Proclear 1-D Multifocal Nondispensing Study: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Proclear 1-D Multifocal Nondispensing Study (NCT01526902), a randomized na study. The primary outcome is Objective Vision Assessments: High Contrast Distance Visual Acuity.

2. Clinical Question

The brief study summary describes a comparison of subjective and objective vision performance between two multifocal soft contact lenses. The primary endpoint addresses objective vision, while the posted secondary endpoints describe subjective high-contrast distance, intermediate, and near visual quality. The reported primary group means were -0.09 logMAR units for PC1DMF and -0.05 logMAR units for Air Optix MF. The registry comparison is expressed as Air Optix MF minus PC1DMF, with a mean difference of 0.04 logMAR units.

This question is specific to the posted assessment after 1 hour of wear. The record does not establish how the lenses compared over longer use or for outcomes beyond the listed measures. The crossover arrangement means each participant was assigned to use both lens pairs in sequence, but period-specific and paired participant-level results are not reported in the registry record.

3. Trial Design

This was a randomized, double-masked, crossover study listed as completed. The registry identifies the study phase as NA and reports enrollment of 49 participants. The condition listed is presbyopia. CooperVision, Inc. is identified as the sponsor. The record lists a study start of 2012-02 and primary completion of 2012-05.

Participants were randomly assigned to an initial lens pair and then crossed over to the alternative pair. The two pairs were omafilcon A / PC 1-D MF and lotrafilcon B / Air Optix MF. The arm descriptions state that the omafilcon A pair included +0.75D over-correction in the non-dominant eye. The description for each sequence gives the same two treatment pairs in opposite order. The registry labels masking as double, but does not describe which roles were masked or how masking was maintained.

The primary endpoint and all three posted secondary endpoints were assessed after 1 hour of lens wear. The primary endpoint is reported for the Per Protocol population. The group summaries list 49 participants for each lens condition. Because this is a crossover study, the same participants could contribute observations under both lens conditions; the arm counts should not be interpreted as evidence of 98 distinct participants.

The registry record does not report the length of each treatment period, any washout interval, the sequence allocation counts, or details of adherence and exclusions from the Per Protocol population. It also does not report the trial's original sample-size assumptions or the statistical analysis plan. These omissions limit interpretation of how the crossover design was handled and how the enrolled sample was chosen.

4. Participant Flow and Accounting

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

Before assignment: The subjects who are current contact lens wearers should attend the first visit wearing their habitual lenses and having worn them that day for at least 2 hours prior to the visit.

Overall Study

Analysis population for the primary outcome, as defined in the registry: 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 Objective Vision Assessments: High Contrast Distance Visual Acuity, measured over After 1 hour of lens wear.

The primary endpoint is objective high-contrast distance visual acuity after 1 hour of lens wear. It was tested using charts at a distance from the participant, with both eyes together under normal lighting conditions. The outcome is expressed in logMAR units, a logarithmic measure of the minimum angle of resolution. The registry description states that 0.0 logMAR corresponds to 20/20 Snellen acuity, positive values indicate poorer acuity, and negative values indicate better acuity than the 20/20 reference.

This endpoint provides a standardized measure of distance acuity under the stated testing conditions. It complements subjective assessments because it is based on chart performance rather than a participant's rating of visual quality. Both types of information can be useful when comparing lens conditions, but they answer different questions: measured acuity concerns chart-based visual performance, while the secondary outcomes concern subjective quality ratings.

The primary outcome is reported as a mean with a standard deviation for each lens condition. The posted result is for the Per Protocol population and the specific assessment after 1 hour. The registry record does not report a longer-term acuity assessment or further details about chart procedures beyond the description given.

7. Results Posted in the Registry

• Air Optix MF: mean -0.05 versus -0.09 on control; difference 0.04 (95% CI 0.01 to 0.07), standardized effect d = 0.50; z-test p = 0.013.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Subjective Overall Vision: High Contrast Distance Visual Quality

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Air Optix MF: mean 88.00 versus 87.00 on control; difference 1.00 (95% CI -4.44 to 6.44), standardized effect d = 0.07; z-test p = 0.718.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Air Optix MF and the control. The interval gives the range of effects that remain compatible with the data.

Subjective Vision Assessments: High Contrast Intermediate Visual Quality

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Air Optix MF: mean 85.00 versus 85.00 on control; difference 0.00 (95% CI -5.94 to 5.94), standardized effect d = 0.00; z-test p = 1.000.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Air Optix MF and the control. The interval gives the range of effects that remain compatible with the data.

Subjective Vision Assessments: High Contrast Near Visual Quality

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Air Optix MF: mean 80.00 versus 81.00 on control; difference -1.00 (95% CI -8.13 to 6.13), standardized effect d = -0.06; z-test p = 0.783.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Air Optix MF and the control. The interval gives the range of effects that remain compatible with the data.

The three posted secondary outcomes cover subjective high-contrast visual quality at distance, intermediate, and near ranges. Across these measures, the group means are close: the distance ratings are 87.0 and 88.0, the intermediate ratings are 85.0 and 85.0, and the near ratings are 81.0 and 80.0 for PC1DMF and Air Optix MF, respectively. The associated unadjusted confidence intervals include zero for all three comparisons. The secondary pattern is therefore one of broadly similar reported ratings, without a clear direction shared across all measures.

This pattern is not identical to the primary objective acuity result, whose posted comparison interval does not include zero. The outcomes measure different aspects of vision: the primary endpoint is chart-based distance acuity, whereas the secondary endpoints are subjective quality ratings. Differences in the measures and their variability mean that agreement is not required, and the secondary results neither overturn nor independently confirm the primary comparison.

Unadjusted secondary results carry less weight when several outcomes are examined because the chance of at least one apparently unusual result can increase with multiple testing. The registry does not report a multiplicity adjustment or a statistical plan specifying the role of each secondary comparison. They are best read as descriptive context alongside the primary result, rather than as a set of separately definitive tests.

Three secondary outcomes are posted, while the registry reports six outcome measures in total. The remaining outcome-measure details are not reported in the registry record. No secondary analysis details are listed, so the summaries do not establish the handling of crossover pairing or missing data for those endpoints.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Subjective Overall Vision: High Contrast Distance Visual Quality
• Subjective Vision Assessments: High Contrast Intermediate Visual Quality
• Subjective Vision Assessments: High Contrast Near Visual Quality

9. Statistical Interpretation

10. Statistical Methods Explained

What does a mean difference describe?

For a continuous outcome, a mean is the arithmetic average of participant measurements in a group. A mean difference compares the averages between two conditions. The registry reports the primary contrast as Air Optix MF minus PC1DMF. Its estimate of 0.04 logMAR units is therefore the difference between the posted means in that stated order. Reversing the order of subtraction would reverse the sign, but not change the underlying separation between the means.

A standard deviation describes how spread out individual measurements are around a group mean. It is not the uncertainty of the mean itself. The primary results give a standard deviation of 0.08 in each condition. A standard error, by contrast, describes the estimated sampling uncertainty of a statistic such as a mean. The registry comparison includes standard errors of 0.011 for each group mean. General explanation: standard errors tend to be smaller than the corresponding participant-level spread when a mean is estimated from a group, because averaging reduces sampling variability.

How should the confidence interval be read?

A confidence interval gives a range of estimates compatible with the observed data under the statistical model and its assumptions. For the primary mean difference, the posted interval runs from 0.008 to 0.072 logMAR units. Since zero is outside that interval, the interval is consistent with a nonzero difference under the stated contrast and calculation. It does not mean that there is a 95% probability that the true difference lies within this particular interval. General explanation: the confidence level describes the long-run behavior of the interval procedure across repeated samples under its assumptions.

The registry gives an unadjusted p-value of 0.013 for the primary comparison. A p-value measures 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 effect size, clinical importance, or the probability that the null hypothesis is true. The word unadjusted matters because the record does not describe a correction for examining multiple outcomes.

Why does the crossover design matter?

In a crossover study, participants receive multiple study conditions in sequence. Results from the same participant can be related across conditions, so a paired analysis may use information about within-participant differences. General explanation: accounting for this pairing can improve precision when measurements from the same person are correlated. A crossover analysis may also need to consider sequence, period, or carryover effects, depending on the protocol and data.

The registry reports group means, standard deviations, and a comparison, but does not report whether the primary comparison used paired participant-level data or how sequence and period were handled. It also does not report the washout interval. Consequently, the posted summaries do not allow readers to independently assess the crossover analysis or determine whether possible period or carryover effects were evaluated. The statistical method behind the registry comparison is not reported in the registry record.

What does over-dispersion mean?

General explanation: over-dispersion occurs when observed variability is greater than a model assumes. It is particularly relevant to count outcomes and some generalized linear models; ignoring it can make uncertainty estimates too small. The outcomes posted in this study are continuous means with standard deviations, not count outcomes. No over-dispersion assessment is reported in the registry record, and the available summaries do not establish whether any such issue arose.

How do the secondary outcomes fit?

The secondary outcomes are continuous subjective visual-quality ratings for high-contrast distance, intermediate, and near vision. Their summaries report means and standard deviations by lens condition, along with unadjusted comparisons. General explanation: testing multiple outcomes creates more opportunities for a nominally unusual result to occur by chance. A multiplicity procedure can address that concern, but no adjustment method is reported in the registry record.

The registry record lists six outcome measures but provides three secondary outcomes in the posted results. It reports no analyses under the listed analysis fields. The registry does not provide a statistical plan describing which outcomes were prespecified for formal testing, how missing observations were handled, or whether the comparisons were adjusted. The posted descriptive summaries and unadjusted comparisons should therefore be read with that uncertainty in mind.

11. Confidence Intervals and Precision

The primary mean difference is 0.04 logMAR units, with a 95% confidence interval from 0.008 to 0.072. The interval is entirely positive under the reported contrast of Air Optix MF minus PC1DMF, while the posted means are -0.05 for Air Optix MF and -0.09 for PC1DMF. The interval's endpoints describe the range of differences compatible with the analysis, rather than a range of individual participant values.

The interval conveys precision around the estimated mean difference, but its interpretation depends on the analysis assumptions. The registry does not report whether the crossover pairing was incorporated, and it does not provide participant-level data or a detailed analysis method. That means the precision calculation cannot be independently evaluated from the posted summaries alone. The registry record also does not report a threshold for a difference considered clinically meaningful, so the interval cannot be judged against such a threshold from this record.

For subjective distance visual quality, the comparison interval runs from -4.437 to 6.437 units on a scale. For intermediate visual quality it runs from -5.94 to 5.94 units on a scale, and for near visual quality it runs from -8.128 to 6.128 units on a scale. These intervals include zero. They provide context for uncertainty in the secondary comparisons, but the registry does not describe adjustment for the multiple outcomes.

General explanation: wider intervals indicate less precise estimates, while narrower intervals indicate greater precision, conditional on the model and study design. Precision is not the same as clinical importance. A narrow interval can still be centered on a small difference, and a broad interval can include differences in more than one direction.

12. 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 sample-size figures are planning illustrations expressed as participants per arm for the continuous outcomes. They are not total event counts. They were calculated using a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The assumed effect to detect is the stated fraction of the observed effect. The original trial's own design assumptions are not reported in the registry record.

The 80% power column gives an illustrative number of participants per arm for a design intended to have an 80% chance of detecting the specified effect under those assumptions. The 90% power column gives the corresponding planning target for a 90% chance. Power is a property of a planned study under assumed conditions; it does not describe the probability that the observed finding is true. These figures are not observed power.

The planning illustrations vary the assumed effect: 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For example, for the primary outcome, planning for 100% of the observed effect gives 63 participants per arm for 80% power and 85 participants per arm for 90% power. Planning for 75% gives 112 and 150 participants per arm, respectively; planning for 50% gives 252 and 337 participants per arm. Smaller effects need more participants for the same target power, because a smaller difference is harder to distinguish from random variation.

These illustrations are not a reconstruction of the trial's original sample-size justification. They use the observed effect as the starting point and rely on the assumptions stated above. The crossover design and the registry's lack of detail about the original analysis strategy should be kept in mind when considering how closely the illustrations correspond to a future design.

13. 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 = 0.040; pooled standard deviation σ = 0.080.
2. n = 2 × (1.96 + 0.842)² × 0.080² / 0.040² = 62.8, rounded up to 63 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 <- 0.04                      # observed difference in means
sigma <- 0.08                     # 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(1526902)
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 = 63 (80% power), 85 (90% power)
 75% of observed effect: n per arm = 112 (80% power), 150 (90% power)
 50% of observed effect: n per arm = 252 (80% power), 337 (90% power)
power.t.test: 63.8 
Simulated power at n = 63 per arm: 0.796 (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.

14. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when several outcomes or comparisons are evaluated. If each is interpreted using an unadjusted significance threshold, the chance of finding at least one result that appears unusual under a no-difference assumption can rise across the set of tests. The registry reports an unadjusted p-value for the primary comparison and unadjusted comparisons for the posted secondary endpoints. A plan for handling multiplicity is not reported in the registry record.

The record lists six outcome measures and provides the primary outcome plus three secondary outcomes. It does not report the details of the other listed measures. The analysis fields do not contain reported analyses. The registry record therefore does not establish whether all listed outcomes were prespecified, whether additional analyses were conducted, or how any testing hierarchy was defined.

The primary population is identified as Per Protocol. The record does not describe the criteria for inclusion in that population or explain how participants who did not complete a treatment sequence were handled. Although 49 participants are listed for each lens condition, missing-data counts and methods are not reported in the registry record. There is no description of imputation, exclusion rules, or sensitivity analyses.

These details matter especially in a crossover study. A complete crossover analysis may depend on observations from both treatment periods for each participant, and incomplete sequences can affect which participants contribute to a paired comparison. The registry does not report sequence-specific completion, period-level data, or the method used to account for within-participant correlation. Thus, readers cannot determine from the posted summaries how missingness or the crossover structure affected the precision estimates.

The registry also does not report an original statistical analysis plan, interim analyses, or sample-size justification. Their presence or absence cannot be inferred from the posted results. These gaps call for caution when treating the unadjusted comparisons as a complete inferential account.

15. 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.

The posted safety figures list 49 participants at risk in each lens group. Zero participants are reported as affected by serious adverse events in either group, and zero are reported as affected by other adverse events in either group. The serious adverse event terms list is empty. These figures describe the adverse-event counts posted in the registry for the stated groups.

The deaths field is not populated for either group, so death counts are not reported in the registry record. The posted zero counts should not be expanded into a claim that no safety events of any kind occurred beyond those categories or reporting conditions. The record does not describe the adverse-event collection period, severity definitions, or whether participants were followed for safety beyond the stated assessment context.

These figures are limited to the recorded groups and the information in the registry. They do not by themselves establish comparative safety, especially without event detail, follow-up duration, and an analysis plan. No medical advice or broader safety conclusion follows from these counts alone.

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

The posted primary result describes a difference in mean high-contrast distance visual acuity after 1 hour of lens wear. The mean values are lower with PC1DMF than with Air Optix MF, and the stated difference for Air Optix MF minus PC1DMF is 0.04 logMAR units. Its 95% confidence interval ranges from 0.008 to 0.072, and the unadjusted p-value is 0.013. This is evidence of a difference under the comparison as reported, with the direction favoring lower measured logMAR values for PC1DMF in the observed summaries.

The result does not by itself establish the practical importance of that difference. The registry does not state a clinically meaningful threshold for the acuity measure. Nor does the result describe visual performance beyond the specific chart assessment after 1 hour. It cannot be generalized from these posted data to different use durations, populations, lens conditions, or outcomes that were not reported.

The crossover design makes details of within-participant analysis relevant, but those details are not reported in the registry record. Without a description of pairing, period effects, missing observations, and the analysis plan, the posted comparison cannot be treated as a full account of every design feature. The subjective secondary outcomes give a different kind of information and their unadjusted results do not provide independent confirmation of the primary comparison.

The safety summary reports zero serious and zero other adverse events for each group, with 49 at risk in each. Death counts are not reported. These limited registry figures should not be interpreted as proof of absence of risk. Overall, the result is a statistical description of the posted outcomes under the stated conditions, not a recommendation about lens choice.

17. Why This Trial Matters Statistically

This trial is statistically interesting because it combines a randomized comparison with a crossover design. Randomization helps allocate the initial lens sequence, while crossover means participants receive both lens pairs. General explanation: when the same participant contributes data under both conditions, the analysis can make use of within-person comparisons, but it needs to account for the relationship between those observations. The registry summaries do not state how that feature was handled.

The study also illustrates why endpoint definition and scale interpretation matter. The primary measure is objective distance acuity in logMAR units, where lower values are described as better acuity. The estimated difference is small in scale units, but its confidence interval excludes zero under the posted comparison. Statistical evidence and clinical importance are separate questions, and the registry record supplies no threshold for deciding the latter.

The secondary outcomes highlight another common issue: several measures may address related but nonidentical aspects of an experience. Their means are close, but they are subjective ratings rather than chart-based acuity. Since no multiplicity adjustment or analysis hierarchy is reported, those outcomes should not be treated as an independent collection of confirmatory tests.

Finally, the study is a useful reminder that registry summaries are not a substitute for a detailed protocol and analysis plan. The record gives design labels, outcome descriptions, group summaries, and safety counts, but does not report crossover analysis details, missing-data handling, or original planning assumptions. Those omissions affect how much can be concluded from otherwise interpretable summary statistics.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The posted results focus on assessment after 1 hour of lens wear. The registry does not report outcomes at longer durations, so the summaries cannot describe longer-term performance. The assessment conditions are stated as high-contrast distance chart testing with both eyes together in normal lighting; results for other testing conditions are not reported in the registry record.

Although the trial is identified as a crossover study, the record does not give the washout interval, treatment-period length, sequence counts, or period-specific outcome summaries. It also does not report whether the comparison used paired observations or how it handled sequence, period, or possible carryover effects. Those omissions are specific concerns for interpretation of a crossover comparison.

The primary outcome population is Per Protocol, but the criteria defining that population and the number excluded are not described. Missing-data counts, imputation methods, and sensitivity analyses are not reported in the registry record. The summaries list 49 participants per lens condition, but those values alone do not explain whether every participant contributed complete observations under both conditions.

The record reports no multiplicity procedure, original statistical analysis plan, or sample-size justification. The posted secondary results are unadjusted, and only three of six listed outcome measures are described in the results. The registry does not provide a threshold for a clinically meaningful difference in the primary scale. These limits restrict conclusions about robustness, clinical relevance, and the full set of outcomes assessed.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Proclear 1-D Multifocal Nondispensing Study — NCT01526902.
• Registry record last updated 2014-04-07; status last verified 2014-03.
• Results first posted 2014-03-06.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

NCT01526902 is the completed Proclear 1-D Multifocal Nondispensing Study, sponsored by CooperVision, Inc. It is listed as a randomized, double-masked crossover study enrolling 49 participants with presbyopia. The study compared omafilcon A / PC 1-D MF with lotrafilcon B / Air Optix MF.

The primary outcome was objective high-contrast distance visual acuity in logMAR units after 1 hour of lens wear, reported for the Per Protocol population. The posted mean difference was 0.04 logMAR units for Air Optix MF minus PC1DMF, with a 95% confidence interval from 0.008 to 0.072 and an unadjusted p-value of 0.013. Three subjective visual-quality outcomes were also posted.

Registry safety counts report zero serious and zero other adverse events in both groups; deaths are not reported. Crossover analysis details, missing-data methods, multiplicity handling, and the original sample-size assumptions are not reported in the registry record.