Single-center, Double-arm, Prospective Clinical Trial to Compare Visual Performance of Non-diffractive Extended Vision and Neutral Aspheric Monofocal Intraocular Lenses: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Single-center, Double-arm, Prospective Clinical Trial to Compare Visual Performance of Non-diffractive Extended Vision and Neutral Aspheric Monofocal Intraocular Lenses (NCT04591054), a randomized na study. The primary outcome is Binocular Intermediate Vision.

2. Clinical Question

3. Trial Design

The registry describes a prospective, randomized, double-masked, parallel-group clinical trial conducted at a single center. It compares two intraocular lens devices: the Extended Vision IOL, described as Vivity, and the Neutral Aspheric Monofocal IOL, described as enVista [MX60E]. The listed conditions are cataract and presbyopia. The registry records enrollment of 56 and reports the trial as completed.

The start date is 2020-11-20, and the primary completion date is 2022-07-26. The registry lists the phase as not applicable. It identifies the primary outcome as binocular intermediate vision, measured as mean logMAR best-distance corrected visual acuity at 66 cm under binocular photopic conditions, with a timeframe of 3 months.

For this outcome, the posted group summaries include 24 participants in the Extended Vision IOL group and 27 in the Neutral Aspheric Monofocal IOL group. These are the reported outcome-group counts; the registry record does not explain the difference between those counts and the enrollment figure. It also does not report the details of recruitment, the randomization sequence, allocation concealment, the procedures used to maintain masking, or reasons participants may not appear in the outcome summaries.

The design identifies the broad comparison but does not by itself establish how every trial procedure was carried out. Specific eligibility criteria, the timing of lens implantation, co-interventions, and the handling of protocol deviations are not reported in the registry record. No secondary outcome results are posted in the record.

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

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 Binocular Intermediate Vision, measured over 3 months.

The primary endpoint is mean binocular best-distance corrected visual acuity at intermediate distance, measured in logMAR at 3 months. Testing is described at 66 cm under binocular photopic conditions. Best-distance correction means visual acuity is assessed with distance correction in place; the endpoint therefore focuses on intermediate acuity under that testing setup rather than uncorrected vision.

Visual acuity is a continuous measure, so the registry reports a group mean and standard deviation for each lens group. In logMAR, lower values correspond to better measured acuity; a negative mean is possible on this scale. The endpoint is used to quantify and compare the groups’ average intermediate visual performance, while the standard deviations describe the spread of individual measurements around each group mean.

A group average does not describe every participant’s result, and a difference in averages does not reveal the full distribution of outcomes. The endpoint also represents one distance, viewing condition, correction, and follow-up time. It does not by itself summarize distance and near acuity, other aspects of vision, or outcomes beyond the stated 3-month timeframe. Those results are not reported in the registry record.

7. Results Posted in the Registry

• Neutral Aspheric Monofocal IOL: mean 0.19 versus -0.02 on control; difference 0.21 (95% CI 0.14 to 0.28), standardized effect d = 1.55; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: each participant’s visual acuity is measured on the logMAR scale, and the reported group-level summaries are means and standard deviations. A mean gives the arithmetic average of the recorded values in a group. A standard deviation describes how dispersed those values are around the mean. Neither summary alone describes the shape of the distribution, possible outliers, or the participant-level pattern of results.

What does the mean difference represent?

The comparison is the Neutral Aspheric Monofocal IOL group mean minus the Extended Vision IOL group mean. The estimated difference is 0.21 logMAR. Under that direction, a positive value means the mean in the comparator group is numerically higher. Because lower logMAR indicates better measured acuity, the group means indicate better average acuity in the Extended Vision IOL group for this endpoint. Keeping the comparison direction explicit matters: reversing the subtraction would reverse the sign without changing the underlying group results.

The difference is an unadjusted comparison of group means. An unadjusted analysis compares the groups without accounting for additional covariates in a regression or other adjustment model. The registry record does not report a covariate-adjusted primary analysis, details of the statistical test used by the trial investigators, or an analysis plan describing how the reported result was selected. The posted inferential comparison can therefore be interpreted as a summary-statistic-based, unadjusted estimate rather than as a documented adjusted model.

What do the p-value and interval address?

The reported p-value is p < 0.001. In general, a p-value evaluates the compatibility of the observed data with a null model that specifies no group difference, given the assumptions of the test. It does not quantify the chance that a treatment is effective, nor does it measure the probability that the observed difference is due to chance. The registry does not report a multiplicity adjustment for this comparison, so the p-value should be read as unadjusted.

A confidence interval gives a range of values compatible with the data and the interval method’s assumptions. For a difference in means, an interval entirely above zero indicates that the estimated difference is positive across the interval. The reported interval is entirely above zero. Its width conveys uncertainty about the size of the difference: a narrower interval indicates greater precision, while a wider interval leaves more uncertainty. The interval does not include every possible source of uncertainty, such as bias from missing data or limitations in trial conduct.

Why does variability matter?

Variation among participants influences how precisely a group mean and the difference between group means can be estimated. The posted standard deviations are 0.13 for the Extended Vision IOL group and 0.14 for the Neutral Aspheric Monofocal IOL group. In general, greater variability makes it harder to distinguish a group difference from the background spread of individual outcomes, all else being equal. The reported standard deviations are descriptive summaries; they do not establish that the outcome distributions are normal or that all assumptions for a particular inferential method were met.

Over-dispersion is a general concern when a model assumes less variability than the data actually contain. If it is present and ignored, standard errors may be too small and confidence intervals too narrow, making evidence appear more precise than it is. The posted outcome is continuous, and the registry record does not report an over-dispersion assessment or identify such a problem. This general concern should not be mistaken for a finding about this trial.

What can be inferred from this analysis?

The inferential result concerns a mean difference in one specified endpoint, at one reported follow-up time, between the two randomized groups. It does not establish that the difference is clinically important, that it applies to other visual outcomes, or that the same pattern would persist at another time. The registry record does not report analyses of participant-level distributions, adjusted estimates, sensitivity analyses, or subgroup results. It also does not report the protocol’s detailed statistical analysis plan. These omissions limit how completely the analysis choices and robustness of the result can be assessed from the registry record alone.

10. Confidence Intervals and Precision

The reported mean difference is 0.21 logMAR, calculated in the direction Neutral Aspheric Monofocal IOL minus Extended Vision IOL. Its confidence interval has both bounds above zero, so the interval is consistent with a positive mean difference under that comparison direction. The interval gives more information than the point estimate alone because it expresses the uncertainty around the estimated difference. The unadjusted p-value is p < 0.001, but the p-value and confidence interval answer different questions: the interval shows a range of plausible effect sizes under its assumptions, while the p-value measures compatibility with a null model.

Precision is not the same as clinical importance. Even an estimate with a confidence interval excluding zero can be too small to matter to patients, or large enough to matter; deciding that requires a meaningful clinical threshold, which is not reported in the registry record. Conversely, a confidence interval does not describe the range of outcomes individual participants experienced. The group means and standard deviations are needed to understand the observed group summaries, but participant-level distributions are not reported.

The precision reflected in the interval also depends on the analysis assumptions and the quality and completeness of the measurements. The registry record does not describe the confidence-interval method, missing-data handling, or an adjusted analysis. The posted interval should therefore be read as uncertainty around the stated unadjusted mean difference, not as a guarantee that all sources of uncertainty have been captured. It pertains to the specified binocular intermediate acuity endpoint at 3 months, not to other outcomes or follow-up times.

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 events. They illustrate sample sizes for detecting specified fractions of the observed mean difference. The assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The trial’s original design assumptions and sample-size justification are not reported in the registry record. These are planning illustrations based on the observed effect, not observed power.

The 80% power column gives the number of participants per arm in the planning calculation intended to provide an 80% chance of detecting the chosen effect under the stated assumptions, if that effect is real and the assumptions hold. The 90% power column describes the corresponding planning target for a 90% chance. These are design concepts, not probabilities that the observed trial result is correct.

For planning at 100% of the observed effect, the figures are 7 participants per arm for 80% power and 9 for 90% power. For planning at 75% of the observed effect, they are 12 and 16 participants per arm, respectively. For planning at 50% of the observed effect, they are 27 and 35 participants per arm, respectively. As the effect to be detected becomes smaller, more participants are needed to achieve the same target power, all else being equal. The figures are illustrative rather than a reconstruction of the trial’s actual design process, and they should be interpreted under the stated planning assumptions.

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 = 0.210; pooled standard deviation σ = 0.135.
2. n = 2 × (1.96 + 0.842)² × 0.135² / 0.210² = 6.5, rounded up to 7 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 <- 0.21                      # observed difference in means
sigma <- 0.135398127982718                     # 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(4591054)
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 = 7 (80% power), 9 (90% power)
 75% of observed effect: n per arm = 12 (80% power), 16 (90% power)
 50% of observed effect: n per arm = 27 (80% power), 35 (90% power)
power.t.test: 7.6 
Simulated power at n = 7 per arm: 0.764 (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. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when more than one outcome, comparison, time point, or analysis is tested. As the number of statistical tests grows, the chance of obtaining at least one apparently notable result by chance can increase. A prespecified hierarchy, adjustment method, or clearly defined primary analysis can help manage this issue. The registry identifies one primary outcome measure, binocular intermediate vision at 3 months, but the detailed statistical analysis plan and any multiplicity strategy are not reported in the registry record.

The trial summary describes a broader visual-performance question covering distance, intermediate, and near acuity. The posted primary outcome result addresses intermediate acuity only, and the record lists no posted secondary outcome results. It is not possible from the registry record to determine whether other outcomes were collected, analyzed, or omitted from reporting, or whether the primary outcome was selected before the data were examined.

The outcome summaries have different reported group counts: 24 for the Extended Vision IOL group and 27 for the Neutral Aspheric Monofocal IOL group. The registry record does not explain this difference or specify whether it reflects missing measurements, exclusions, or another analysis-population definition. Details about the number randomized to each arm, withdrawals, protocol deviations, and reasons for missing outcome data are not reported in the registry record.

The record also does not describe how missing values were handled, whether the analysis followed an intention-to-treat principle, or whether a per-protocol or other population was used. These details matter because excluding participants or handling missing outcomes differently can affect estimates and their uncertainty. The registry record does not report sensitivity analyses to examine whether alternative assumptions about missing data change the result. Without these details, the posted mean difference and interval can be described, but the robustness of the result to missingness and analysis-population choices cannot be assessed from the registry record.

14. 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 0% reporting threshold.

Most frequent non-serious adverse event terms

The registry reports serious adverse events affecting 0 participants in the Extended Vision IOL group and 0 in the Neutral Aspheric Monofocal IOL group. Deaths are reported for 0 participants in each group. For other adverse events, the record reports 3 affected participants in the Extended Vision IOL group and 5 in the Neutral Aspheric Monofocal IOL group. The listed groups at risk are 24 and 27, respectively.

These are counts of participants with reported events, not a complete description of event type, severity, timing, or duration. The registry does not list serious adverse-event terms, and it does not provide further detail about the other adverse events in the registry record reported. The record also does not describe the event-collection method, follow-up completeness, or rules used to classify events as serious or other adverse events. Therefore, the counts describe what is posted but do not establish that no unreported events occurred, or that the groups had equivalent safety profiles. A zero count in the posted serious-event field is not proof of zero risk.

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

The posted result indicates a difference in average binocular intermediate visual acuity between the two lens groups at 3 months. The mean was -0.02 logMAR for the Extended Vision IOL group and 0.19 logMAR for the Neutral Aspheric Monofocal IOL group. The stated comparison, comparator minus intervention, is 0.21 logMAR, and the unadjusted p-value is p < 0.001. Since lower logMAR values indicate better acuity, the observed group means favor the Extended Vision IOL on this specific measure and under the stated testing conditions.

The result does not establish that either device is best for every person, that the average difference is clinically important, or that the same comparison would hold for distance or near acuity. The registry record does not report a threshold for clinical importance, individual-level outcome distributions, or results for those other visual measures. The endpoint is limited to best-distance corrected binocular testing at 66 cm under photopic conditions, at the 3-month timeframe.

A statistically notable comparison is not a complete account of benefit, risk, or patient experience. The record reports no serious adverse events or deaths in either group, and it reports other adverse events in both groups; details about the types and circumstances of those events are not reported. The result also cannot establish longer-term outcomes, because later follow-up results are not reported in the registry record.

The trial is described as randomized and double-masked, but the registry record does not report the operational details needed to evaluate how those safeguards were implemented. Missing-data handling, analysis populations, and a detailed statistical plan are also not reported. The posted result is best understood as an unadjusted comparison of the group means for one endpoint, with uncertainty described by its confidence interval, rather than as a definitive answer to every question about these devices.

16. Why This Trial Matters Statistically

This trial illustrates why statistical interpretation begins with the outcome definition and comparison direction. The endpoint is not a broad judgment of visual performance: it is mean binocular best-distance corrected acuity at intermediate distance, tested at 66 cm under photopic conditions at 3 months. The difference is defined as the neutral aspheric monofocal group minus the extended vision group. Stating both details helps prevent a positive numerical difference from being misread without regard to the scale’s direction.

It also demonstrates why an estimate, its uncertainty, and its context should be considered together. The mean difference is 0.21 logMAR, the reported confidence interval lies above zero, and the unadjusted p-value is p < 0.001. These quantities support a comparison of group averages, but they do not answer whether the difference is important to patients or how much individual outcomes overlap. Clinical importance and individual variability require context beyond a p-value.

The registry reports a randomized, double-masked design, while leaving important implementation and analysis details unreported. Knowing what is not described is part of interpreting a result: the record does not explain the differing outcome-group counts, identify the analysis population, or describe missing-data handling. Those details affect how confidently the posted summaries can be generalized beyond the analyzed measurements.

Finally, the planning illustrations show that sample-size calculations depend on the effect a future study aims to detect. Smaller target effects require more participants under the stated assumptions. Because these calculations use the observed effect and are not the original trial’s documented design justification, they should not be used as evidence that the trial was adequately powered for every relevant outcome.

17. 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 has several limits relevant to this comparison. It reports one primary outcome result, for binocular intermediate visual acuity at 3 months, and no secondary outcome results. Although the study summary describes interest in distance, intermediate, and near acuity, results for distance and near vision are not reported in the registry record. The findings therefore address a narrow part of the broader visual-performance question.

The outcome summaries include different numbers of participants by group, and the record does not explain why. It does not report the number assigned to each group, the analysis population, withdrawals, missing measurements, exclusions, or how missing data were handled. Without those details, it is not possible to assess whether the posted outcome summaries represent all randomized participants or whether missingness could have affected the comparison.

Although the study is described as randomized and double-masked, the randomization and masking procedures are not detailed. The registry record also does not report participant eligibility criteria, baseline characteristics, the statistical analysis plan, the method used for the confidence interval, or whether any covariate-adjusted or sensitivity analyses were conducted. The clinical importance threshold for the logMAR difference is not reported.

The safety information is limited to counts for serious adverse events, other adverse events, and deaths, with no serious-event terms listed and no descriptions of the other events. The record does not describe the method or completeness of adverse-event collection. Finally, the primary endpoint is reported at 3 months; longer-term results are not reported in the registry record. These gaps constrain assessment of reproducibility, generalizability, and the completeness of the outcome picture.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Single-center, Double-arm, Prospective Clinical Trial to Compare Visual Performance of Non-diffractive Extended Vision and Neutral Aspheric Monofocal Intraocular Lenses — NCT04591054.
• Registry record last updated 2023-08-21; status last verified 2023-08.
• Results first posted 2023-08-21.
• 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.

21. Record Summary

The registry record describes a completed, single-center, prospective, randomized, double-masked, parallel-group trial comparing Vivity, an Extended Vision IOL, with enVista [MX60E], a Neutral Aspheric Monofocal IOL. It lists cataract and presbyopia as conditions and records enrollment of 56.

The posted primary outcome is mean binocular best-distance corrected visual acuity at intermediate distance, measured at 66 cm under photopic conditions at 3 months. The group means are -0.02 logMAR and 0.19 logMAR, with a mean difference of 0.21 logMAR in the comparator-minus-intervention direction. The unadjusted p-value is p < 0.001, and the reported confidence interval lies above zero.

The registry reports 0 serious adverse events and 0 deaths in each group, with other adverse events reported for 3 participants in the Extended Vision IOL group and 5 in the Neutral Aspheric Monofocal IOL group. No secondary outcome results are posted. Details on missing data, analysis populations, and the trial’s original sample-size justification are not reported in the registry record.