Clinical Performance of Two Daily Disposable Toric Soft Contact Lenses: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Clinical Performance of Two Daily Disposable Toric Soft Contact Lenses (NCT04908488), a randomized na study. The primary outcome is Least Squares Mean Distance VA (logMAR) With Study Lenses.

2. Clinical Question

This is a comparison of visual-acuity measurements under two lens conditions, not a comparison of separate parallel groups: participants were randomized to one of two lens sequences and used both lens types. The reported arm summaries give a least squares mean of -0.08 for P1fA and -0.07 for AMfA. The posted unadjusted re-calculation expresses the contrast as AMfA minus P1fA. These values describe the observed outcome in the analyzed participants; they do not, by themselves, establish whether a prespecified non-inferiority criterion was met.

3. Trial Design

The registry describes a randomized, double-masked crossover study with enrollment of 115 participants. One sequence wore P1fA first and AMfA second; the other wore AMfA first and P1fA second, with sequence assigned by randomization. Each lens type was worn in both eyes and in a daily disposable modality for 8 -0/+3 days. The crossover structure means participants contributed measurements under both lens conditions, while the randomized order helps balance which lens was worn first.

The listed interventions are verofilcon A toric contact lenses and etafilcon A toric contact lenses. The registry’s brief summary identifies these with PRECISION1 for Astigmatism and 1-DAY ACUVUE MOIST for ASTIGMATISM, respectively. The sponsor is Alcon Research. The listed study dates are 2021-07-01 for start and 2021-09-22 for primary completion, and the status is completed.

The primary outcome is least squares mean distance visual acuity in logMAR with study lenses. It was assessed at Day 8 (-0/+3 days) for each lens type. The registry reports one outcome measure and one analysis. The reported analysis is a mixed effects repeated measures model, with the result described as a least squares means difference and the analysis type identified as non-inferiority.

The registry record does not report the original sample-size justification, planned non-inferiority margin, detailed visit schedule, washout procedures, or the model’s full specification. It also does not report whether period, sequence, or carryover effects were included in the model. Those details matter for understanding the assumptions used in a crossover analysis, so they should not be inferred from the study design label alone.

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 115 enrolled, 1 participant was exited from the study prior to randomization as a screen failure. This reporting group includes all subjects/eyes exposed to any study lenses evaluated in this study (114).

First Wear Period (8 -0/+3 Days)

Reasons for not completing this period:

Second Wear Period (8 -0/+3 Days)

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Full Analysis Set: All randomized subjects who are exposed to any study lenses evaluated in this study with non-missing response

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 Analysis Set: All subjects/eyes exposed to any study lenses evaluated in this study.

6. Primary Endpoint

The registry lists the primary outcome as Least Squares Mean Distance VA (logMAR) With Study Lenses, measured over Day 8 (-0/+3 days), each study lens type.

The primary endpoint is least squares mean distance visual acuity, measured in logMAR while participants wore each study lens. Visual acuity was collected separately for each eye using logMAR charts. The assessment timeframe is Day 8 (-0/+3 days) for each lens type. The primary outcome population is the Full Analysis Set: randomized participants exposed to any study lenses who had a non-missing response.

LogMAR expresses visual acuity on a logarithmic scale. The registry explains that 0.0 corresponds to 20/20 Snellen acuity and that a negative value denotes better than 20/20 visual acuity. The posted least squares means are -0.08 for P1fA and -0.07 for AMfA. These are model-based averages, rather than counts of participants meeting a threshold.

In general, a continuous outcome can preserve gradations in measurement rather than reducing results to categories such as success or failure. Visual acuity is relevant to a lens comparison because the endpoint records distance vision while each lens is being worn. A least squares mean can also reflect a model’s treatment of repeated observations and other included terms. The registry does not report enough model detail to identify all such adjustments. The endpoint describes visual acuity at the specified assessment; it does not by itself represent comfort, wear time, adverse effects, or other aspects of lens performance.

7. Results Posted in the Registry

• AMfA: mean -0.07 versus -0.08 on control; difference 0.01 (95% CI -0.01 to 0.03), standardized effect d = 0.16; z-test p = 0.239.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry identifies a mixed effects repeated measures model for the primary analysis. In general, a repeated measures model is used when measurements are linked because the same participant contributes observations under more than one condition or at more than one occasion. A mixed effects model can represent that within-participant structure and can estimate treatment-condition means while accounting for correlation among observations. The registry does not report the model formula, covariance structure, included terms, or handling of period and sequence, so the exact implementation cannot be reconstructed from the record.

What does a least squares mean represent?

In general, a least squares mean is a model-based estimate of an average for a condition, potentially adjusted for terms included in the model. It is not necessarily the arithmetic average of all raw measurements. The posted arm values are -0.08 for P1fA and -0.07 for AMfA, each with a reported standard error of 0.006. The registry does not describe which model terms generated those estimates or whether the standard errors incorporate the crossover pairing in a particular way.

Why does the crossover design matter?

In a crossover study, each participant receives both conditions in an assigned order. This allows each participant’s observations to contribute to the comparison, and in general can reduce the influence of stable between-participant differences. It also makes period and possible carryover effects important considerations. A period effect would mean outcomes differ by the time or phase of measurement, while carryover refers to an effect of an earlier condition persisting into a later condition. The registry describes randomized order but does not report washout procedures or whether these effects were assessed or included in the model. It is therefore not possible to say how the sponsor’s analysis addressed them.

What is the re-calculation?

The additional unadjusted re-calculation contrasts the two posted arm means and gives AMfA minus P1fA as 0.01, with a 95% confidence interval that crosses zero and an unadjusted p-value of 0.239. It uses an approximate pooled standard deviation derived from the posted standard errors and sample sizes. Because this is a simple summary-statistic re-calculation, it does not reproduce the repeated measures model or its treatment of within-participant correlation. It should be read as a complementary, approximate comparison rather than as an alternative sponsor analysis.

In general, a p-value measures how incompatible data are with a specified null hypothesis under the assumptions of an analysis. It is not the probability that the null hypothesis is true, and it does not measure clinical importance. The re-calculated p-value is unadjusted and is not a substitute for the registry’s non-inferiority analysis. The sponsor’s p-value is not reported in the registry record.

How should the confidence interval be read?

In general, a confidence interval describes a range of estimates compatible with the data and the method used, at the stated confidence level. A wide interval indicates less precision than a narrow one, while an interval spanning zero for a difference does not rule out a zero contrast under that analysis. The re-calculated interval spans zero. The sponsor analysis is recorded as having a 95% confidence interval, but the lower and upper entries are both -0.01. As recorded, those entries do not convey a usable interval width. The record does not clarify whether this reflects reporting or rounding.

The trial is labeled non-inferiority, a framework that differs from a conventional test for any difference. In general, a non-inferiority conclusion requires a prespecified margin and an appropriate interval-based comparison against that margin. The registry does not report the margin, the original decision rule, or enough detail to evaluate the sponsor model’s conclusion. No conclusion about whether the criterion was satisfied should be inferred from the result label alone.

The record lists one primary outcome and one analysis, with no secondary outcomes posted. This limits the multiplicity questions raised by a large set of reported endpoints, but does not establish what analyses may have been planned or conducted outside the registry results. The statistical analysis plan, original sample-size rationale, interim analyses, and model diagnostics are not reported in the registry record. In general, these details help readers assess prespecification, model adequacy, and the extent to which reported results reflect the planned analysis.

10. Confidence Intervals and Precision

The unadjusted re-calculation gives a 95% confidence interval for AMfA minus P1fA that includes zero. This means the posted summary statistics are compatible with no difference as well as with effects in either direction under that calculation. Its p-value is 0.239. The interval’s width is important: an interval that includes zero does not establish that the conditions are equivalent, and the point estimate alone does not show how precisely the contrast is known.

The registry reports standard errors of 0.006 for each least squares mean. A standard error describes uncertainty in an estimated mean under the analysis used; it is not the spread of individual participants’ measurements. The additional re-calculation uses an approximate pooled standard deviation based on these standard errors and the arm counts. It does not use the crossover model’s participant-level covariance information, which is not available in the record. Its interval therefore represents an approximate unadjusted analysis, not the precision of the sponsor’s repeated measures estimate.

The sponsor analysis is recorded with a 95% confidence interval whose lower and upper limits are each -0.01. Those identical entries do not communicate the interval’s width as recorded. The registry does not clarify whether the entries reflect rounding or another reporting issue. Its p-value is not reported. The sponsor estimate and interval should therefore be described as posted, without interpreting the interval as evidence of high precision.

In general, greater precision is supported by more information and lower variability, but precision depends on the design and analysis as well as the number of observations. The registry reports 112 P1fA and 110 AMfA observations in the outcome summaries, but does not give the paired-data structure or the model details needed to independently assess the sponsor estimate’s uncertainty. The posted results permit a limited summary of precision, not a full evaluation of the 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 display gives participants per arm for 80% power and participants per arm for 90% power. These are planning illustrations based on the observed effect, not the trial’s original design calculations. They assume a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each planning row uses a stated fraction of the observed effect as the effect to detect: 100%, 75%, or 50%. The registry does not report the trial’s own original sample-size assumptions or justification.

For 100% of the observed effect, the display gives 628 participants per arm for 80% power and 840 participants per arm for 90% power. For 75% of the observed effect, it gives 1,116 participants per arm for 80% power and 1,494 participants per arm for 90% power. For 50% of the observed effect, it gives 2,510 participants per arm for 80% power and 3,360 participants per arm for 90% power.

In general, power is the chance that a planned analysis will reject its null hypothesis under a specified effect and assumptions. The 80% column describes a planning target with 80% power under the listed assumptions; the 90% column uses a higher target. Smaller effects are harder to distinguish from random variation, so planning for a smaller fraction of the observed effect requires more participants per arm. These figures are not observed power and should not be confused with the number enrolled in this crossover trial. The listed assumptions use an equal-allocation two-arm normal approximation, whereas the trial is described as a randomized crossover study, so the illustrations are not a reconstruction of its design-specific sample-size calculation.

The event-count convention for time-to-event outcomes does not apply to this continuous endpoint. The displayed figures are participants per arm, not total events.

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 = 0.010; pooled standard deviation σ = 0.063.
2. n = 2 × (1.96 + 0.842)² × 0.063² / 0.010² = 627.3, rounded up to 628 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 <- 0.01                      # observed difference in means
sigma <- 0.0632165110768324                     # 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(4908488)
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 = 628 (80% power), 840 (90% power)
 75% of observed effect: n per arm = 1,116 (80% power), 1,494 (90% power)
 50% of observed effect: n per arm = 2,510 (80% power), 3,360 (90% power)
power.t.test: 628.3 
Simulated power at n = 628 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.

13. Analyses Reported by the Sponsor

The registry’s reported analysis is a mixed effects repeated measures model, with a least squares means difference of -0.01 and a 95% confidence interval recorded with both limits at -0.01. No sponsor-analysis p-value is reported. The record labels this a non-inferiority analysis, but does not report the non-inferiority margin or decision rule. The posted entries therefore do not allow a reader to verify the non-inferiority interpretation.

The additional re-calculation is a simple unadjusted comparison of the posted arm summaries. It expresses the difference as AMfA minus P1fA, gives 0.01, and reports an interval crossing zero with p = 0.239. Its direction is opposite to the sign of the sponsor’s reported difference, consistent with the contrasts being expressed in a different order, but the registry does not explicitly state the sponsor contrast order in the result entry. The re-calculation also does not reproduce the repeated measures model.

The registry does not flag a discrepancy between the analyses. The sponsor’s model remains the primary reported analysis, while the re-calculation is a supplementary check based on summary statistics. Neither should be used to claim non-inferiority without the margin and a readable sponsor confidence interval.

14. Multiplicity, Missing Data and Analysis Populations

The registry reports one primary outcome measure and one analysis, and no secondary outcomes are posted. This is a narrow set of posted endpoints, but it does not establish the full scope of analyses conducted or planned. A statistical analysis plan and details of any interim analyses are not reported in the registry record. It is therefore not possible to assess whether the registry entries capture every planned comparison or whether any multiplicity adjustment was contemplated.

Multiplicity arises when several hypotheses or outcomes are tested: the chance of at least one apparently notable result can increase as the number of tests grows. In general, prespecified outcome hierarchies or adjustment procedures can help address that issue. No multiplicity procedure is reported. The single posted primary outcome means that the displayed results alone do not reveal a broad family of secondary tests, but absence of posted secondary results should not be treated as proof that none were analyzed.

The primary outcome population is described as randomized participants exposed to any study lenses with a non-missing response. That definition identifies the Full Analysis Set, but the record does not report participant flow, reasons for missing measurements, or a detailed missing-data method. The arm summaries list 112 for P1fA and 110 for AMfA, while enrollment is 115. The record does not explain these differences. Because the study is crossover, the numbers may describe condition-specific available outcomes, but the reporting does not permit a definitive account of the participant-level pattern.

In general, missing data can affect estimates if the likelihood of an observation being missing is related to its outcome or treatment condition. Methods such as likelihood-based analysis or imputation depend on assumptions, and sensitivity analyses can examine how conclusions change under alternative assumptions. The registry does not report the missing-data assumptions, imputation procedures, or sensitivity analyses used for the primary result.

The record also does not report whether all randomized participants were analyzed according to their assigned sequence, whether any participants were excluded after randomization, or how nonadherence was handled. These issues are relevant to interpreting randomized crossover results, but should not be filled in by assumption.

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 serious adverse event terms

Serious events with the highest arm-level rate: atrial fibrillation (0.9%).

The serious adverse event entries show zero affected in the pretreatment group, the P1fA ocular group, the AMfA ocular group, and the AMfA nonocular group. The P1fA nonocular group lists 1 serious adverse event affected among 114 at risk. The registry also lists atrial fibrillation as a top serious term at 0.9%. Deaths are listed as 0 in every group.

The group denominators differ across entries: the ocular groups list 228 at risk for P1fA and 226 for AMfA, while the nonocular entries list 114 and 113. The record does not explain these denominators or whether they represent participants, eyes, or another reporting unit. In particular, these figures should not be summed to infer a unique number of participants across the crossover conditions.

In general, adverse-event counts describe events recorded during the stated study reporting periods; they do not alone establish whether an event was caused by a study intervention. The registry’s serious-event figures should be read as reported counts, not as a causal comparison or a complete characterization of safety. Non-serious event details and the method for attributing events are not reported in the registry record.

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

The posted results describe mean distance visual acuity at the specified assessment under two lens conditions. The least squares means are -0.08 for P1fA and -0.07 for AMfA. The registry states that a negative logMAR value denotes better than 20/20 visual acuity. The unadjusted re-calculation gives an AMfA-minus-P1fA estimate of 0.01, with an interval that includes zero and an unadjusted p-value of 0.239. This indicates that the summary-statistic comparison does not precisely distinguish the mean outcomes.

That finding is not proof that the lens conditions are equivalent. Failure to distinguish a difference from zero in an unadjusted analysis is different from demonstrating that any difference is small enough to be clinically unimportant. Equivalence requires prespecified bounds and an analysis designed for that question. Non-inferiority likewise requires a margin and an appropriate interval-based criterion. Although the registry labels the sponsor analysis as non-inferiority, the margin is not reported and its confidence-limit entries are identical as recorded, so the conclusion cannot be evaluated from those entries.

The outcome is limited to distance visual acuity measured with study lenses at Day 8 (-0/+3 days). It does not capture all possible aspects of lens performance, and the posted result should not be generalized beyond the measured endpoint, study conditions, and analyzed population. The trial’s crossover design is relevant because the same participants used each lens type, but details about period effects, carryover, and the model specification are absent.

The safety entries report one serious adverse event affected in the P1fA nonocular category and none in the other listed categories, with zero deaths recorded. These counts are descriptive and do not, on their own, establish causation or a comparative safety profile. Taken together, the registry provides outcome and safety summaries, but important analysis and reporting details are absent. No treatment recommendation or broader claim follows from these data alone.

17. Why This Trial Matters Statistically

This study is statistically interesting because it uses a randomized crossover design for a continuous visual-acuity outcome. In general, a crossover comparison can make within-participant contrasts informative: each participant experiences both conditions, so stable differences between participants may contribute less to the contrast than in a parallel-group design. At the same time, crossover analyses rely on design and modeling choices that account for repeated observations and may need to address period and carryover effects.

The registry reports a mixed effects repeated measures model, which is a method suited in general to correlated observations. However, the model specification is not reported. That gap matters because the sponsor’s estimate is the key analysis for this design, while the available unadjusted re-calculation uses summary statistics and does not reproduce the within-participant analysis.

The contrast also illustrates why a point estimate, a confidence interval, and a testing framework should be read together. The arm means are close, and the unadjusted interval crosses zero, but that alone does not prove equivalence. The posted analysis is labeled non-inferiority, a question that depends on a prespecified margin. The margin is not reported, and the sponsor interval is recorded with identical limits. As a result, the record does not permit a clear assessment of the non-inferiority claim.

Finally, the planning illustrations show how sample-size requirements depend on the effect a future study aims to detect and the desired power. They are illustrative calculations based on the observed effect, not the original trial’s design rationale. Separating these calculations from the study’s actual analysis helps prevent a common misreading: planning power is not a retrospective measure of whether a completed trial had an adequate 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 primary limitation for statistical interpretation is incomplete reporting of the sponsor analysis. The registry identifies a mixed effects repeated measures model but does not provide its full specification, the confidence interval is recorded with both limits at -0.01, and no p-value is posted. The non-inferiority margin and decision criterion are also not reported. These omissions prevent independent assessment of the principal inferential claim.

The available re-calculation is based on summary statistics and an approximate pooled standard deviation. It is unadjusted and does not reproduce the participant-level repeated measures analysis. The registry does not provide the paired observations or covariance information needed to reconstruct the crossover comparison independently. Therefore, the re-calculated interval and p-value should not be treated as a substitute for the sponsor result.

Other design and analysis details are not reported, including washout procedures, handling or assessment of period and carryover effects, model diagnostics, and the original sample-size justification. The record also does not explain the difference between enrollment of 115 and the outcome counts of 112 and 110, or report reasons for missing measurements and missing-data sensitivity analyses.

Only one outcome and one analysis are posted, with no secondary outcomes. The registry does not report a statistical analysis plan or any interim analysis details, so prespecification and the full scope of analyses cannot be evaluated. Safety denominators vary across categories and their reporting unit is not explained. These limitations constrain interpretation of the posted estimates and do not establish that any unreported procedure was or was not performed.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Clinical Performance of Two Daily Disposable Toric Soft Contact Lenses — NCT04908488.
• Registry record last updated 2022-10-18; status last verified 2022-09.
• Results first posted 2022-09-23.
• 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

The registry describes a completed randomized, double-masked crossover study sponsored by Alcon Research, with enrollment of 115 participants. It compared bilaterally worn verofilcon A toric contact lenses (P1fA) and etafilcon A toric contact lenses (AMfA), each used daily for 8 -0/+3 days. The primary outcome was least squares mean distance visual acuity in logMAR at Day 8 (-0/+3 days) for each lens type.

The posted least squares means are -0.08 for P1fA and -0.07 for AMfA. The sponsor analysis is identified as a mixed effects repeated measures non-inferiority analysis, but its margin is not reported and its confidence limits are recorded as the same value. An unadjusted re-calculation gives an AMfA-minus-P1fA difference of 0.01, with an interval spanning zero and p = 0.239. The registry also reports one serious adverse event affected in the P1fA nonocular category and zero deaths in all listed groups. Missing-data, model, and design details limit further interpretation.