Accommodative Relief for Uncomfortable Non-Presbyopes: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Accommodative Relief for Uncomfortable Non-Presbyopes (NCT03544216), a randomized na study. The primary outcome is Contact Lens Dry Eye Questionnaire-8 (CLDEQ-8) Score.

2. Clinical Question

Because the study used a crossover model, participants were assigned to a lens sequence and received both study lens types. One sequence began with single vision lenses and then changed to multifocal lenses; the other began with multifocal lenses and then changed to single vision lenses. This design allows within-participant observations across the study lenses, but interpretation depends on how the analysis accounts for repeated observations and sequence. Those details are not reported in the registry record.

3. Trial Design

The registry lists a randomized, single-masked, crossover study sponsored by Ohio State University. Its status is completed. The recorded start date is 2017-02-02, and the primary completion date is 2018-05-06. The study is listed with phase NA, which is not applicable to this device comparison.

Participants were allocated to one of two sequences. The Single Vision First group wore a single vision lens for the first two weeks and then crossed over to the multifocal lens for the second two weeks. The Multifocal first group followed the reverse order. Thus, both groups received both study interventions, but in a different order. The registry does not describe any washout period between lens periods, and it does not report whether period or carryover effects were considered in the analysis.

The primary outcome was collected at baseline and after two weeks of wear with each study lens. The registry also reports CLDEQ-8 summaries for habitual contact lenses. It is not clear from the record whether habitual lens results were collected at a distinct study visit or how they entered the sponsor’s analysis.

The outcome summaries list 84 observations for each lens condition. In a crossover study, those figures should not be interpreted as independent groups of different participants: the sequence descriptions say that participants received both study lenses. The registry does not provide a participant flow account, the number completing each period, or details on exclusions from the analyses.

Randomization is stated, but the method used to generate or conceal allocation is not reported in the registry record. Single masking is recorded, but the identity of the masked people is not reported. The original sample-size rationale and the trial’s intended statistical model are also not reported in the registry record.

4. Participant Flow and Accounting

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

Overall Study

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 Contact Lens Dry Eye Questionnaire-8 (CLDEQ-8) Score, measured over Baseline and after 2 weeks of contact lens wear with each study lens (single vision and multifocal).

The primary endpoint was the Contact Lens Dry Eye Questionnaire-8 (CLDEQ-8) score. This is a continuous questionnaire score intended to capture symptoms of contact lens discomfort. The registry specifies a scale from 0-37 points and says that higher point values indicate more or worse symptoms. It records the mean and standard deviation for each lens condition.

Using a symptom questionnaire makes the endpoint relevant to the study’s stated question: whether discomfort ratings differ after wearing different types of contact lenses. A continuous score retains gradations in reported symptoms rather than reducing responses to a simple yes-or-no classification. In general, a mean describes the group’s average score, while the standard deviation describes how spread out individual scores are around that average. These are general interpretations of the statistics, not additional findings about individual participants.

The registry identifies baseline measurement and measurement after two weeks of wear with each study lens. It does not report a minimally important difference or explain how a change in score should be interpreted as meaningful to participants. Nor does it report the instrument’s component-level results or the handling of incomplete questionnaires. Consequently, the posted group means describe average scores, but they do not by themselves show how many individuals experienced a particular degree of change.

7. Results Posted in the Registry

• CLDEQ-8 With Single Vision Contact Lens: mean 12.80 versus 14.30 on control; difference -1.50 (95% CI -3.57 to 0.57), standardized effect d = -0.22; z-test p = 0.156.
• CLDEQ-8 With Habitual Contact Lenses: mean 19.00 versus 14.30 on control; difference 4.70 (95% CI 2.88 to 6.52), standardized effect d = 0.78; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry identifies generalized linear models as the method for its reported analyses. It does not give the model family, link function, covariates, treatment coding, covariance structure, or details about how repeated observations were handled. The statistical description is therefore incomplete: the method name alone is not enough to reproduce the sponsor’s estimates or determine precisely which hypothesis each test addresses.

What does a mean difference describe?

A mean difference is the difference between two group averages, with the sign depending on the order used for subtraction. For the posted recalculation, the multifocal mean is the reference and the comparison mean is subtracted from it. Thus, the single vision comparison is reported as -1.5, whereas the habitual-lens comparison is 4.7. The negative sign in the first comparison reflects the ordering of those means; the score scale itself still runs in the direction stated in the registry, where higher scores indicate worse symptoms.

These recalculations use posted group means and standard deviations. They are simple unadjusted comparisons and do not reproduce a crossover analysis that models the paired nature of measurements from the same participant. In a crossover study, each participant’s results under both lens types may be correlated. A model that accounts for that correlation can have different uncertainty from a calculation that treats the summarized conditions as separate groups. The sponsor’s analysis takes precedence because the record flags a discrepancy between the sponsor result and the recalculation.

What do standard deviations and intervals contribute?

A standard deviation describes the variability of scores among observations within a condition. It is not the same as the uncertainty in a group mean or a confidence interval for a treatment contrast. A confidence interval for a mean difference describes a range of values compatible with the data and the assumptions of the calculation. Narrower intervals indicate greater precision under those assumptions; wider intervals indicate more uncertainty. The recalculated intervals are based on the posted summaries and should not be mistaken for sponsor-model intervals.

The recalculation labels its p-values as unadjusted. In general, an unadjusted p-value is obtained for an individual comparison without correction for testing multiple hypotheses. When multiple outcomes or contrasts are tested, repeated testing can increase the chance of at least one apparently small p-value under null conditions. Whether and how the sponsor addressed multiplicity is not reported in the registry record. The five listed model analyses make that omission relevant, but the record does not identify which analyses were primary, exploratory, or adjusted.

Why does over-dispersion matter?

In general, over-dispersion occurs when observed variability exceeds what a model’s assumed distribution expects. If it is not addressed where relevant, standard errors can be too small and inferential results can appear more certain than warranted. The registry names generalized linear models but does not state the outcome distribution or whether over-dispersion was assessed or accommodated. Since the endpoint is a bounded questionnaire score, the selected model and its assumptions matter; the registry does not report enough information to assess their fit.

What is special about crossover data?

General statistical considerations for crossover designs include within-participant correlation, treatment sequence, period effects, and possible carryover from one treatment period to the next. A paired analysis can account for the fact that two measurements from the same participant are not independent. Period terms can distinguish treatment differences from changes that occur over time, while sequence terms can represent the assigned order. The record confirms a crossover design and describes the order of lens use, but it does not report whether or how these features were included in the generalized linear models. No washout period is described in the registry record.

The posted summary-statistic calculations do not model these design features. They are useful as transparent, unadjusted reference calculations, not as replacements for the sponsor’s analysis. Given the flagged discrepancy, interpretation should prioritize the sponsor’s own analysis while recognizing that its model specification and contrast estimates are not sufficiently described in the registry record to evaluate in detail.

10. Confidence Intervals and Precision

The recalculated comparison of single vision with multifocal lenses has a mean difference of -1.5 and an interval from -3.573 to 0.573. Because the interval spans zero, the simple unadjusted calculation is compatible with no mean difference as well as with differences in either direction. This does not prove that the lens conditions are equivalent; the interval permits a range of values, and the registry does not define an equivalence margin.

The habitual-lens comparison with multifocal lenses has a recalculated mean difference of 4.7 and an interval from 2.879 to 6.521. This interval is entirely above zero in the unadjusted calculation. It indicates greater precision around a positive average difference than a point estimate alone would convey, but it does not account for the crossover structure or replace the sponsor’s model-based analysis.

In general, an interval expresses uncertainty about an estimate under specified statistical assumptions. Its width reflects both the amount and variability of information and the method used to calculate it. The record does not state a confidence level for these recalculated intervals, so no confidence percentage should be inferred from the registry record. The sponsor’s analyses list p-values but do not provide effect estimates or intervals, limiting the ability to assess the precision of the sponsor’s treatment contrasts.

All confidence intervals and p-values based on posted summaries are unadjusted recalculations. Because the discrepancy flag is true, the sponsor’s own analysis takes precedence. The underlying paired data, full model output, and detailed analysis plan are not reported in the registry record, so the posted summary statistics cannot resolve the difference between approaches.

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 figures are planning illustrations expressed as participants per arm, not total events. They use the observed recalculated effect as a reference and show alternative planning scenarios for detecting 100%, 75%, or 50% of that effect. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. For each effect scenario, the two power columns indicate the participants per arm associated with 80% power and 90% power, respectively. In plain language, these are planning targets for the chance of detecting the specified effect if the assumptions hold.

For the single vision comparison, planning for 100% of the observed effect lists 328 participants per arm for 80% power and 439 participants per arm for 90% power. Planning for 75% lists 583 participants per arm for 80% power and 781 participants per arm for 90% power. Planning for 50% lists 1,312 participants per arm for 80% power and 1,756 participants per arm for 90% power.

For the habitual-lens comparison, planning for 100% of the observed effect lists 26 participants per arm for 80% power and 35 participants per arm for 90% power. Planning for 75% lists 46 participants per arm for 80% power and 62 participants per arm for 90% power. Planning for 50% lists 104 participants per arm for 80% power and 138 participants per arm for 90% power.

The pattern illustrates a general principle: smaller effects are harder to distinguish from random variation, so planning to detect a smaller effect requires more participants. These calculations are not observed power. They are not the trial’s original design calculation, whose assumptions are not reported in the registry record, and their equal-arm planning framework does not reflect all features of the crossover design.

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 = -1.500; pooled standard deviation σ = 6.855.
2. n = 2 × (1.96 + 0.842)² × 6.855² / -1.500² = 327.8, rounded up to 328 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 <- -1.5                      # observed difference in means
sigma <- 6.85456052566465                     # 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(3544216)
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 = 328 (80% power), 439 (90% power)
 75% of observed effect: n per arm = 583 (80% power), 781 (90% power)
 50% of observed effect: n per arm = 1,312 (80% power), 1,756 (90% power)
power.t.test: 328.8 
Simulated power at n = 328 per arm: 0.798 (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. Analyses Reported by the Sponsor

The registry lists generalized linear model analyses with p-values, but it does not provide the model estimates, confidence intervals, detailed contrasts, or sufficient model specifications to reconstruct the sponsor’s results. One listed analysis includes all three lens conditions and has p < 0.001. Four other analyses are listed for the multifocal and single vision conditions, with p-values of 0.5, 0.7, 0.3, and 0.047. The record does not say which model terms or hypotheses correspond to those four values, so they should not be treated as a clearly identified set of treatment-effect tests.

The summary-statistic recalculations are unadjusted and do not account explicitly for the crossover structure. The registry flags a discrepancy between those recalculations and the sponsor’s own analysis. Accordingly, the sponsor’s own analysis takes precedence. This does not make the recalculation a substitute for the sponsor’s model: it provides a transparent comparison based on the posted means and standard deviations, while the sponsor analysis is the trial’s reported inferential analysis.

The limited sponsor reporting prevents a complete assessment of why its results differ from the recalculation. Model specification, treatment of repeated measurements, period and sequence terms, missing data, and multiplicity procedures are not reported in the registry record. Readers should therefore avoid attaching a specific interpretation to the listed p-values beyond the information explicitly associated with each analysis.

14. Multiplicity, Missing Data and Analysis Populations

The registry reports one primary outcome measure and five analyses. It does not identify which of the five generalized linear model analyses were prespecified primary tests, how the analyses relate to one another, or whether any adjustment for multiple testing was used. In general, when several hypotheses are tested, the interpretation of individual p-values can depend on whether testing was planned and whether a multiplicity procedure was applied. The relevant procedures are not reported in the registry record.

The posted summaries also do not provide a participant flow account or report missing questionnaire data. The numbers contributing to each lens-condition summary are listed as 84, but the record does not explain whether these represent all enrolled participants, only participants with complete observations, or a particular analysis population. The inclusion and exclusion rules for the sponsor’s models are not reported. It is therefore not possible to assess whether missing outcomes or departures from the planned analysis population could affect the results.

For a crossover study, a complete analysis description would ordinarily clarify how repeated observations within participants were handled and whether period, treatment sequence, or carryover were included. Those details are not reported in the registry record. The record also does not describe the approach to incomplete periods or whether participants were analyzed according to their randomized sequence.

The registry’s model label and p-values alone do not resolve these questions. Nor does the unadjusted recalculation address them. The reported material supports a description of the posted condition means and the listed model p-values, but it does not permit a full appraisal of multiplicity control, missing-data assumptions, or the analysis population.

15. 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 lists serious adverse events and deaths for the single vision and multifocal contact lens groups. For each group, 84 participants are listed as at risk; the reported number affected by a serious adverse event is 0, and the reported number of deaths is 0. The record also lists 84 at risk for other adverse events in each group and reports 0 affected in each.

These figures describe what was recorded in the registry for the stated groups. A zero count does not establish that no adverse events of any kind occurred outside the events captured and reported, nor does it establish that risks are absent. The registry does not list serious adverse-event terms, and the absence of listed terms should be read alongside the reported zero counts rather than as a detailed event-by-event safety account.

The study is a crossover trial in which participants received both study lenses in sequence. The adverse-event summaries do not explain how exposure time, event attribution, or repeated exposure was handled. The record also does not provide a fuller safety narrative. These limitations constrain comparisons between the lens conditions; the figures should be interpreted as registry-reported counts, not as definitive evidence about safety.

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

The registry describes average CLDEQ-8 scores after use of multifocal, single vision, and habitual contact lenses, with higher scores representing more or worse symptoms. The posted means are 14.3 with multifocal lenses, 12.8 with single vision lenses, and 19.0 with habitual lenses. The simple unadjusted recalculations indicate a mean difference of -1.5 for single vision compared with multifocal lenses and 4.7 for habitual lenses compared with multifocal lenses. Those calculations have different levels of precision, as reflected by their respective intervals.

These findings do not establish that one lens type is clinically better or worse. The registry does not provide a threshold for a meaningful CLDEQ-8 difference, individual participant changes, or detailed sponsor estimates for the contrasts. The sponsor’s generalized linear model results are listed as p-values without enough information to identify all corresponding hypotheses or evaluate the estimates. Because the registry flags a discrepancy, the sponsor’s own analysis takes precedence over the unadjusted recalculations.

In general, statistical evidence about an average difference is not the same as evidence about the experience of every participant. Group means can conceal variation between people, and the standard deviations indicate that scores varied within conditions. The record does not report how many participants improved, worsened, or remained unchanged across lens periods.

The crossover design means participants received both study lenses in different orders. This can support within-participant comparisons when the analysis appropriately accounts for repeated measurements and period effects. The registry does not report enough analytical detail to determine how these features were handled. The posted results therefore support a careful description of average scores and reported tests, but not a definitive conclusion about the size or practical importance of a lens effect.

17. Why This Trial Matters Statistically

This trial raises several statistical issues that matter when interpreting clinical research. First, the crossover design means the observations under different lens conditions are related within participants. Treating them as independent groups can misstate uncertainty if the relationship between measurements is ignored. The registry confirms the crossover sequence but does not describe how the sponsor’s model handled within-participant dependence.

Second, a simple contrast of means is not automatically equivalent to the trial’s primary analysis. The recalculations use the posted means and standard deviations, whereas the sponsor reports generalized linear models. Model structure, treatment of period and sequence, and missing-data handling can affect both estimates and uncertainty. The discrepancy flag is therefore important: the sponsor’s own analysis takes precedence, while the summary-based calculations remain an unadjusted reference.

Third, statistical significance and practical importance are different questions. The registry reports p-values and group averages, but it does not specify a minimally important difference for the CLDEQ-8. A p-value alone does not describe the magnitude of a difference or its relevance to participants. Confidence intervals help describe uncertainty around an estimate, but the sponsor’s reported analyses do not include effect estimates or intervals in the registry record.

Finally, multiple listed model analyses and limited reporting make it difficult to understand the full inferential plan. The registry does not state which tests were prespecified or whether multiplicity was addressed. Making those elements explicit would help readers distinguish the main comparison from additional analyses and assess how much confidence to place in individual test results.

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 registry record has several limitations specific to interpreting this trial. It describes the randomized crossover sequences and the two-week lens periods, but does not report whether there was a washout period or whether period, sequence, or carryover effects were modeled. Since every participant in the sequence descriptions received both study lenses, accounting for within-participant correlation is particularly relevant. The analysis details available in the record do not establish how this was done.

The record reports means and standard deviations for all three lens conditions, but does not provide individual paired data or the covariance between a participant’s scores under different conditions. Consequently, the recalculated comparisons cannot reproduce a paired analysis. The record also does not explain the relationship between the habitual-lens observations and the randomized study-lens periods.

The sponsor’s generalized linear model analyses are reported through p-values without corresponding effect estimates, interval estimates, model terms, or a clear description of the hypotheses represented by each test. A discrepancy is flagged between sponsor results and recalculations. The sponsor analysis takes precedence, but the information needed to evaluate the source of the discrepancy is not reported in the registry record.

There is no reported minimally important CLDEQ-8 difference, detailed account of missing outcomes, analysis-population definition, multiplicity procedure, or original sample-size justification. Participant characteristics beyond the stated age range and myopic contact lens wear are not described. These omissions limit assessment of generalizability, precision, and the robustness of the statistical conclusions.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Accommodative Relief for Uncomfortable Non-Presbyopes — NCT03544216.
• Registry record last updated 2019-02-15; status last verified 2019-01.
• Results first posted 2019-02-15.
• 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

NCT03544216, titled “Accommodative Relief for Uncomfortable Non-Presbyopes,” is a completed randomized, single-masked crossover study sponsored by Ohio State University. It enrolled 84 participants described as myopic contact lens wearers in the non-presbyopic age range of 30-40 years. Participants received multifocal and single vision contact lenses in opposite orders.

The primary outcome was the CLDEQ-8 score, measured at baseline and after two weeks of wear with each study lens. Higher scores indicate more or worse symptoms. Posted means were 14.3 with multifocal lenses, 12.8 with single vision lenses, and 19.0 with habitual contact lenses.

The registry lists generalized linear model analyses but does not provide sufficient detail to interpret every listed p-value or reproduce the sponsor’s analysis. Unadjusted recalculations are available, and the discrepancy flag means the sponsor’s own analysis takes precedence. The registry does not report the original sample-size rationale, detailed missing-data methods, multiplicity approach, or full crossover model specification.