Clinical Assessment of a Customized Free-form Progressive Addition Lens Spectacle: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Clinical Assessment of a Customized Free-form Progressive Addition Lens Spectacle (NCT01234207), a randomized na study. The primary outcome is Visual Acuity, High Contrast, Distance Chart.

2. Clinical Question

The question concerns a measured visual performance outcome, not only a subjective preference or satisfaction rating. The registry summary says the study also aimed to compare subjective satisfaction and preference, but the primary outcome listed in detail is visual acuity measured using a distance chart. The posted group means are close in magnitude: the control-spectacle mean is -0.12 logMAR and the test-spectacle mean is -0.11 logMAR. The reported mean difference for test versus control is 0.01 logMAR.

In a crossover study, each participant receives both study conditions in sequence. This allows a comparison that can use measurements from the same person under each condition, while randomizing the order helps distribute sequence order across participants. The registry record describes randomized order and a washout period, but does not report a participant-level paired estimate or details of how sequence and period effects were handled in the analysis. The results therefore address the posted group summaries and contrast; they do not by themselves resolve every methodological question about the crossover comparison.

3. Trial Design

This was a randomized, double-masked crossover study comparing two types of progressive addition lens spectacles. The registry identifies 95 enrolled participants and describes two randomized orders: standard spectacles followed by customized free-form spectacles, or customized free-form spectacles followed by standard spectacles. The primary outcome description says that presbyopic subjects wore each type for 1 week, with a 1-week washout period between wear periods. The record lists the study status as completed.

The control condition was standard, non-free-form, non-customized PAL spectacles. The test condition was individually customized free-form surfaced PAL spectacles. Because the same participant was scheduled to experience both conditions, this design differs from a parallel-group trial in which separate groups remain on separate treatments. The randomized order is relevant because visual measurements could be affected by sequence or by changes over time; the registry record does not provide further details about how those possibilities were addressed.

Double masking is the masking designation in the record. It does not identify which people were masked or describe how masking was maintained, so those details are not reported in the registry record. The study is listed with phase NA. The sponsor is the University of California, Berkeley. The recorded start is 2009-02 and primary completion is 2009-10.

The registry lists eight outcome measures, while the detailed primary outcome concerns high-contrast distance visual acuity. The outcome timeframe is after 1 week of wear of the test spectacles and after 1 week of wear of the control spectacles. The measurement description names Baily-Lovey charts and the M&S Technologies Smart System II visual acuity projection system. Although the registry summary says subjective satisfaction and preference were also part of the study purpose, no secondary results are posted. The registry record does not report the original design assumptions, the trial's statistical analysis plan, or details of the analysis population.

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: 95 subjects were recruited, all of whom met the eligibility criteria and completed the study.

First Intervention

1-Week Washout Period

Second Intervention

Analysis population for the primary outcome, as defined in the registry: 95 presbyopic subjects wearing standard, non-free-form, non-customized PAL spectacles for 1 week, and individually customized, free-form surfaced PAL spectacles for 1 week, in randomized order, with a 1-week washout period

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 Visual Acuity, High Contrast, Distance Chart, measured over Post-1 week of wear of Test Spectacles and post-1 week of wear of Control Spectacles.

The primary endpoint is mean high-contrast visual acuity at distance, measured in logMAR. The record describes a standard clinical assessment using Baily-Lovey charts and the M&S Technologies Smart System II visual acuity projection system. Measurements were taken after 1 week of wear of each spectacle type. The endpoint therefore compares a measured aspect of distance vision under the two spectacle conditions, rather than a subjective report of satisfaction.

Visual acuity is used to quantify the ability to resolve detail under specified testing conditions. The high-contrast designation indicates that the test concerns targets with strong contrast against their background. In general, logMAR is a logarithmic scale used to express visual acuity; lower values correspond to better acuity. That general interpretation helps explain the direction of the scale, but it does not establish what difference would matter to participants in this particular study.

The outcome is summarized as a mean and standard deviation for each condition, with a reported mean difference and confidence interval for test versus control. A mean describes the central value of the group measurements, while a standard deviation describes how dispersed measurements are around that mean. The registry record does not report a threshold for a clinically important difference, nor does it report a separate endpoint definition for subjective preference or satisfaction. The posted primary endpoint should therefore be interpreted as a comparison of the stated visual acuity measure, not as a complete account of every outcome the study intended to examine.

7. Results Posted in the Registry

• Test Spectacles: mean -0.11 versus -0.12 on control; difference 0.01 (95% CI -0.01 to 0.03), standardized effect d = 0.15; z-test p = 0.290.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry reports a continuous primary outcome summarized by a mean and standard deviation. The outcome is high-contrast distance visual acuity in logMAR, measured after each 1-week wear period. The posted summaries give a mean of -0.12 logMAR for control spectacles and -0.11 logMAR for test spectacles. A mean is the arithmetic average of the observations in a condition. A standard deviation describes how much individual observations tend to vary around that average; it is not a confidence interval and does not give the precision of the estimated mean difference by itself.

What does the mean difference represent?

The reported contrast is the mean difference for test versus control. It is 0.01 logMAR, corresponding to the difference between the two posted group means in the stated direction. A contrast is useful because it puts the comparison on the outcome's measurement scale. Its sign indicates which condition has the higher numerical mean, while its magnitude describes the size of that numerical separation. For logMAR, the clinical meaning of a particular separation depends on the outcome scale and on a meaningful-difference threshold. Such a threshold is not reported in the registry record.

The registry also reports an unadjusted p-value of 0.29. In general, a p-value evaluates how unusual data at least as incompatible with a null hypothesis would be if that null model and its assumptions held. It is not a measure of the probability that the null hypothesis is correct. It does not tell whether the observed difference is important to participants, and it cannot establish that the two conditions are equivalent. Interpretation should consider the estimate, the confidence interval, the design, and the analysis assumptions together rather than relying on a p-value alone.

Why does the crossover structure matter?

In a crossover design, participants receive more than one condition in sequence. A comparison can take advantage of within-person information: each person's measurement under one condition can be related to that person's measurement under the other. In general, paired observations are statistically dependent, and an analysis that recognizes that dependence can differ from one that treats observations as independent. The record specifies randomized order and a 1-week washout period, but does not state whether the reported contrast came from a paired analysis, how the within-person correlation was modeled, or whether period and sequence were included in the analysis. Those details are not reported in the registry record.

The reported standard deviations describe measurements within each condition. They do not show how strongly the two measurements from the same participant are correlated. That within-person association is important for the precision of a paired contrast. The record reports a pooled standard deviation as part of the comparison summary, but does not describe its role in the trial's own analysis. It is therefore not possible to reconstruct the crossover analysis from the posted group means and standard deviations alone without adding assumptions.

What does the confidence interval add?

A confidence interval expresses uncertainty around an estimate using a range of values that are compatible with the observed data under the method's assumptions. In repeated use of a valid procedure, intervals at a stated confidence level would cover the target parameter at their nominal rate. The registry comparison reports an interval for the mean difference that includes zero. Thus, under the reported calculation, the compatible values include no difference as well as differences in either direction. The interval does not assign probabilities to individual values within its range, and it does not account for analysis features that are not described.

The confidence interval is linked to the standard error, which represents the estimated sampling variability of an estimate. The record lists standard errors for the condition means, but those are not a substitute for a documented standard error of a paired crossover contrast. A standard error for a difference depends on the design and on how observations are related. The reported interval is best interpreted as the interval attached to the posted contrast, not as proof that all design considerations have been fully documented.

What can be inferred from the analysis record?

The registry lists eight outcome measures and zero analyses. The primary outcome is described, and a numerical comparison is posted, but the registry record does not describe a full statistical analysis plan. It does not report the original sample-size justification, any interim analysis plan, the primary analysis population, model covariates, missing-data method, or adjustment for multiple outcome testing. The absence of those details does not demonstrate that the study did not use such methods; it means the methods are not reported in the registry record.

General statistical practice distinguishes a prespecified primary analysis from exploratory or unadjusted comparisons. Prespecification can limit selective emphasis on results, while multiplicity procedures may control error rates when many hypotheses are tested. Neither the detailed prespecified plan nor an adjustment method is available in the registry record. The posted unadjusted p-value should therefore be described as unadjusted, not as evidence that any potential multiplicity concern was addressed.

Finally, statistical significance, precision, and clinical importance are different concepts. A p-value summarizes evidence relative to a null model; a confidence interval describes uncertainty about the size and direction of an estimate; clinical importance requires context and a meaningful threshold. The registry supplies the first two types of information for this primary comparison, but does not report a clinical importance threshold. The results can be described on the measured scale without claiming that the observed separation matters to patients.

10. Confidence Intervals and Precision

The reported mean difference for test versus control is 0.01 logMAR. Its confidence interval extends from a small negative value to a small positive value and crosses zero. This means the interval includes no difference under the calculation used, along with possible differences in either direction. It is not evidence that the true difference is exactly zero, and it does not show that every value in the interval is equally plausible.

A confidence interval conveys precision by showing the range of effect estimates compatible with the data and the interval method. A narrower interval generally indicates greater precision than a wider one, assuming the same scale and method. Here, the interval spans both sides of zero, so the direction of the underlying difference is not determined by the interval. The record does not identify a threshold for a clinically important difference, which prevents a direct assessment of whether the interval rules out differences that would matter in practice.

The group means and standard deviations are not enough to describe all uncertainty in a crossover comparison. Each participant contributed measurements under both conditions, so the relationship between the paired measurements can affect the uncertainty of the contrast. The registry record does not report that relationship or explain whether the interval accounts for it. The reported interval should be read as the uncertainty attached to the posted contrast, with that analysis detail unresolved.

The unadjusted p-value is 0.29. It is consistent with the interval crossing zero, but it does not replace the interval or quantify the range of plausible effects. Neither result establishes equivalence. A conclusion of equivalence would require a clinically justified margin and a suitable analysis, and those 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 event counts. The displayed calculations are planning illustrations based on the observed effect, rather than the trial's original design assumptions. They use a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The original trial's sample-size assumptions are not reported in the registry record.

For the full observed effect, the illustration gives 668 participants per arm for 80% power and 894 participants per arm for 90% power. For planning for 75% of the observed effect, the figures are 1,187 participants per arm for 80% power and 1,588 participants per arm for 90% power. For planning for 50% of the observed effect, they are 2,669 participants per arm for 80% power and 3,573 participants per arm for 90% power.

In general, power is the chance that a specified analysis will reject its null hypothesis if a particular effect is truly present, under the assumptions used in the calculation. The 80% and 90% columns therefore describe alternative planning targets: the latter targets a higher chance of detecting the specified effect, under the stated assumptions. Smaller effects are harder to distinguish from random variation and require more participants in these illustrations.

These figures are not observed power. They are prospective planning illustrations derived from the observed effect and specified calculation assumptions, not a description of the trial's achieved power or its original enrollment plan. Their relevance depends on whether the calculation assumptions match the intended future design and analysis.

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 = 0.010; pooled standard deviation σ = 0.065.
2. n = 2 × (1.96 + 0.842)² × 0.065² / 0.010² = 667.2, rounded up to 668 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 <- 0.01                      # observed difference in means
sigma <- 0.0651920240520265                     # 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(1234207)
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 = 668 (80% power), 894 (90% power)
 75% of observed effect: n per arm = 1,187 (80% power), 1,588 (90% power)
 50% of observed effect: n per arm = 2,669 (80% power), 3,573 (90% power)
power.t.test: 668.1 
Simulated power at n = 668 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.

13. Multiplicity, Missing Data and Analysis Populations

The registry lists eight outcome measures, but reports no secondary results. The detailed primary outcome concerns high-contrast distance visual acuity. The registry record does not describe a complete prespecified hierarchy of outcomes, state how many hypotheses were planned for formal testing, or report a multiplicity adjustment. The posted p-value is unadjusted. When several outcomes or comparisons are examined, the chance of at least one small p-value can increase; in general, adjustment or a prespecified testing strategy can address that issue. Whether either was used in this trial is not reported in the registry record.

The record lists zero analyses. Although a numerical primary comparison is posted, detailed methods for that analysis are not reported. There is no reported interim analysis plan, so it is not possible to determine from the registry record whether interim testing was planned or conducted. The original statistical plan is also not reported; assumptions about modeling, covariates, or a decision rule would be speculative.

Missing-data handling is not reported. The outcome summaries list 95 observations for each condition, but the record does not explain whether these represent all randomized participants with complete measurements, how incomplete or unavailable measurements were treated, or whether any imputation was used. In general, missingness can affect estimates when the availability of a measurement is related to the outcome or condition. Without a reported method and participant flow for the endpoint, the possible impact cannot be assessed from these summaries.

The analysis population is not reported in sufficient detail to determine whether the comparison followed an intention-to-treat principle, used only participants with measurements under both conditions, or followed another definition. The crossover design makes this distinction particularly relevant because a complete within-person comparison generally requires measurements under both conditions. The registry record also does not state how period, sequence, or carryover concerns were analyzed. These omissions limit assessment of the statistical methods but do not establish that the study failed to address them.

14. Safety Results

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

Deaths

Other (non-serious) adverse events

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

The registry records zero serious adverse events for the control-spectacle condition and zero for the test-spectacle condition. It also records zero other adverse events for each condition, and zero deaths for each. The adverse-event figures are recorded against 95 at risk in each condition. These are the safety counts posted in the registry record.

A zero recorded count means that no event was entered for that category in the registry results; it does not prove that an event is impossible or that a condition has no risk. Interpretation also depends on how events were defined, collected, followed, and attributed. The registry record does not provide additional detail about those procedures or describe event severity beyond the serious-versus-other categorization.

Because this is a crossover study, participants experienced both spectacle conditions in randomized order. The record presents adverse-event counts separately by condition, but does not explain the method for assigning events, handling timing across periods, or accounting for repeated exposure. The counts should therefore be read as the reported registry totals rather than as a detailed comparative safety analysis. They do not establish that the two conditions have identical safety profiles.

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

The result describes the posted primary visual-acuity comparison after 1 week of wear of each spectacle type. The control mean was -0.12 logMAR, the test mean was -0.11 logMAR, and the reported mean difference for test versus control was 0.01 logMAR. The confidence interval crosses zero, and the unadjusted p-value is 0.29. These statistics indicate that the registry's estimate is close to zero and that the interval does not determine a direction of difference.

This does not demonstrate that the two conditions are equivalent. Equivalence is a specific statistical claim that requires a prespecified acceptable range of differences and an analysis designed to assess that range. Neither an equivalence margin nor such an analysis is reported in the registry record. The result also does not prove that there is no difference: the confidence interval includes values on either side of zero, and the record does not provide a clinical importance threshold with which to judge the interval.

The result applies to the measured high-contrast distance visual-acuity endpoint and the stated wear periods. It does not establish what participants preferred, how satisfied they were, or what happened for other unreported outcomes. The registry summary says satisfaction and preference were study aims, but no secondary results are posted. The primary outcome alone cannot substitute for those measures.

The available summaries also do not provide enough information to evaluate all aspects of the crossover analysis. The record does not state whether the contrast was based on a paired model, how period or sequence effects were considered, or how missing data were handled. These gaps do not change the reported means, but they limit assessment of the assumptions behind the estimated difference and its interval.

Accordingly, the careful interpretation is descriptive: the posted group means are close, the estimated difference is small on the logMAR scale, and the reported uncertainty includes no difference. The results do not establish superiority, equivalence, or the absence of a clinically important effect. Such conclusions would require additional design, analysis, and clinical-context information not reported in the registry record.

16. Why This Trial Matters Statistically

This trial is statistically notable because it used a randomized crossover design to compare two spectacle conditions. In general, crossover designs can make efficient use of within-person comparisons when the outcome is measured under each condition. The design also creates analysis requirements: repeated measurements from the same person are related, and order or period can matter. The registry identifies randomization of order and a washout period, while leaving key analysis details unreported.

The posted means are close, and the estimate is accompanied by an interval that crosses zero. This illustrates why a point estimate and its uncertainty should be read together. A small estimated difference is not the same as a precise demonstration of no meaningful difference. Without a clinically important threshold, the numerical scale alone cannot determine what degree of separation would matter. Nor does a non-significant p-value establish equivalence.

The trial also illustrates the difference between a registry outcome listing and a complete statistical report. Eight outcome measures are listed, but no secondary results or analysis details are reported. This makes it difficult to assess the breadth of planned testing, the handling of missing measurements, and the analysis population. Clear reporting of these elements would help readers distinguish a prespecified confirmatory comparison from other analyses.

Finally, the planning illustrations show how sample-size requirements depend on the effect a study aims to detect and the desired power. They are based on the observed effect and stated assumptions, not on the trial's original design. Reading them as planning aids rather than as observed power prevents a common misinterpretation. Together, the design and reporting features make this record a useful example of why effect estimates, precision, design structure, and analysis transparency all matter when interpreting clinical trial statistics.

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 main limitations of interpretation arise from details not reported in the registry record. Although the study is described as a randomized crossover, the record does not state whether the primary comparison used a paired analysis or how within-person correlation was handled. Nor does it report whether the analysis accounted for sequence, period, or possible carryover effects. The presence of a washout period is documented, but its sufficiency or the analysis of its implications cannot be assessed from the record.

The registry does not report the trial's original sample-size justification or the statistical analysis plan. The planning illustration is based on the observed effect and stated assumptions, so it should not be treated as evidence about the original design. The record also does not report a clinically meaningful difference threshold, which limits interpretation of the size of the estimated effect and the confidence interval.

There is no reported account of missing measurements, participant flow for the primary endpoint, or the analysis population. Although the outcome summaries list 95 observations in each condition, the record does not explain how those observations relate to enrollment or whether incomplete crossover measurements occurred. The registry lists eight outcome measures but no secondary results, and does not report a multiplicity strategy. These omissions make it difficult to assess the possibility of selective reporting or the full set of outcome findings.

The masking designation is double, but the record does not specify who was masked or how. The adverse-event results are limited to the posted counts and do not describe event definitions, collection procedures, timing, or attribution. Finally, the primary result concerns high-contrast distance visual acuity after the stated wear periods. It should not be generalized to subjective satisfaction or preference, for which no results are posted, or to outcomes beyond those described in the registry.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Clinical Assessment of a Customized Free-form Progressive Addition Lens Spectacle — NCT01234207.
• Registry record last updated 2017-04-18; status last verified 2017-04.
• Results first posted 2017-04-18.
• 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

NCT01234207 is a completed randomized, double-masked crossover study sponsored by the University of California, Berkeley. The registry lists 95 enrolled participants with presbyopia and compares standard, non-free-form, non-customized PAL spectacles with individually customized free-form surfaced PAL spectacles. The recorded start is 2009-02, and primary completion is 2009-10. The phase is listed as NA.

The primary outcome is mean high-contrast distance visual acuity in logMAR after 1 week of wear of each spectacle type, with a 1-week washout period. The posted means are -0.12 for control spectacles and -0.11 for test spectacles; the reported mean difference is 0.01, with an unadjusted p-value of 0.29 and a confidence interval that crosses zero. The registry lists eight outcome measures, no analyses, and no secondary results. It records zero serious adverse events, zero other adverse events, and zero deaths in each condition.