A Study to Evaluate the Feasibility of a High Add Multi Focal Contact Lens: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Study to Evaluate the Feasibility of a High Add Multi Focal Contact Lens (NCT01518868), a randomized na study. The primary outcome is Visual Acuity.

2. Clinical Question

3. Trial Design

This was a randomized, double-masked crossover study sponsored by Bausch & Lomb Incorporated. Its status is completed. The record lists the study start as 2012-01 and primary completion as 2012-02. The trial had no applicable phase designation. A total of 126 participants were enrolled, and the primary visual-acuity outcome description reports 238 eyes assessed.

In a crossover study, participants receive more than one treatment condition, allowing outcomes under those conditions to be compared within the same participant or eye. Here, the record states that participants or eyes received both treatment groups. This design feature is relevant when interpreting the comparison: measurements from the same participant or eye may be related, rather than independent. The registry record does not report the treatment sequences, period structure, washout interval, or the statistical method used to account for within-participant or within-eye correlation.

The two device interventions were the investigational multifocal high-add soft contact lens and the PureVision multifocal contact lens. Both were described for daily wear. The primary outcome was assessed at two weeks of follow-up. Symptoms or complaints were listed as a secondary outcome. The record does not report additional details about the duration of each treatment period, the number of visits, or how symptoms and complaints were measured.

Random allocation means treatment assignment followed a random process, while double masking means the record describes the study as masked at two levels. The identities of the masked parties and the procedures used to maintain masking are not reported in the registry record. The design and enrollment are known, but the registry record does not give the original sample-size justification or a detailed statistical analysis plan.

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 238 eyes assessed for visual acuity for this outcome measure. 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 in this cross-over study.

6. Primary Endpoint

The registry lists the primary outcome as Visual Acuity, measured over At 2 weeks follow up.

The primary endpoint was visual acuity at two weeks of follow-up. It was measured as distance, high-contrast acuity using the logarithm of the minimum angle of resolution, or logMAR. This is a continuous measure: each assessed eye contributes a numerical value, and the group summaries describe the average and variability of those values.

Visual acuity is used in this study because the stated objective was to evaluate product performance of two multifocal contact lenses. A continuous endpoint retains more information about the measured level of acuity than a simple classification into broad outcome categories. In general, logMAR expresses visual acuity on a logarithmic scale; lower values correspond to better measured acuity. That scale interpretation does not, by itself, establish whether a difference between groups is important to participants.

The registry record reports 119 eyes for each treatment group, with mean values of 0.079 logMAR for the investigational lens and 0.09 logMAR for PureVision. The outcome description says participants or eyes received both groups, so these counts should be understood in the context of a crossover rather than as two independent sets of participants. The record does not report a threshold for a meaningful difference in acuity, or details about the testing procedure beyond distance high-contrast logMAR measurement.

7. Results Posted in the Registry

• PureVision Contact Lens: mean 0.09 versus 0.08 on control; difference 0.01 (95% CI -0.01 to 0.04), standardized effect d = 0.11; z-test p = 0.380.

8. Statistical Interpretation

9. Statistical Methods Explained

The endpoint is a continuous outcome, so the central summaries are means and standard deviations. A mean gives the arithmetic average of the observed logMAR values, while a standard deviation describes how dispersed individual measurements are around that average. For the investigational lens, the mean was 0.079 and the standard deviation was 0.102. For PureVision, the mean was 0.09 and the standard deviation was 0.091. These summaries describe the observed measurements, but they do not show how the crossover structure was handled in the comparison.

What does a mean difference represent?

The posted comparison is a mean difference of 0.011 logMAR, expressed as PureVision relative to the investigational lens. A positive value in this direction means the PureVision group mean is numerically higher in the posted summary. Because lower logMAR values correspond in general to better measured acuity, the direction of the numerical difference should be read with that scale convention in mind. A difference in averages is not by itself a judgment about clinical importance; the registry record does not report a threshold for a meaningful difference.

What does the p-value tell the reader?

The unadjusted p-value is 0.38. In general, a p-value describes how unusual data at least as incompatible with a no-difference model would be if that model and the test assumptions were correct. It is not the probability that there is no difference, and it does not measure the size or importance of the observed difference. A p-value should be considered alongside the estimate, confidence interval, study design, and analysis assumptions.

The record labels the comparison unadjusted, and the number of posted analyses is zero. It does not describe a sponsor-reported inferential model or adjustments. The registry record also does not report whether the p-value came from a paired analysis, an analysis treating observations as independent, or another method. No claim about the appropriateness of a particular method can be made from the available description alone.

Why does crossover structure matter?

In a crossover study, an individual may contribute outcomes under both treatments. Those outcomes can be correlated because they come from the same person or eye. In general, a paired analysis uses the within-person or within-eye relationship, which can affect the estimated uncertainty compared with an analysis that treats observations as unrelated. A suitable crossover analysis may also need to consider treatment sequence and period effects. The registry record confirms crossover allocation but does not report the sequence, periods, or modeling approach. The posted summary comparison therefore cannot, on its own, establish how those design features were incorporated.

What is the role of a confidence interval?

A confidence interval gives a range of effect estimates compatible with the observed data under the method's assumptions. The interval for the mean difference extends from -0.014 to 0.036 in the registry comparison, crossing zero. In general, an interval crossing zero means the data are compatible with no mean difference as well as with differences in either direction. The interval does not resolve clinical importance because no meaningful-difference threshold is reported. Its interpretation also depends on the underlying analysis being appropriate for the design.

What is not described?

The registry record does not report the original statistical analysis plan, the analysis population, the handling of missing outcome data, or the method used to account for the crossover design. It also does not report a sample-size justification, interim analyses, or a multiplicity strategy. These omissions matter because choices about population, missingness, within-participant dependence, and multiple outcomes can affect both estimates and uncertainty. They should not be filled in by assumption. The numerical comparison can be described as posted, while the exact inferential procedure behind it remains not reported in the registry record.

In general, standard deviations and confidence intervals answer different questions. The standard deviations characterize observed dispersion in each treatment group; the confidence interval characterizes uncertainty in the estimated between-treatment difference under a statistical method. The reported means and standard deviations do not provide enough information to reconstruct every design-specific analysis decision. Since the study is crossover, a calculation based only on group-level summaries may not preserve the pairing of measurements. The registry comparison is therefore most cautiously read as a posted unadjusted estimate whose relationship to the crossover analysis is not explained.

10. Confidence Intervals and Precision

The reported mean difference is 0.011 logMAR for PureVision relative to the investigational lens. The confidence interval has a negative lower endpoint and a positive upper endpoint, so it includes zero and values on both sides of zero. This indicates that the estimate is not precise enough to confine the plausible direction of the difference to one side. The interval also permits differences larger than the point estimate in either direction.

Precision concerns the range of values compatible with the data and the analysis assumptions, not whether the estimated difference is important. The registry record does not give a threshold for a clinically meaningful difference in visual acuity. Consequently, even a narrower interval would need to be interpreted against an appropriate threshold before drawing conclusions about practical importance.

The unadjusted p-value of 0.38 is consistent with the interval's inclusion of zero, but the interval is more informative about the range of effect estimates than the p-value alone. The group standard deviations, 0.102 and 0.091, describe variability in observed values and do not replace the uncertainty interval for the treatment contrast.

Precision also depends on the analysis matching the study design. Participants or eyes received both treatment groups, but the registry record does not describe whether the comparison accounts for the resulting within-participant or within-eye correlation. The reported interval should therefore be interpreted as the interval attached to the posted comparison, with the analysis details 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 expressed as participants per arm, not as total events. The planning illustration assumes a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. It considers effects set at 100%, 75%, and 50% of the observed effect. These are planning assumptions for an illustration based on the observed effect; the registry record does not report the trial's own original design assumptions.

The 80% power column gives the number of participants per arm that the illustration estimates would be needed for an 80% chance of detecting the specified effect under those assumptions. The 90% power column gives the corresponding number for a 90% chance. These are conditional planning quantities, not predictions about what happened in the completed trial. The entries are 1,213 and 1,623 participants per arm for 100% of the observed effect; 2,155 and 2,885 for 75%; and 4,849 and 6,491 for 50%.

The values increase as the assumed effect becomes smaller: a smaller difference is harder to distinguish from random variation, so the illustration calls for more participants. These figures are not observed power. They do not describe the trial's achieved power, its actual enrollment target, or the reason the trial enrolled 126 participants. The registry record does not report the original sample-size justification. The assumptions also specify a two-arm equal-allocation planning calculation, while the clinical study itself is described as a crossover; readers should not treat the illustration as a reconstruction of the trial's own design planning.

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 = 0.011; pooled standard deviation σ = 0.097.
2. n = 2 × (1.96 + 0.842)² × 0.097² / 0.011² = 1,212.0, rounded up to 1,213 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 <- 0.011                      # observed difference in means
sigma <- 0.0966566086721441                     # 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(1518868)
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 = 1,213 (80% power), 1,623 (90% power)
 75% of observed effect: n per arm = 2,155 (80% power), 2,885 (90% power)
 50% of observed effect: n per arm = 4,849 (80% power), 6,491 (90% power)
power.t.test: 1213 
Simulated power at n = 1,213 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. Multiplicity, Missing Data and Analysis Populations

The registry record lists visual acuity as the primary outcome and symptoms or complaints as a secondary outcome. It reports two outcome measures in total and one posted secondary outcome. The primary comparison discussed in the registry record concerns visual acuity at two weeks. Detailed results for the symptoms or complaints outcome are not included in the record.

Multiplicity arises when several outcomes, time points, or comparisons are examined. In general, conducting multiple tests can increase the chance that at least one result appears notable by chance. Statistical plans can address this issue in different ways, but the registry record does not report a multiplicity strategy or adjustment. The unadjusted p-value of 0.38 should therefore be understood as unadjusted, not as the result of a stated family-wise or other multiplicity procedure.

Information about missing data is also not reported in the registry record. The outcome description gives 238 eyes assessed, with 119 observations for each treatment group, but it does not explain whether all enrolled participants contributed to the primary outcome, how incomplete measurements were handled, or whether any imputation or sensitivity analysis was used. Enrollment was 126 participants, and the outcome counts are stated in eyes; these units are not interchangeable. The record does not provide a participant-level flow or an accounting of missing observations.

The analysis population is not reported in the registry record. There is no description of whether the primary comparison included all randomized participants, only participants who completed both treatment conditions, or another defined group. Nor does the record describe how the crossover structure was incorporated into the analysis. These details are important for understanding which observations contributed to the estimate and how uncertainty was calculated.

The record lists zero posted analyses. This does not establish that no analysis was conducted; it means the registry record does not supply a detailed analysis description. Accordingly, the stated outcome and numerical comparison can be reported, while conclusions about missing-data handling, analysis populations, and multiplicity control remain unavailable.

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 the investigational contact lens, the record lists 126 participants at risk for serious adverse events and zero affected. For PureVision, it also lists 126 at risk and zero affected. The record likewise lists 126 at risk for other adverse events in each treatment group and zero affected in each. These are the posted counts for the categories named in the registry record.

Zero affected in these categories means no events were recorded in the posted counts; it does not demonstrate that the risk is absent. The record does not give additional details about event definitions, collection procedures, exposure time, or the handling of events across the crossover treatment periods. Since the same participants may have received both treatment groups, the two group counts should not automatically be read as independent groups of different people.

Deaths are not reported in the registry record. The safety figures describe event counts in this record and do not provide enough information to compare safety more broadly or to characterize uncommon events. No medical advice or treatment recommendation follows from these counts.

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

The posted data describe average distance high-contrast logMAR visual acuity after two weeks for two contact-lens conditions in a randomized, double-masked crossover study. The mean was 0.079 for the investigational lens and 0.09 for PureVision. The reported mean difference was 0.011 logMAR, with an unadjusted p-value of 0.38 and a confidence interval extending across zero.

These results do not establish that the lenses have identical visual-acuity results. The interval includes values in both directions, and the point estimate is only one value within that range. Nor do the data establish that one lens has an important advantage. The registry record does not report a threshold for a meaningful difference, and the precision of the comparison leaves uncertainty about the direction and magnitude of any difference.

The study's crossover design is relevant: participants or eyes received both treatment groups, which can create correlated measurements. The registry record does not report the statistical method used to account for that feature. It also does not describe missing-data procedures, analysis populations, multiplicity handling, or the original sample-size rationale. These omissions limit how fully the comparison can be evaluated from the registry record.

Interpretation is also limited to the outcome and time point reported. Visual acuity was assessed at two weeks, and symptoms or complaints were listed as a secondary outcome, but detailed secondary results are not reported in the record. The findings do not by themselves establish broader product performance, durability beyond the stated follow-up, or outcomes in groups not described in the record. They are best read as a posted short-term numerical comparison with uncertainty, not as a definitive claim of equivalence or superiority.

16. Why This Trial Matters Statistically

This study illustrates why the design and the numerical estimate must be read together. A crossover design allows outcomes under both lens conditions to be recorded in the same participant or eye, but that structure creates a dependence between observations. A comparison that accounts for the pairing may have different uncertainty from one that treats observations as independent. The registry record confirms crossover treatment but does not report how the analysis handled the pairing, making that statistical detail important to interpretation.

It also illustrates the difference between a point estimate and its precision. The mean difference is 0.011 logMAR, while the confidence interval spans negative and positive values. The estimate alone gives a direction and magnitude for the observed contrast; the interval conveys that a wider range remains compatible with the data and method. The unadjusted p-value of 0.38 cannot replace that information or establish equivalence.

The planning illustration provides another useful distinction: sample-size calculations depend on a chosen effect size and assumptions about allocation, significance level, and the statistical approximation. The displayed planning values change as the target fraction of the observed effect changes. They are planning quantities, not an explanation of the actual enrollment or evidence that the study was designed around those assumptions.

Finally, an outcome record can identify a primary measure without documenting the full analysis path. Missing-data methods, the analysis population, multiplicity handling, and crossover-specific modeling are not reported. Recognizing these gaps is part of sound statistical reading: numerical results can be described accurately while the limits of the available analysis documentation remain explicit.

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 provides limited detail about the study procedures and statistical analysis. It identifies randomization, double masking, and crossover design, but does not report treatment sequences, period definitions, or any washout interval. It also does not identify which parties were masked or explain how masking was maintained. Such details can matter when evaluating possible period, sequence, or measurement effects.

The primary outcome description reports 238 eyes assessed, while enrollment is stated as 126 participants. It gives 119 eyes for each treatment condition and says participants or eyes received both groups. The record does not provide a participant flow, clarify the relationship between eyes and participants in the analysis, or describe whether outcomes from two eyes of the same participant were modeled as correlated. The analysis method for the crossover structure is not reported.

The registry record does not report the original sample-size justification, a detailed statistical analysis plan, missing-data procedures, analysis populations, or multiplicity control. The posted comparison is unadjusted, but its exact test or model is not described. The record lists symptoms or complaints as a secondary outcome but does not supply detailed results for it in the outcome information.

Follow-up for the primary endpoint is stated as two weeks. The record does not provide further follow-up results or a meaningful-difference threshold for visual acuity. It also does not give detailed adverse-event definitions or exposure-time information, and deaths are not reported in the registry record. These limitations constrain interpretation of the posted short-term comparison and safety counts.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: A Study to Evaluate the Feasibility of a High Add Multi Focal Contact Lens — NCT01518868.
• 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

The registry record describes a completed randomized, double-masked crossover study of an investigational multifocal high-add soft contact lens and a PureVision multifocal contact lens for presbyopia. Enrollment was 126 participants. The primary outcome was distance high-contrast logMAR visual acuity at two weeks, assessed in 238 eyes.

The mean values were 0.079 logMAR for the investigational lens and 0.09 for PureVision. The posted mean difference for PureVision relative to the investigational lens was 0.011, with an unadjusted p-value of 0.38 and a confidence interval spanning zero. The record lists symptoms or complaints as a secondary outcome, but detailed results are not reported in the registry record.

Zero serious and zero other adverse events were recorded among 126 at risk in each treatment group; deaths are not reported. Details of crossover analysis, missing-data handling, analysis populations, multiplicity, and the original sample-size justification are not reported.