Multifocal Contact Lens Use in Previous Contact Lens Wearers With Near Vision Demands: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Multifocal Contact Lens Use in Previous Contact Lens Wearers With Near Vision Demands (NCT00965237), a randomized na study. The primary outcome is Overall Satisfaction With the Lenses.

2. Clinical Question

The study used a crossover arrangement: one sequence began with multifocal lenses and moved to single-vision lenses plus reading glasses, while the other sequence used the reverse order. This means the comparison concerns the two lens regimens as experienced in the study, not simply two parallel groups assigned to remain on separate treatments. The registry record does not report how the statistical analysis accounted for the paired observations or the sequence in which regimens were worn.

The primary outcome was a retrospective subject rating of overall satisfaction, recorded on a numerical scale from 1, completely dissatisfied, to 100, excellent and completely satisfied. The result therefore addresses reported satisfaction in this study and under its stated one-week wear timeframe. It does not, by itself, answer broader questions about vision performance, long-term use, or other outcomes that were not posted as secondary measures.

3. Trial Design

This was a randomized, unmasked crossover study of multifocal contact lens use in previous contact lens wearers with near-vision demands. The registry lists the study condition as presbyopia and describes its purpose as evaluating multifocal lenses in people who had discontinued contact lens wear because of age-related near-vision demands. The study is listed as completed, with a reported enrollment of 16.

Participants followed one of two sequences. In one, lotrafilcon B multifocal contact lenses were worn first, followed by lotrafilcon B single-vision contact lenses with over-reader spectacles. In the other, single-vision contact lenses with over-reader spectacles were worn first, followed by multifocal lenses. Both contact lens products were described as bilateral and daily wear; the spectacles were worn as needed. The crossover structure allows the same study population to experience both regimens, but the registry record does not explain the statistical model used to handle the within-subject relationship, sequence, or any period effects.

Randomization was listed as the allocation method, and masking was listed as none. The study is listed as phase NA. Its start is recorded as 2009-08 and its primary completion as 2009-12. CIBA VISION is listed as the sponsor. The registry describes a per-protocol primary analysis and posts results for both lens regimens, with 16 observations reported for each. The record does not report additional details about the randomization procedure, the criteria for inclusion in the per-protocol analysis, or the trial's original statistical design assumptions.

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.

Period 1, One Week of Wear

Period 2, One Week of Wear

Analysis population for the primary outcome, as defined in the registry: Analysis conducted per protocol

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 Overall Satisfaction With the Lenses, measured over 1 week of wear.

The primary endpoint was overall satisfaction with the lenses, expressed as a mean score in units on a scale. The subject assessed satisfaction retrospectively after one week's wear and recorded a numerical rating on a scale from 1, completely dissatisfied, to 100, excellent and completely satisfied. The registry labels the measure a single retrospective assessment of one week's wear time.

Satisfaction is a direct report of how subjects experienced the lens regimen. In this trial, it offers a way to compare the perceived acceptability of multifocal lenses with single-vision lenses accompanied by reading glasses. A mean gives the average reported rating within a regimen, while the standard deviation describes how spread out individual ratings were around that average. These summaries address the reported satisfaction outcome; they do not establish how subjects performed on other measures or whether the same ratings would persist with longer use.

The registry does not report a minimum difference that would be considered important to subjects, nor does it describe a validated interpretation threshold for the scale. It also does not report other posted secondary outcomes. As a result, the primary result is best read as a comparison of average ratings on the stated scale, with the precision and analysis limitations considered alongside it.

7. Results Posted in the Registry

• Lotrafilcon B Single Vision Contact Lens + Reading Glasses: mean 64.40 versus 82.50 on control; difference -18.10 (95% CI -31.38 to -4.82), standardized effect d = -0.94; z-test p = 0.008.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: each subject provided a numerical satisfaction rating, and the registry reports means and standard deviations. A mean summarizes the center of a set of ratings. A standard deviation describes how much ratings tend to vary around that mean. These are complementary summaries: two regimens can have different average ratings while also showing considerable variation among subjects.

What does the mean difference represent?

The posted contrast is expressed as the single-vision-plus-reading-glasses mean minus the multifocal mean. Its estimate is -18.1. The sign depends on this order of subtraction: a negative value means the first regimen's mean was lower than the second regimen's mean in the posted summary. The estimated contrast is not itself a rating for an individual subject. It summarizes the difference between regimen averages.

How should the confidence interval be read?

A confidence interval describes the uncertainty around an estimated contrast under the assumptions of the statistical method. The reported interval is -31.38 to -4.819. A narrower interval would indicate greater precision than a wider interval, all else equal. The interval does not give a range containing every subject's rating, and it does not mean that the true effect has a particular probability of lying inside those specific endpoints. Its interpretation depends on the method and assumptions used to construct it.

The registry does not report the method used for the confidence interval or the comparison model. That omission matters because this was a crossover trial. Measurements from the same subject across regimens are generally related, rather than independent. In a crossover analysis, that relationship can affect the estimated uncertainty; period or sequence effects may also be relevant. The registry record does not state whether or how these features were modeled, so a reader cannot verify the analysis approach from the posted information alone.

What does the p-value add?

The unadjusted p-value is 0.008. A p-value assesses how unusual data at least as incompatible with a specified null hypothesis would be if that hypothesis and the statistical model were correct. It is not a measure of the probability that the null hypothesis is true, nor does it measure the importance of a difference to subjects. Because it is explicitly unadjusted, it should not be read as accounting for multiple comparisons. The registry does not report a multiplicity adjustment or a broader testing plan.

The study describes a per-protocol primary analysis. In general, per-protocol analyses focus on participants who meet specified adherence or protocol criteria, while other analysis populations can include participants according to their randomized assignment. The record does not give the criteria defining this study's per-protocol population or report an alternative analysis population. That makes it difficult to assess how exclusions or deviations may have influenced the result.

Randomization can help balance factors that affect outcomes, but the registry record does not provide details about the sequence-generation or allocation-concealment procedures. Masking is listed as none, so the record does not indicate that subjects or study personnel were masked. For a subjective satisfaction rating, expectations or awareness of the lens regimen could influence responses; the record does not describe procedures to assess or mitigate that possibility.

Finally, the result should be distinguished from design planning. The registry lists planning illustrations based on fractions of the observed effect, but the trial's own original sample-size assumptions are not reported in the registry record. Those planning illustrations do not establish that the trial was designed around the observed difference. Nor do they alter the interpretation of the observed comparison or its confidence interval.

10. Confidence Intervals and Precision

The reported mean difference is -18.1, with a confidence interval from -31.38 to -4.819. The interval communicates uncertainty around the estimated contrast: under the method's assumptions, values across that range are compatible with the data at the confidence level used. The registry record does not state the confidence level or the method used to calculate the interval.

The interval lies entirely below zero, which is consistent with the negative direction of the reported contrast, single-vision contact lenses plus reading glasses minus multifocal contact lenses. The interval's width also shows that the estimate is not exact: effects ranging from a more pronounced negative difference to one closer to zero remain compatible with the posted interval. The interval does not describe the range of individual satisfaction ratings.

The standard deviations provide another view of variability in the observed ratings: 14.5 for the multifocal regimen and 22.9 for the single-vision-plus-reading-glasses regimen. They indicate that individual ratings varied around each regimen's mean. They do not reveal the correlation between a subject's ratings across the two crossover regimens. Since that relationship can affect precision in a crossover comparison, its absence from the posted summaries is a limitation.

The study reports a per-protocol analysis and does not describe missing-data handling or the analysis model. Those omissions make it harder to assess whether the confidence interval fully reflects the design and the available observations. The interval is useful for expressing uncertainty around the posted estimate, but it cannot resolve questions about analysis choices that are 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 illustrative calculations based on the observed effect, rather than the study's own reported design assumptions. The registry record does not report the original sample-size justification or planning assumptions for this trial.

The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is set at the stated fraction of the observed effect. The figures are given for planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For each assumed effect, the two power columns describe the participants per arm needed for 80% power and for 90% power. In plain terms, power is the probability that a study using the stated assumptions would detect an effect of the chosen size if that effect were present.

The planning figures are 18 and 24 participants per arm for planning for 100% of the observed effect; 32 and 42 participants per arm for planning for 75% of the observed effect; and 71 and 95 participants per arm for planning for 50% of the observed effect. Within each pair, the first figure is for 80% power and the second is for 90% power.

Smaller effects are harder to distinguish from random variation, so planning to detect a smaller fraction of the observed effect requires more participants. These calculations are planning illustrations, not a description of what the study actually observed and not observed power. They should not be read as evidence that the original trial had a particular probability of detecting its result.

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 = -18.100; pooled standard deviation σ = 19.166.
2. n = 2 × (1.96 + 0.842)² × 19.166² / -18.100² = 17.6, rounded up to 18 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 <- -18.1                      # observed difference in means
sigma <- 19.1658550552799                     # 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(965237)
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 = 18 (80% power), 24 (90% power)
 75% of observed effect: n per arm = 32 (80% power), 42 (90% power)
 50% of observed effect: n per arm = 71 (80% power), 95 (90% power)
power.t.test: 18.6 
Simulated power at n = 18 per arm: 0.788 (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 lists one primary outcome measure, overall satisfaction with the lenses, and no posted secondary outcome measures. It also lists zero analyses. This describes what is recorded in the registry; it does not establish that no other analyses were conducted or that no other outcomes were collected.

The posted comparison includes an unadjusted p-value. The registry record does not report whether the study tested additional outcomes, time points, subgroups, or alternative models, or whether any multiplicity adjustment was planned or performed. When several statistical comparisons are considered, the chance of at least one apparently notable result can increase. Without a reported testing plan, it is not possible to determine whether multiplicity is relevant to the posted result or whether an adjustment was used.

The primary population is described as per protocol. The registry record does not specify the eligibility or adherence criteria for that analysis population, explain whether exclusions occurred, or report an intention-to-treat analysis. It also does not describe how missing satisfaction ratings were handled. If data were unavailable for some observations, the approach to those missing values could affect the estimate and its uncertainty; the record does not provide enough detail to assess this.

Because the study used a crossover design, the statistical plan would ideally clarify how repeated measurements within subjects, sequence, and period were treated. The registry record does not report that information, nor does it describe any interim analyses or a detailed statistical analysis plan. These omissions limit assessment of the comparison's assumptions and of how completely the posted analysis represents the study's intended analysis.

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 5% reporting threshold.

The registry reports serious adverse event figures for the multifocal contact lens group and the single-vision contact lens group. For each group, 16 were listed as at risk and zero as affected by a serious adverse event. The registry also reports zero affected by other adverse events in each group, with 16 listed as at risk in each case.

These are recorded counts for the categories shown in the registry. A zero affected count means no affected participants were recorded for that category in the posted results; it does not prove that an event could not occur or establish the safety of a lens regimen. The record does not provide descriptions of non-serious events, event rates over a stated duration, or further detail about adverse-event ascertainment.

Death counts are not reported in the registry record. The posted adverse-event information should be interpreted as a limited record of the reported counts, not as a complete assessment of safety across settings or duration of use.

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

The posted primary results show mean satisfaction ratings of 82.5 for multifocal contact lenses and 64.4 for single-vision contact lenses plus reading glasses after one week of wear. The reported contrast, comparator minus multifocal, is -18.1, with a confidence interval from -31.38 to -4.819 and an unadjusted p-value of 0.008. These figures describe the observed comparison in this study and its reported per-protocol analysis.

The results do not establish how every subject would rate either regimen, because group averages do not show each person's responses. They do not show how satisfaction might change with longer use, and the registry does not report other posted secondary outcomes that could address different aspects of the lens experience. The record also does not provide a threshold for interpreting what size of satisfaction difference subjects would consider important.

The crossover design means subjects experienced both regimens in differing sequences, but the registry does not report how the analysis handled paired observations, sequence, or period effects. The study was unmasked, and the endpoint was a subject-reported satisfaction rating. These design and reporting features should inform interpretation, especially when considering whether the estimate applies beyond this study.

The sample-size planning figures are illustrations based on the observed effect, not evidence that the trial had a specified probability of detecting its result. The registry does not report the original design assumptions. Similarly, the adverse-event counts are limited to the categories and counts posted; they do not constitute a comprehensive safety conclusion.

In short, the posted data indicate a higher average satisfaction rating for the multifocal regimen within this study, while leaving uncertainty about the analysis details, the importance of the difference to subjects, and how well the result generalizes. They should not be treated as medical advice or as proof of an outcome beyond the satisfaction measure that was recorded.

16. Why This Trial Matters Statistically

This study illustrates why trial design and analysis details matter alongside an effect estimate. In a crossover study, each subject experiences both regimens, which can make within-subject comparisons informative. At the same time, measurements from the same subject are related, and the order or period in which a regimen is experienced may influence the result. The registry identifies the crossover sequences but does not report the statistical method used to address these features.

The primary endpoint is a subjective satisfaction rating rather than an objective measurement. That makes the endpoint directly relevant to subjects' reported experience, while also making unmasked treatment assignment a consideration when interpreting the ratings. The posted means and standard deviations give a useful overview of central tendency and variability, but they do not show paired individual responses or explain how expectations may have affected ratings.

The reported mean difference and confidence interval make clear that an estimate should be read with its uncertainty, rather than as a fixed quantity. The unadjusted p-value supplies a test statistic context, but it does not establish clinical importance or resolve questions about missing data, multiplicity, or analysis-population choices. Those aspects are not fully described in the registry record.

The study also illustrates the distinction between observed results and planning calculations. The sample-size illustrations are built from fractions of the observed effect, whereas the trial's original design assumptions are not reported. Planning calculations can help readers understand how assumptions about effect size and power relate to sample requirements, but they cannot substitute for the original design rationale.

For biostatisticians and clinical researchers, the record is a reminder to consider the outcome definition, sequence structure, analysis population, and uncertainty together. The numerical result is informative, but the unreported methods limit how completely it can be evaluated.

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 contains limited detail about the crossover analysis. Although it describes the sequence order for both regimens, it does not report whether the statistical method accounted for within-subject correlation, treatment sequence, or period effects. This makes it difficult to assess whether the reported uncertainty reflects the study design appropriately.

The primary outcome was assessed retrospectively after one week's wear, and the study was unmasked. The record does not describe steps to reduce the influence of expectations on a subject-reported rating. Nor does it report a threshold for a difference considered important to subjects, so the practical meaning of the estimated contrast cannot be determined from the record alone.

The primary analysis population is described as per protocol, but the criteria for that population are not reported. Missing-data methods and reasons for any missing measurements are also not reported in the registry record. These gaps prevent assessment of how exclusions or unavailable observations may have affected the result.

The record lists one primary outcome and no posted secondary outcome measures, but it does not provide a detailed statistical analysis plan or explain whether other comparisons were considered. The unadjusted p-value therefore cannot be evaluated in the context of a complete testing strategy. The original sample-size justification is not reported, and the posted planning calculations are based on the observed effect rather than the trial's original design.

Finally, the posted satisfaction results cover the specified one-week wear timeframe. The registry does not report longer-term satisfaction outcomes, and the adverse-event information is limited to the posted counts. These limits constrain interpretation to the outcomes and details recorded for this study.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Multifocal Contact Lens Use in Previous Contact Lens Wearers With Near Vision Demands — NCT00965237.
• Registry record last updated 2012-07-10; status last verified 2012-01.
• Results first posted 2011-03-14.
• 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

NCT00965237, titled “Multifocal Contact Lens Use in Previous Contact Lens Wearers With Near Vision Demands,” is listed as a completed randomized, unmasked crossover study sponsored by CIBA VISION. The registry records a start of 2009-08, primary completion of 2009-12, and enrollment of 16. The study concerns people with presbyopia who had previously stopped wearing contact lenses because of near-vision demands.

The primary outcome was overall satisfaction after one week of wear, rated on a scale from 1 to 100. The posted means were 82.5 for multifocal lenses and 64.4 for single-vision lenses plus reading glasses. The reported comparator-minus-multifocal mean difference was -18.1, with a confidence interval from -31.38 to -4.819 and an unadjusted p-value of 0.008.

The primary analysis was per protocol. The registry record does not report the detailed crossover analysis method, missing-data handling, or original sample-size assumptions. Serious and other adverse-event counts affected zero participants in each posted group; deaths are not reported in the registry record.