An Evaluation of the Effectiveness of Dual Focus Soft Contact Lenses in Slowing Mypoia Progression: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for An Evaluation of the Effectiveness of Dual Focus Soft Contact Lenses in Slowing Mypoia Progression (NCT01729208), a randomized na study. The primary outcome is Change in Refractive Error Relative to Baseline.

2. Clinical Question

3. Trial Design

The registry record describes a randomized, double-masked, parallel-group clinical evaluation of two soft contact lens devices. Participants were allocated to a dual focus soft contact lens or a single vision soft contact lens. The study is identified as multicentre in its official title and is marked completed in the registry. Its recorded phase is not applicable.

The registry lists an enrollment of 144. For the posted primary outcome, results are reported for 58 participants in the dual focus group and 60 in the single vision group. These outcome denominators are not the same as the enrollment figure. The registry record does not explain the difference, so the reason should not be inferred from the reported numbers alone. The adverse-event summaries use different at-risk denominators; these are described separately in the safety interpretation.

The primary outcome was mean change in refractive error relative to baseline, measured at 12 months. The registry also lists secondary outcomes concerning biomicroscopic findings and adverse events. It reports 13 outcome measures overall and 7 posted secondary outcomes. The record does not establish whether every listed measure was collected at the same visits or in the same analysis population.

The registry record does not report the original sample-size justification, the intended analysis population, details of the randomization procedure, or which individuals were masked. It also does not report the trial’s full statistical analysis plan. The design labels establish the broad structure of the comparison, but they do not resolve these operational or analytic details.

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.

Baseline

Reasons for not completing this period:

12 Months Follow-up

Reasons for not completing this period:

24 Months Follow-up

Reasons for not completing this period:

36 Months Follow-up

Reasons for not completing this 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.

Population: Subjects were randomized to wear dual focus soft contact lens and single vision soft contact lens.

6. Primary Endpoint

The registry lists the primary outcome as Change in Refractive Error Relative to Baseline, measured over 12 months.

The primary endpoint is the mean change in refractive error from baseline to 12 months, measured in diopters using cycloplegic auto-refraction. A mean is a measure of the central value of a continuous outcome: it describes the average change in the group, rather than the change for every participant. The registry reports the group means and standard deviations.

Refractive error is relevant to the stated study question because the trial was designed to evaluate change in myopia over time. Expressing the endpoint as change relative to baseline focuses the comparison on how the measured refractive error shifted during the stated follow-up period, rather than on the final measurement alone. Cycloplegic auto-refraction is the measurement approach named in the registry record; the record does not give further procedural detail in the primary outcome description.

A group mean can conceal variation among individual participants. The standard deviation describes the spread of observed values around the mean, while the difference between group means summarizes the average contrast. Neither statistic describes the full distribution or the range of individual experiences. The registry does not report the primary outcome population in its outcome description, and it does not provide individual participant data. Interpretation is therefore limited to the posted group summaries and comparison.

7. Results Posted in the Registry

• Single Vision Soft Contact Lens: mean -0.58 versus -0.18 on control; difference -0.40 (95% CI -0.54 to -0.26), standardized effect d = -1.00; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is continuous: refractive error is measured in diopters, and the registry reports a mean and standard deviation for each arm. A continuous outcome can take values across a scale rather than being limited to categories such as event versus no event. Reporting means makes the average change easy to compare, while standard deviations give a sense of how dispersed the participant measurements are around those averages.

What does the mean difference describe?

A mean difference subtracts one group mean from the other according to a specified comparison order. Here, the posted comparison is framed as single vision relative to dual focus, with a mean difference of -0.4 diopters. The negative sign is meaningful only together with that order: it indicates that the single vision group’s average change was lower than the dual focus group’s average change. Reversing the order would reverse the sign, without changing the underlying separation between the means. The registry’s comparison is an unadjusted group contrast; the record does not describe covariate adjustment for this estimate.

What does a standard deviation tell the reader?

A standard deviation describes the spread of observations around a mean. It is not the uncertainty of the mean itself, and it is not a confidence interval. The reported standard deviations, 0.39 and 0.41 diopters, suggest that there was variation in the outcome within both groups. Without a distribution plot or participant-level results, they do not reveal whether values were symmetric, clustered, or influenced by unusually high or low observations. Similar standard deviations also do not imply that each participant’s response was similar across groups.

How should the p-value be understood?

The registry reports an unadjusted p-value of <0.001 for the comparison. In general, a p-value describes how compatible the observed data, or data more extreme, are with a specified null hypothesis under the assumptions of the test. It is not the probability that the null hypothesis is true, and it does not quantify the size or practical importance of the difference. The registry record does not identify the test used, its assumptions, or whether any additional analyses informed the reported result. The p-value should therefore be read as the posted statistical result, not as a complete account of the analytic procedure.

What does a confidence interval add?

In general, a confidence interval presents a range of effect estimates compatible with the data under a particular method and confidence level. It conveys uncertainty about the estimated contrast more directly than a p-value alone. The posted comparison interval has both bounds on the negative side of zero. This is consistent with the reported unadjusted p-value and the direction of the mean difference. The registry record does not specify the confidence level or interval-construction method in the available outcome information, so the interval should be interpreted without attributing an unreported procedure to it.

What is not established by the statistical summary?

A randomized comparison is intended to compare groups formed through allocation, but the registry’s broad design label does not describe the allocation sequence, concealment, or implementation. The record also does not state which participants, clinicians, or assessors were masked, despite identifying the study as double-masked. It does not report whether the analysis followed assignment as randomized, whether it was restricted to participants completing follow-up, or whether any other population was used. These are relevant details when judging possible sources of bias, but their absence from the registry record does not demonstrate that any particular procedure was or was not followed.

The outcome is measured at 12 months, but the registry summary does not provide individual visit patterns, adherence, reasons for missing measurements, or a method for handling missing data. Nor does it report model diagnostics or the handling of multiple outcomes. The record therefore supports interpretation of the posted group summaries and comparison, while leaving important aspects of the analysis and data completeness unreported. General statistical concepts can help explain what the numbers mean, but cannot fill in those missing trial-specific details.

10. Confidence Intervals and Precision

The reported mean difference is -0.4 diopters, with an interval whose lower and upper bounds are both negative. Because zero is outside the reported interval, the interval supports a difference between the group means under the method used to calculate it. The registry record does not state the confidence level or the interval method in the primary outcome description; those details are therefore not reported in the registry record.

In general, a confidence interval represents the uncertainty around an estimated effect under a specified statistical procedure. A narrower interval indicates greater precision than a wider interval, all else being comparable. The interval is not a range that contains a fixed proportion of individual participants’ outcomes, and it is not a guarantee that the true effect lies within its limits. It concerns the estimated group contrast, not the spread of individual refractive-error changes.

The group means are accompanied by standard deviations of 0.39 and 0.41 diopters, and the primary outcome denominators are 58 and 60. These summaries provide context for the variability and amount of outcome information reported, but they do not substitute for the comparison interval. The registry record does not provide confidence intervals for each group mean, participant-level measurements, or further information about missing outcome data. It is therefore not possible to assess from the posted summary how the interval might change under different assumptions or analyses.

The interval and unadjusted p-value are consistent in indicating a group contrast in the posted primary result. Precision is distinct from clinical importance: an estimate can be precise without answering whether its magnitude matters for a particular decision or participant. The registry record does not define a threshold for a clinically important difference, so the statistical interval alone cannot establish that judgment.

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 sample-size display is a planning illustration based on the observed mean difference, not a report of the trial’s original sample-size calculation. Its 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 to a stated fraction of the observed effect. The registry record does not report the assumptions used for the trial’s own original design or sample-size justification.

For this continuous-outcome comparison, the displayed figures are participants per arm, not total events. The entries describe planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. For each effect size, one column gives the participants per arm for 80% power and another gives the participants per arm for 90% power. In plain terms, power is the probability of detecting an effect of the specified size at the chosen significance level under the planning assumptions, if that effect is present. The 90% target represents a higher planned chance of detection than the 80% target and is associated with a larger participant requirement in the displayed scenarios.

The displayed requirements rise as the assumed effect gets smaller: planning for a smaller contrast requires more participants per arm to achieve the stated power under the same assumptions. The 80% and 90% columns are hypothetical planning values, not evidence about the probability that this completed trial detected its effect. This is not observed power. These figures should not be read as the trial’s enrollment target or as a reconstruction of the protocol’s design, because the registry record does not report the original planning assumptions.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -0.400; pooled standard deviation σ = 0.400.
2. n = 2 × (1.96 + 0.842)² × 0.400² / -0.400² = 15.7, rounded up to 16 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 <- -0.4                      # observed difference in means
sigma <- 0.400297303306533                     # 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(1729208)
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 = 16 (80% power), 22 (90% power)
 75% of observed effect: n per arm = 28 (80% power), 38 (90% power)
 50% of observed effect: n per arm = 63 (80% power), 85 (90% power)
power.t.test: 16.7 
Simulated power at n = 16 per arm: 0.781 (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 13 outcome measures overall and 7 posted secondary outcomes. The secondary outcome labels include biomicroscopic findings and adverse events, with some labels repeated in the record. The presence of several outcomes raises a general statistical consideration: when many hypotheses are tested, the chance of at least one apparently unusual result can increase if each test is considered separately. Whether and how that issue was addressed in this trial is not reported in the registry record.

The primary comparison is accompanied by an unadjusted p-value. The registry does not report a multiplicity adjustment, a hierarchy for testing outcomes, or a prespecified distinction between confirmatory and exploratory analyses beyond identifying the primary outcome. It would be inappropriate to infer that an adjustment was or was not performed in a separate analysis not described in the registry. The available record supports only the statement that the posted comparison p-value is unadjusted.

The primary outcome description does not name the population included in the analysis. The posted arm denominators are 58 and 60, while enrollment is recorded as 144. The registry record does not explain how the analysis population was defined, why its denominators differ from enrollment, or whether those numbers reflect missing measurements, exclusions, or another reason. It also does not state whether participants were analyzed according to randomized assignment, whether only participants with observed measurements were included, or whether another population definition was used.

Missing-data handling is not reported in the registry record. In general, missing measurements can affect an estimate if the likelihood of having an observed result is related to participant characteristics or outcomes. Methods for addressing missingness rely on assumptions, and the assumptions and method need to be described to judge their plausibility. The registry summary does not provide reasons for missingness, imputation procedures, sensitivity analyses, or a flow of participants through follow-up. Consequently, the reported means and comparison should be understood as posted summaries, without claims about how missing data were handled or how robust results are to alternative assumptions.

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 5% reporting threshold.

The registry reports 0 serious adverse events among 70 participants at risk in the dual focus group and 0 among 74 participants at risk in the single vision group. It also reports 0 other adverse events in each group and 0 deaths in each group. These are the posted safety counts; they are not the same denominators as the primary endpoint denominators of 58 and 60.

A count of zero means that no event of the corresponding type was recorded in the stated at-risk group in the registry summary. It does not show that the underlying risk is necessarily zero, and it does not establish that no event could occur outside the recorded observation or reporting process. The record does not provide further details about event definitions, collection procedures, duration of safety observation, or whether every type of event was assessed in the same way.

The registry lists adverse events among the secondary outcomes, but the brief safety summary does not provide event narratives or a breakdown of non-serious event types. The numbers should therefore be read as a compact account of reported counts, not as a comprehensive description of safety experience or a comparison with enough detail to characterize rare events.

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

The posted primary result shows different mean changes in refractive error between the two randomized groups at 12 months. The dual focus group mean was -0.18 diopters, and the single vision group mean was -0.58 diopters. The reported mean difference, ordered as single vision relative to dual focus, was -0.4 diopters. The reported comparison interval lies on the negative side of zero, and the unadjusted p-value is <0.001. Together, these statistics describe a group-level contrast in the specified endpoint and timeframe.

The result does not say that every participant experienced a change equal to their group mean, or that each participant in one group had a different result from every participant in the other. Standard deviations of 0.39 and 0.41 diopters indicate variation within both groups. Group averages and a comparison interval cannot show the full distribution of individual responses, and the registry does not post participant-level data in the record.

The result also does not, by itself, establish the clinical importance of the difference. The registry does not report a threshold for a meaningful change or provide context for interpreting such a threshold. Nor does the primary endpoint answer questions about outcomes other than refractive error, longer-term results, or participants’ experiences beyond the measures listed in the record. The available follow-up timeframe for the primary result is 12 months.

There are limits to assessing the analysis. The registry does not report the primary analysis population, missing-data handling, original sample-size assumptions, or a full statistical plan. It records enrollment of 144 but posts primary outcome denominators of 58 and 60, without explaining the relationship. These gaps do not invalidate the posted summary, but they constrain evaluation of how it was produced and how broadly it should be interpreted. The careful conclusion is about the reported group comparison, not an unqualified claim about all outcomes or all participants.

16. Why This Trial Matters Statistically

This trial illustrates why a clinical result should be read through both its estimate and its uncertainty. The group means describe average changes, while the mean difference places the contrast on the same outcome scale and the interval conveys precision under its statistical method. The p-value provides a related measure of statistical compatibility with a null comparison, but it does not replace the effect estimate or indicate clinical importance.

The distinction between within-group spread and uncertainty in a group contrast is also important. The standard deviations describe variation in participant measurements around the group means. The comparison interval addresses uncertainty in the estimated difference between means. These quantities answer different questions and should not be treated as interchangeable. The posted summaries allow a reader to distinguish them, while the absence of individual data limits assessment of distributions and outlying observations.

The record also demonstrates why denominators need attention. The enrollment figure and the arm-specific denominators for the primary outcome are different, and the adverse-event summaries use their own at-risk denominators. Without an explanation of participant flow and analysis populations, these counts cannot be combined or treated as if they describe the same set of observations. The missing information matters for understanding completeness and potential bias, not merely for reproducing a calculation.

Finally, planning illustrations based on an observed effect are not the same as the trial’s original design justification. They can show how assumed effect size and desired power relate to participant requirements under stated assumptions, but they cannot reconstruct the protocol’s choices. Separating trial results, uncertainty, planning scenarios, and unreported methods is essential to a statistically responsible reading of a registry result.

17. Limitations

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

The primary outcome description identifies the measure and timeframe but does not report the analysis population or the number of participants with missing measurements. Although the registry records enrollment of 144, the posted primary outcome results use arm denominators of 58 and 60. The record does not explain this difference, so no reason for it can be assigned from the available information.

The registry calls the trial double-masked but does not state which parties were masked or describe the procedures used to maintain masking. It identifies randomization but does not report the sequence-generation or allocation-concealment methods. These details would help readers assess how the design was implemented; they are not reported in the registry record.

The record does not report the trial’s original sample-size justification, the statistical test or model for the primary comparison, the confidence level or construction method for the reported interval, or a full analysis plan. It also does not describe multiplicity handling, missing-data methods, adherence, or sensitivity analyses. Those omissions limit evaluation of assumptions and robustness.

The primary endpoint is a 12-month refractive-error measure, so the posted result should not be extended to later timeframes or outcomes not represented by that endpoint. The registry lists other outcome measures, but the record summary does not give full results for every listed measure in the registry record described. Safety summaries report zero counts for the categories presented, but event definitions and observation details are not included. These limitations define the scope of what the posted registry information can support.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: An Evaluation of the Effectiveness of Dual Focus Soft Contact Lenses in Slowing Mypoia Progression — NCT01729208.
• Registry record last updated 2020-02-24; status last verified 2020-02.
• Results first posted 2020-02-24.
• 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, parallel-group evaluation of dual focus versus single vision soft contact lenses in children with myopia. It lists enrollment of 144 and identifies mean change in refractive error at 12 months as the primary outcome.

The posted primary outcome means were -0.18 diopters for the dual focus group and -0.58 diopters for the single vision group, with a reported mean difference of -0.4 diopters and an unadjusted p-value of <0.001. Primary outcome denominators were 58 and 60. The record does not explain the difference between those denominators and enrollment or report the primary analysis population.

The safety summary reports zero serious adverse events, zero other adverse events, and zero deaths in each arm, using at-risk denominators of 70 and 74. Original sample-size assumptions, missing-data methods, and a full statistical analysis plan are not reported in the registry record.