A Study to Evaluate the Product Performance of a Low Add MultiFocal Soft Contact Lens: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Study to Evaluate the Product Performance of a Low Add MultiFocal Soft Contact Lens (NCT01539694), a randomized na study. The primary outcome is Visual Acuity.

2. Clinical Question

This is a product-performance comparison rather than a registry record of a broad clinical-outcome evaluation. Its primary endpoint is a continuous measurement of visual acuity. The posted arm means and the mean difference describe the measured scores in the outcome population; they do not by themselves establish whether a difference matters to participants or how it relates to other visual experiences.

The study also lists symptoms and complaints as a secondary outcome. The record reports two outcome measures but does not post a secondary-outcome analysis. Therefore, the primary comparison is the only posted efficacy-style numerical result described in detail in this record. The record does not report a separate research question for symptoms or complaints.

3. Trial Design

The study is listed as randomized, double-masked, and crossover. It enrolled 126 participants and is marked completed. The registered phase is NA. The stated objective was to evaluate the product performance of an investigational multifocal low-add soft contact lens. The listed condition is presbyopia.

The two devices were the investigational LD118033 multifocal low-add soft contact lens and the PureVision multifocal low-add soft contact lens. Both are described as daily-wear lenses. In a crossover design, participants receive both treatment conditions at different points in the study rather than remaining in only one condition. The registry record confirms that participants and eyes received both treatment groups, but it does not report the treatment sequence, the length of each treatment period, or whether a washout period was used.

The study began in 2012-01, and primary completion is recorded as 2012-02. The primary outcome was assessed at 1 week follow up. The record reports 124 eligible, dispensed participants and 248 eyes for the primary outcome population. Each posted arm summary has an n of 124. Because both treatment groups were received by participants and eyes, the two arm summaries should not be read as independent groups of different participants.

Although randomization and masking are recorded, the method used to generate or conceal the allocation, who was masked, and how masking was maintained are not reported in the registry record. The protocol details and original statistical analysis plan are also not reported in the registry record. The design label alone does not establish which statistical method was used to account for the paired nature of crossover data.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Analysis population for the primary outcome, as defined in the registry: There were 124 eligible, dispensed participants (248 eyes). Participants/eyes received both treatment groups.

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: Demography was collected for 124 eligible, dispensed participants. Participants received both treatment groups.

6. Primary Endpoint

The registry lists the primary outcome as Visual Acuity, measured over At 1 week follow up.

The primary endpoint is visual acuity measured at 1 week follow up. The record describes the assessment as distance high-contrast logarithm of the minimum angle of resolution, or logMAR. It is a continuous outcome, and the posted summaries use means and standard deviations.

A continuous measure can retain gradations in the observed response rather than reducing results to categories such as improved or not improved. Reporting a mean describes the central value of the observations in an arm, while the standard deviation describes how dispersed individual observations are around that mean. These summaries help characterize the recorded visual-acuity scores, but they do not show the full distribution of scores or how results varied within each participant.

Distance high-contrast visual acuity is used as a direct measurement of one aspect of visual performance under the assessment conditions described in the record. It does not, on its own, capture every aspect of vision, daily functioning, comfort, or satisfaction. The registry lists symptoms and complaints as a secondary outcome, but does not post a numerical analysis for that outcome.

The record does not specify a threshold for a clinically meaningful change in logMAR, nor does it explain how the endpoint was selected or how it was intended to relate to participants’ experience. The endpoint therefore supports a statistical comparison of the measured scores, while the clinical importance of any observed difference remains uncharacterized in the registry record.

7. Results Posted in the Registry

• PureVision Multifocal Contact Lens: mean 0.01 versus 0.02 on control; difference -0.02 (95% CI -0.04 to 0.00), standardized effect d = -0.24; z-test p = 0.054.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary measure is continuous, so the registry reports a mean and standard deviation for each lens condition. In general, a mean is the arithmetic center of a set of measurements. A standard deviation describes the spread of observations around that center. Neither statistic alone tells whether the observations are symmetric, whether there are unusual values, or how measurements from the same participant relate across conditions.

The posted arm means are 0.023 for LD118033 and 0.005 for PureVision, with standard deviations of 0.078 and 0.069, respectively. The comparison is reported as a mean difference of -0.018 for PureVision relative to LD118033. A mean difference expresses the contrast in the original measurement units, logMAR in this case. It is therefore directly interpretable on the scale of the endpoint, although the record does not give a clinical-importance threshold for that scale.

The record also reports an unadjusted p-value of 0.054 and a confidence interval for the mean difference. An unadjusted p-value is the result before any adjustment for multiple comparisons; whether any adjustment was intended or performed is not reported in the registry record. In general, a p-value evaluates how unusual data at least as discordant with a null hypothesis would be under the model used. It is not a measure of effect size, clinical importance, or the probability that a result happened by chance.

The confidence interval communicates uncertainty around the estimated mean difference. Its bounds span values on both sides of zero. In general, intervals are useful because they show a range of effect sizes compatible with the data and the analysis assumptions, rather than reducing interpretation to a threshold test. Their validity depends on the analysis model and the way observations are treated. The registry record does not report the model used to construct this interval.

The crossover structure has an important statistical implication. Measurements from the same participant under two conditions are usually correlated. A paired analysis can use the within-participant contrast and its variability; an analysis that treats the conditions as independent may not represent that structure appropriately. This is a general consideration for crossover studies, not a statement about which method the investigators used. The registry record does not report whether the posted comparison was paired, how the analysis handled repeated measurements, or whether period, sequence, or carryover effects were assessed.

The posted comparison includes a pooled standard deviation of 0.074 and a standardized effect estimate of -0.244. A standardized effect expresses a mean contrast relative to a measure of variability, which can help describe scale-free magnitude. However, the registry record does not explain the exact calculation or its role in the analysis. These values should not be mistaken for the study’s original statistical design assumptions or for a clinical threshold.

Over-dispersion is a general concern when the observed variability is greater than the model assumes. If that occurs, uncertainty estimates can be too narrow and tests can appear more decisive than warranted. The registry record does not report an assessment of over-dispersion, and the outcome is a continuous measure rather than a count outcome for which over-dispersion is often discussed. More generally, checking whether a model’s assumptions fit the observed data is important, but the registry does not describe diagnostic checks.

The planning illustration uses the observed effect as its starting point and applies a two-sided significance level of 0.05, equal allocation, and a normal approximation. It considers planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For those scenarios, the listed participants per arm for 80% power are 263, 468, and 1,051, respectively. The participants per arm for 90% power are 352, 626, and 1,407, respectively. These are planning illustrations, not the original trial’s design justification; the trial’s original sample-size assumptions are not reported in the registry record.

In general, power is the chance that a planned analysis will reject a null hypothesis under a specified alternative and the assumptions used for planning. The planning columns describe target power levels under the stated assumptions; they do not describe the probability that the observed result is true. Smaller effects require more participants to detect under otherwise similar assumptions because they are harder to distinguish from random variation. The registry record does not report the original sample-size justification, the statistical analysis plan, or the analysis population rules.

The numerical summaries cannot fully describe the data structure of a crossover trial. Participant-level paired differences, period-specific values, missingness patterns, and protocol deviations could affect interpretation, but these details are not reported in the registry record. The methods used for the posted primary comparison therefore remain incompletely described.

10. Confidence Intervals and Precision

The reported mean difference is -0.018, with a confidence interval whose lower bound is negative and whose upper bound is positive. Because zero lies within the interval, the data do not rule out no mean difference under the interval’s analysis assumptions. The interval also includes values in either direction, so the result is not precise enough to pin down a single direction of difference.

A confidence interval is a range of estimates compatible with the data and the statistical method used to construct it. In general, a narrower interval indicates greater precision, while a wider interval indicates greater uncertainty. Precision is distinct from clinical importance: even a precisely estimated difference would need to be interpreted against a meaningful threshold, and the registry record does not report such a threshold for this outcome.

The p-value of 0.054 is consistent with the interval’s inclusion of zero. The registry record presents the p-value as unadjusted. It does not report the details of the model or whether the interval and test account for the crossover pairing. Since participants and eyes received both lens conditions, the relationship between repeated measurements matters to uncertainty estimates.

The arm-level standard deviations describe spread within each condition, but precision for a crossover contrast also depends on the variability of within-participant differences. That paired variability is not reported. The confidence interval should therefore be interpreted as the registry’s reported uncertainty summary, with the analysis details and the underlying paired data not reported in the registry record.

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 are planning illustrations based on the observed effect, rather than the trial’s own design calculation. The stated assumptions 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 the stated fraction of the observed effect.

For planning at 100% of the observed effect, the figures are 263 participants per arm for 80% power and 352 participants per arm for 90% power. For planning at 75% of the observed effect, the figures are 468 participants per arm for 80% power and 626 participants per arm for 90% power. For planning at 50% of the observed effect, the figures are 1,051 participants per arm for 80% power and 1,407 participants per arm for 90% power.

The 80% power column means the number of participants per arm estimated to give an 80% chance of detecting the specified effect under the planning assumptions, if that effect and those assumptions hold. The 90% power column expresses the corresponding target at a higher probability of detection. Smaller effects need more participants because they are harder to distinguish from random variation under otherwise similar assumptions.

These figures are not observed power. They do not show the probability that the trial’s result is correct, and they do not establish what sample size the investigators originally intended. The original design assumptions and sample-size justification are not reported in the registry record. The posted outcome population and the planning illustrations serve different purposes: one describes the recorded trial results, while the other explores sample sizes under stated hypothetical 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 = -0.018; pooled standard deviation σ = 0.074.
2. n = 2 × (1.96 + 0.842)² × 0.074² / -0.018² = 262.7, rounded up to 263 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 <- -0.018                      # observed difference in means
sigma <- 0.0736376262518015                     # 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(1539694)
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 = 263 (80% power), 352 (90% power)
 75% of observed effect: n per arm = 468 (80% power), 626 (90% power)
 50% of observed effect: n per arm = 1,051 (80% power), 1,407 (90% power)
power.t.test: 263.7 
Simulated power at n = 263 per arm: 0.799 (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

The registry record lists visual acuity as the primary outcome and symptoms/complaints as a secondary outcome. It reports two outcome measures, but only the primary outcome has a posted numerical summary in the record. A posted secondary-outcome analysis is not reported in the registry record.

When a study evaluates multiple outcomes, time points, or comparisons, the chance of at least one apparently unusual result can increase. Statistical procedures that account for multiple testing may be used, but the registry record does not report whether any multiplicity adjustment was planned or applied. The posted p-value is identified as unadjusted. Without a prespecified analysis plan, it is not possible to determine from the registry record how the primary and secondary outcomes were prioritized or how multiple analyses were handled.

The record identifies 124 eligible, dispensed participants and 248 eyes for the primary outcome population, and states that participants and eyes received both treatment groups. It does not report how many participants or eyes contributed valid measurements at each assessment, how missing observations were handled, or whether any participants were excluded from the primary analysis after dispensing. The reasons for any missing data are not reported in the registry record.

The analysis population definitions are not reported in the registry record. In particular, the record does not describe whether the primary analysis followed an intention-to-treat principle, included only participants who completed both treatment periods, or used another population definition. The record also does not explain how deviations from assigned treatment, incomplete crossover participation, or data from both eyes were managed.

These gaps matter because outcome availability and analysis-population choices can affect estimates and uncertainty. For a crossover study, details about pairing, treatment sequence, period, and any carryover assessment are also relevant. Those methods are not reported in the registry record, so the posted summary cannot resolve how these considerations were handled.

14. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

For LD118033, the record lists 126 participants at risk for serious adverse events and reports 0 serious adverse events. It also lists 126 participants at risk for other adverse events and reports 0 other adverse events. For PureVision, the corresponding figures are 126 at risk for serious adverse events with 0 reported, and 126 at risk for other adverse events with 0 reported.

These are the registry’s recorded counts for the listed adverse-event categories. They should not be interpreted as evidence that no adverse experiences of any kind occurred, because the record reports only the event categories and counts shown. The record does not provide event-term detail for non-serious events, and the serious-event terms list is empty.

Deaths are recorded as null for both groups, so a death count is not reported in the registry record. The adverse-event summaries do not include enough detail to assess event ascertainment, severity beyond the serious/non-serious distinction, timing, or attribution. The crossover design also means the same participants received both lens conditions; the registry record does not explain how exposure periods were considered in the safety summaries.

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

The primary result is a comparison of mean distance high-contrast visual-acuity scores at 1 week follow up. The posted means are 0.023 for LD118033 and 0.005 for PureVision, and the reported mean difference is -0.018. The interval includes zero and the unadjusted p-value is 0.054. Together, these summaries indicate that the registry reports a small numerical difference with uncertainty that includes no difference.

This result does not establish that the two lenses are equivalent. Demonstrating equivalence or non-inferiority generally requires a prespecified margin and an analysis designed for that question; such a margin and analysis are not reported in the registry record. Nor does the result establish that one lens is clinically superior. The record does not state a clinically meaningful difference threshold or provide an interpretation of the observed contrast in relation to participants’ experiences.

The finding is limited to the recorded endpoint, measurement conditions, and follow-up. Visual acuity is one aspect of visual performance, and it does not fully represent comfort, symptoms, satisfaction, or functioning in daily activities. Symptoms/complaints are listed as a secondary outcome, but the numerical analysis is not reported in the registry record.

The registry does not report the statistical method used for the primary comparison, the handling of within-participant correlation, missing data, or analysis populations. Those omissions limit the assessment of how robustly the reported uncertainty reflects the crossover design. The posted summary can describe the observed numerical contrast, but it cannot answer questions that require unreported protocol details or participant-level results.

The most supportable reading is therefore descriptive and cautious: the registry posts a mean difference of -0.018, an interval spanning zero, and an unadjusted p-value of 0.054 for the primary outcome. This alone does not establish a clinically meaningful effect, equivalence, or a definitive conclusion about either lens.

16. Why This Trial Matters Statistically

This trial illustrates why a statistical comparison must be read alongside the design. A crossover study exposes participants to both conditions, creating related observations rather than two wholly separate participant groups. Recognizing that structure is essential when interpreting standard errors, confidence intervals, and tests. The registry identifies the crossover design and confirms receipt of both treatment groups, but does not report the method used to model that relationship.

The result also illustrates the difference between an estimated effect, its uncertainty, and its clinical meaning. The mean difference is reported on the logMAR scale, while its confidence interval includes zero. The p-value is 0.054, but a threshold-based reading of that value cannot replace consideration of the interval, the endpoint’s scale, the design, or a clinically meaningful threshold. No such threshold is reported in the registry record.

Planning illustrations can help show how sample-size needs vary with the effect a study aims to detect. The listed figures rise as the assumed effect becomes smaller, and the higher power target also entails larger planning counts. These are hypothetical planning calculations based on the observed effect, not evidence that the completed trial had a particular probability of finding an effect or that its original design used those assumptions.

Finally, the record demonstrates the value of complete reporting. Details on crossover analysis, missing observations, multiplicity, and the listed secondary outcome would help readers assess the result’s reliability and scope. Where these details are absent, statistical interpretation should remain tied to the posted summaries rather than extending to claims the registry cannot support.

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 primary outcome population is described as 124 eligible, dispensed participants and 248 eyes, while the record lists 124 observations for each treatment group. It does not explain the relationship between these analysis counts, the handling of two eyes from a participant, or whether both eyes contributed in the same way to the analysis. This limits interpretation of the effective amount of independent information in the summaries.

The study is a crossover, but treatment order, period-specific results, washout details, and analysis of possible period or carryover effects are not reported in the registry record. The record also does not specify the statistical model used for the mean difference or whether it accounted for the repeated measurements on participants and eyes. These are particularly relevant uncertainties for the interval and p-value.

The registry does not report a clinical-importance threshold for the visual-acuity measure, a complete analysis plan, or details about missing data and exclusions. The secondary outcome of symptoms/complaints is listed, but its numerical results are not reported. The record gives adverse-event counts but does not report deaths as numerical counts or describe event timing, severity detail beyond the categories, or ascertainment methods.

The posted follow-up for the primary endpoint is 1 week. Longer-term outcome information is not reported in the registry record. The record also does not report the original sample-size justification or the assumptions used in the trial’s own planning. The sample-size illustrations based on the observed effect should not be taken as a substitute for that missing design information.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: A Study to Evaluate the Product Performance of a Low Add MultiFocal Soft Contact Lens — NCT01539694.
• Registry record last updated 2020-09-30; status last verified 2020-09.
• Results first posted 2020-09-30.
• 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

NCT01539694 is a completed randomized, double-masked crossover study of an investigational LD118033 low-add multifocal soft contact lens and a PureVision multifocal soft contact lens for participants with presbyopia. Enrollment was 126. The primary endpoint was distance high-contrast visual acuity in logMAR at 1 week follow up.

The primary-outcome population is described as 124 eligible, dispensed participants and 248 eyes, with both treatment groups received by participants and eyes. The posted means were 0.023 for LD118033 and 0.005 for PureVision. The mean difference for PureVision compared with LD118033 was -0.018, with a confidence interval spanning zero and an unadjusted p-value of 0.054.

Symptoms/complaints were listed as a secondary outcome, but a numerical secondary analysis is not reported in the registry record. The record reports 0 serious and 0 other adverse events for each lens group, with deaths recorded as null. Details of the crossover analysis, missing-data handling, multiplicity, and original sample-size justification are not reported in the registry record.