period in which each lens was used. If those correlations are ignored, uncertainty estimates may differ from those of an analysis that models the repeated measurements. The posted group summaries do not contain the participant-level information needed to reconstruct such a model.

What does the confidence interval communicate?

The unadjusted 95% confidence interval gives a range of values compatible with the re-calculation under its statistical assumptions. Its endpoints are 0.391 and 0.449. The interval is relatively close to the reported estimate, which indicates precision for this particular unadjusted comparison. This precision does not establish that the analysis matches the trial's intended crossover or non-inferiority estimand.

General statistical explanation: a confidence interval reflects both the estimate and its uncertainty under a specified method. It is not a range guaranteed to contain the true effect, nor does it account for design features that were not incorporated into the method. A narrow interval can accompany an analysis that answers a different question from the sponsor's planned analysis. Interpretation therefore depends on both the numeric interval and whether the model corresponds to the clinical and design question.

What is a least squares mean difference?

The registry reports a sponsor analysis with the parameter described as a least squares mean difference. In general, a least squares mean is a model-based estimate, often adjusted for terms in a statistical model. It can differ from a direct subtraction of reported group means because the model, covariates, weighting, or analysis population may differ. The registry gives the sponsor estimate as -0.05 and an upper 95% confidence limit of 0.04, but does not report the lower confidence limit, model method, or p-value. It also does not report the contrast direction in enough detail to interpret the sign independently.

Because the sponsor estimate is classified as non-inferiority, its interpretation ordinarily depends on a pre-specified margin and a confidence interval evaluated against that margin. General statistical explanation: a non-inferiority analysis asks whether the result rules out an unacceptable loss relative to a comparator, according to a defined margin. The margin is essential to that judgment. It is not reported in the registry record, so the posted estimate alone cannot establish whether the decision criterion was met.

Why does over-dispersion matter?

General statistical explanation: over-dispersion arises when observed variability is greater than a statistical model assumes. It can make standard errors too small and confidence intervals too narrow if a model fails to account for the extra variability. For a continuous outcome, the relevant issue is whether the chosen model adequately represents the distribution and dependence in the data. The registry does not report enough model detail to assess this issue for the sponsor analysis. The posted standard deviations describe spread in the groups but do not establish whether the fitted model had over-dispersion or whether any correction was used.

In a crossover study, dependence between repeated measurements from the same participant is another design feature that matters. General statistical explanation: accounting for within-participant correlation can improve the estimate of uncertainty and may be important when comparing measurements under different conditions. Period and sequence can also matter if outcomes vary over time or if the order of lens exposure affects later measurements. The registry identifies a randomized crossover design and the two sequences, but does not report whether the sponsor model included participant, period, sequence, or carryover terms.

The registry reports one primary outcome measure and one analysis. This does not establish that no other analyses were conducted; it describes what is posted. The statistical method for the sponsor analysis is not reported in the registry record. As a result, readers can distinguish the posted descriptive group summaries and the simple unadjusted re-calculation from the sponsor's model-based non-inferiority estimate, but cannot fully reproduce or audit the sponsor analysis from the registry entry.

10. Confidence Intervals and Precision

For the unadjusted comparison, the posted estimate is a mean difference of 0.42, with a 95% confidence interval from 0.391 to 0.449. This interval expresses uncertainty around the re-calculated mean difference under the method used for that comparison. Its endpoints are fairly close to the estimate, so the re-calculation is numerically precise as an unadjusted summary comparison. The interval does not show whether the calculation accounts for repeated measurements, period, or sequence in the crossover design.

The registry separately reports a sponsor least squares mean difference of -0.05 and a 95% confidence interval with an upper limit of 0.04. A lower limit is not reported in the registry record. The sponsor analysis is identified as non-inferiority, but the non-inferiority margin is also not reported. The available interval therefore cannot be assessed against the required margin from the registry information alone. The sign and magnitude should not be compared directly with the unadjusted estimate without the sponsor contrast direction and model details.

General statistical explanation: precision concerns the uncertainty around an estimate, whereas validity concerns whether the analysis answers the intended question under appropriate assumptions. A narrow interval can be precise for an unadjusted contrast while still differing from the result of a model tailored to a crossover design. Confidence intervals should be read together with the estimand, model, and missing-data approach. Those details are not fully reported for the sponsor analysis.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm, not total event counts. They are illustrations based on the observed effect and are not the trial's original design justification. The registry's assumptions for this illustration are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to a stated fraction of the observed effect. The original trial's sample-size assumptions are not reported in the registry record.

For planning at 100% of the observed effect, the listing gives 1 participant per arm for 80% power and 2 participants per arm for 90% power. At 75% of the observed effect, it gives 2 participants per arm for 80% power and 2 participants per arm for 90% power. At 50% of the observed effect, it gives 4 participants per arm for 80% power and 5 participants per arm for 90% power. These small illustration values arise from applying the stated approximation to the unusually large unadjusted standardized effect; they should not be interpreted as a recommended design size for a crossover non-inferiority trial.

In plain language, the 80% power column describes the planned sample size under which the assumed effect would be detected by the illustrative test in 80% of repeated studies, if its assumptions hold. The 90% column uses a higher target probability of detecting that assumed effect. Smaller effects need more participants, as the listed figures illustrate. Power depends on the effect size and other design assumptions, so changing the assumed effect changes the planning requirement.

This is not observed power. It is a planning illustration based on the observed effect, and it does not recover the trial's actual design rationale, account for all crossover features, or establish the performance of the sponsor's non-inferiority analysis.

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 = 0.420; pooled standard deviation σ = 0.095.
2. n = 2 × (1.96 + 0.842)² × 0.095² / 0.420² = 0.8, rounded up to 1 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 <- 0.42                      # observed difference in means
sigma <- 0.0951624958747826                     # 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(6461455)
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 = 1 (80% power), 2 (90% power)
 75% of observed effect: n per arm = 2 (80% power), 2 (90% power)
 50% of observed effect: n per arm = 4 (80% power), 5 (90% power)
power.t.test: 2.3 
Simulated power at n = 1 per arm: NA (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-reported result is a least squares mean difference of -0.05, classified as a non-inferiority analysis, with a 95% confidence interval whose upper limit is 0.04. The lower confidence limit and p-value are not reported in the registry record. The record does not report the non-inferiority margin, the model method, or enough detail about the contrast direction to independently interpret the sign.

The posted re-calculation is a separate, unadjusted comparison of the group means: mean difference 0.42, 95% confidence interval from 0.391 to 0.449, and p < 0.001. The difference between these reported estimates should not be resolved by substituting the simple re-calculation for the sponsor's analysis. The estimates may represent different contrasts or analysis methods, but the registry entries do not establish the specific reason for their difference.

The sponsor analysis is the result relevant to the recorded non-inferiority question, while the unadjusted re-calculation is a descriptive check based on posted summary statistics. Because the margin, complete interval, and model specification are missing, the registry record does not permit a full independent assessment of the sponsor's non-inferiority conclusion.

14. Multiplicity, Missing Data and Analysis Populations

The registry posts one primary outcome measure and one analysis, and it lists zero secondary outcomes. Those entries describe the analyses posted in the registry record. They do not establish that no additional outcomes or analyses were collected or examined. The multiplicity plan, including whether any adjustment was intended or used, is not reported in the registry record.

The primary population is described as the Full Analysis Set with data at visit. The record does not define this set in detail or state whether all randomized participants were included in it. It also does not report the number or pattern of missing Day 30 measurements, reasons for missingness, or the method used to handle missing data. Missing-data handling can affect an estimate if participants with observed outcomes differ systematically from those without them; the registry information is insufficient to assess that possibility.

The study is a randomized crossover, but the reported sponsor method is not specified. The record does not state whether the analysis accounted for participant-level pairing, period, sequence, or carryover. It also does not provide the non-inferiority margin or a complete confidence interval for the sponsor result. These omissions limit independent assessment of how the sponsor analysis addressed the design and its decision criterion.

The registry reports a sponsor least squares mean difference and separately permits an unadjusted re-calculation from group summaries. These analyses should remain clearly distinguished. Without the model specification and analysis-population details, the registry record does not support reconstruction of the sponsor's analysis or confirmation that the simple comparison targets the same estimand.

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.

The registry lists adverse-event counts across pretreatment and lens-related categories. It reports zero serious adverse events in each listed category, zero other adverse events in each listed category, and zero deaths in each listed category. The record also lists no serious adverse-event terms.

The at-risk counts differ across the categories: 85 for pretreatment, 166 for LID230451 ocular, 83 for LID230451 nonocular, 168 for ULTRA MFfA ocular, and 84 for ULTRA MFfA nonocular. These counts are reported as category-specific at-risk figures. In a crossover study, categories can relate to different treatment periods or event groupings, so these counts should not be added or interpreted as a unique-participant total.

Zero recorded events in these categories means that the registry reports no events of those types for the listed groups. It does not establish that no events occurred outside the recorded categories or that the study can rule out uncommon harms. The registry record does not provide additional detail on event definitions, collection procedures, or the duration and completeness of safety follow-up beyond the listed treatment categories.

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

The central statistical result is not a single estimate that answers every question. The registry posts group means for binocular distance acuity, an unadjusted re-calculation, and a separate sponsor-reported non-inferiority analysis. The group means are -0.5 for LID230451 and -0.08 for ULTRA MFfA on the logMAR scale. The unadjusted comparison is 0.42 with a 95% confidence interval from 0.391 to 0.449 and p < 0.001. Because lower, more negative logMAR values indicate better acuity, the scale direction matters when describing the observed difference.

The sponsor's least squares mean difference is -0.05, with a reported upper 95% confidence limit of 0.04. This estimate is labeled as a non-inferiority analysis, but its lower confidence limit, model details, contrast direction, and non-inferiority margin are not reported in the registry record. Those missing details prevent a complete independent interpretation of the sponsor analysis. The unadjusted comparison cannot fill those gaps because it is not established as the same estimand or model.

The endpoint measures acuity under specified conditions with study lenses in place, at a stated visit in each wear period. It does not, by itself, describe every aspect of lens performance, longer-term use, or outcomes beyond the recorded visual acuity measure. The record lists no secondary outcomes, so it does not offer posted secondary measures to broaden that interpretation.

The posted safety record reports zero serious adverse events, zero other adverse events, and zero deaths in the listed categories. These counts describe the registry entries and are not proof that the risk of an event is absent. Overall, the record supports a focused description of the visual-acuity summaries and the reported safety counts, while important details needed to evaluate the sponsor's non-inferiority conclusion remain unreported.

17. Why This Trial Matters Statistically

This trial is statistically notable because it combines a crossover design with a continuous visual-acuity endpoint and a sponsor analysis labeled non-inferiority. These features make the distinction between a simple comparison of group means and a model-based analysis important. In a crossover, the same participant may contribute measurements under both lenses, so within-participant dependence and period effects may influence the estimate and its uncertainty.

The registry makes it possible to compare the descriptive summaries with the sponsor's reported least squares mean difference. The two estimates are not numerically alike, and the record does not give the model details needed to explain the relationship. This illustrates a broader point in clinical statistics: estimates can answer different questions when their estimands, analysis populations, or models differ. A small p-value from a simple comparison is not a substitute for evaluating a non-inferiority analysis against its pre-specified margin.

The endpoint also has a direction that can be easy to misread. More negative logMAR values indicate better visual acuity, so interpretation needs to follow the scale definition rather than assume that a larger value is necessarily better. Reporting the scale, measurement distance, lighting conditions, and timing helps readers understand what the outcome represents.

Finally, the registry entry demonstrates why completeness of statistical reporting matters. The sponsor's lower confidence limit, non-inferiority margin, analysis method, and missing-data approach are not reported. These details would be needed for a fuller independent assessment of the primary analysis. The posted result remains informative as a registry record, but its limitations constrain the conclusions that can be drawn from it.

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 does not report the sponsor model method, the non-inferiority margin, or the lower limit of the sponsor's 95% confidence interval. The sponsor analysis also lacks a posted p-value. Without these details, the stated non-inferiority analysis cannot be fully evaluated against its decision criterion or reproduced from the record.

The unadjusted re-calculation uses group summaries and does not show whether participant-level pairing, period, sequence, or carryover were incorporated. The registry does not explain the relation between this re-calculation and the sponsor's least squares mean difference. The estimates should therefore not be interpreted as though they were outputs from the same analysis.

The record identifies the primary population as the Full Analysis Set with data at visit but does not define the set or report missing-data methods. It does not give details about the randomization procedure, masking implementation, or how the crossover analysis addressed period and sequence. The enrollment and reported group sizes do not establish how many participants contributed data in both periods.

The posted record lists one outcome measure and no secondary outcomes. It does not provide a multiplicity strategy or establish whether additional analyses were conducted. Safety results are reported as event counts by category, with no serious or other events and no deaths listed; event definitions and additional follow-up details are not reported in the registry record. These are limitations of the available record, not evidence that the unreported procedures or analyses were absent.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Clinical Performance Evaluation of Two Frequent Replacement Silicone Hydrogel Multifocal Toric Contact Lenses — NCT06461455.
• Registry record last updated 2025-12-24; status last verified 2025-12.
• Results first posted 2025-12-24.
• 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

NCT06461455 is a completed, randomized, double-masked crossover study sponsored by Alcon Research. It enrolled 95 participants with presbyopia and astigmatism and compared LID230451 lehfilcon A multifocal toric lenses with ULTRA MFfA samfilcon A multifocal toric lenses in randomized sequences.

The primary endpoint was mean binocular distance visual acuity at 4 meters, measured in logMAR at Day 30 (-2/+1) of each 30-day (-2/+1) wear period. The posted group means were -0.5 and -0.08. The unadjusted re-calculation gave a mean difference of 0.42, with a 95% confidence interval from 0.391 to 0.449 and p < 0.001. The separate sponsor-reported non-inferiority analysis gave a least squares mean difference of -0.05 and an upper 95% confidence limit of 0.04.

The non-inferiority margin, sponsor model method, lower confidence limit, and missing-data approach are not reported in the registry record. The listed adverse-event categories report zero serious events, zero other events, and zero deaths.