Clinical Investigation of the Next-Generation Intraocular Lenses: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Clinical Investigation of the Next-Generation Intraocular Lenses (NCT03372434), a randomized na study. The primary outcome is Distance Corrected Intermediate Visual Acuity.

2. Clinical Question

This is a question about a measured visual-acuity outcome at a specified follow-up, not a complete account of every outcome relevant to cataract surgery or lens selection. The registry record describes the study as a 6-month investigation, while the posted primary outcome is measured at 1 month. The record also describes bilateral implantation and an analysis limited to the first operative eye. Therefore, the posted group estimates should be read as measurements from that defined eye and visit, not as a summary of both eyes or of the entire follow-up period.

3. Trial Design

The registry describes NCT03372434 as a completed, randomized, double-masked, parallel clinical investigation of three intraocular lens models in participants with cataract. The listed allocation is randomized, and the study summary describes subject and evaluator masking. The three groups received Model ZFR00, Model ZYR00, or the TECNIS Multifocal control, Model ZLB00. The record lists phase as not applicable.

The study summary describes a prospective, multicenter investigation lasting 6 months, to be conducted at up to 14 sites in the United States. It states that the study would enroll up to 260 subjects to achieve approximately 220 randomized and bilaterally implanted subjects, with approximately 195 evaluable subjects at 1 and 6 months. These are the study summary's planned figures. The registry's enrollment field reports 225. The posted primary outcome has group counts of 76, 72, and 73; the reason these counts differ from the summary's approximate evaluable target is not reported in the registry record.

Participants were to receive the same assigned lens in both eyes. The first eye operated on was designated the primary study eye. The primary outcome was assessed at 1 month, although the overall study summary describes 6 months of follow-up. The registry reports a study start date of 2018-01-16, a primary completion date of 2018-07-11, and a completed status.

The registry record does not report the randomization sequence method, how allocation was concealed, or the precise procedures used to maintain masking. It also does not report the trial's original sample-size justification or the detailed protocol for follow-up and analysis. These omissions limit what can be inferred about the operational details of the design, even though randomization, masking, parallel groups, and the intended bilateral assignment are described.

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: 225 subjects were implanted with a study lens in at least one eye. Two hundred and twenty five (225) subjects had a study IOL in the first eye.

Overall Study

Analysis population for the primary outcome, as defined in the registry: Safety population

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 Distance Corrected Intermediate Visual Acuity, measured over 1 month.

The primary endpoint is distance-corrected intermediate visual acuity at 1 month. Visual acuity was assessed separately in each eye under photopic, or well-lit, conditions, using best distance correction and a high-contrast ETDRS chart positioned at 66 cm from the spectacle plane. The outcome is measured in logMAR, the logarithm of the minimum angle of resolution. As specified in the registry description, a lower numeric value represents better acuity.

Distance correction is used during assessment so that the measurement reflects intermediate acuity under the stated correction condition rather than an uncorrected view. The standardized chart, viewing distance, lighting condition, and correction help define what the recorded outcome represents. They do not make the result a measure of every aspect of visual function or of participants' experience in daily activities.

The registry specifies a mean and standard deviation for this continuous outcome. The analysis was prespecified for the first operative eye only, even though participants were intended to receive the same lens in both eyes. This distinction matters: the posted endpoint is not an average across both eyes. It is a group summary for the designated study eye at a defined visit, using the safety population. The registry record does not report a primary endpoint at a later visit in the posted results.

7. Results Posted in the Registry

• Model ZLB00: mean 0.22 versus 0.10 on control; difference 0.12 (95% CI 0.08 to 0.16), standardized effect d = 0.92; z-test p = <0.001.
• Model ZYR00: mean 0.15 versus 0.10 on control; difference 0.05 (95% CI 0.01 to 0.09), standardized effect d = 0.37; z-test p = 0.025.

8. Statistical Interpretation

9. Statistical Methods Explained

The posted outcome is continuous: each eye has a logMAR measurement, and the registry reports a mean and standard deviation for each device group. A mean describes the center of the observed measurements, while a standard deviation describes how much the measurements vary around that center. These summaries answer different questions. A smaller standard deviation indicates less spread in the observed values; it does not by itself show that a group mean is estimated with greater precision.

What does the mean difference represent?

The comparisons are expressed as mean differences, with the Model ZFR00 mean as the reference and each other group as the comparison. For Model ZLB00, the posted group means are 0.098 and 0.219, and the recalculated difference is 0.121. For Model ZYR00, the posted means are 0.098 and 0.147, and the recalculated difference is 0.049. The positive direction means that the comparison group's mean logMAR is higher than the Model ZFR00 mean. Since the registry states that lower logMAR represents better acuity, the direction of a mean difference needs to be read together with that scale definition.

A group mean difference does not mean that every participant had that difference, nor does it describe the distribution of individual responses. Participants may have measurements above or below their group mean. The mean comparison compresses those individual observations into a group-level summary, and its uncertainty depends on the spread and the number of observations as well as the comparison method.

How should the confidence intervals be read?

A confidence interval gives a range of values compatible with the estimate under the statistical method used. It expresses uncertainty about a group-level difference rather than a range containing a stated proportion of individual participant measurements. For Model ZLB00 versus Model ZFR00, the recalculated interval is 0.079 to 0.164. For Model ZYR00 versus Model ZFR00, it is 0.006 to 0.092. Both intervals are above zero, but they are unadjusted intervals; the registry record does not report a procedure for accounting for multiple comparisons.

The intervals are simple unadjusted recalculations from posted summary statistics. The registry record does not report a sponsor analysis of these comparisons. Accordingly, the calculated estimates and intervals should be interpreted as descriptive statistical reconstructions from the posted means, standard deviations, and group counts, rather than as a replacement for a trial team's prespecified model or analysis.

What do the p-values add?

The unadjusted p-values are p < 0.001 for Model ZLB00 compared with Model ZFR00 and p = 0.025 for Model ZYR00 compared with Model ZFR00. In general, a p-value describes the compatibility of data with a null model under specified statistical assumptions. It is not the probability that the null model is true, and it does not measure the magnitude or importance of an effect. A small p-value can coexist with uncertainty about the practical interpretation of a difference.

These p-values are labelled unadjusted. The comparisons share a reference group, so looking at more than one comparison raises a multiplicity question: repeated testing can make the chance of at least one apparently unusual result larger than for a single test. The registry record does not report whether or how this issue was addressed in the trial's own analysis. No adjusted p-values or sponsor analysis are posted for these comparisons.

Why do the assessment details matter?

The outcome is tied to an assessment protocol: monocular measurement under photopic conditions, with best distance correction and a high-contrast ETDRS chart at 66 cm. Standardized measurement conditions help define the endpoint and make its meaning more specific. They also delimit interpretation. The result does not directly describe binocular visual acuity, uncorrected vision, performance under other lighting or contrast conditions, or patient-reported experience.

The registry says the analysis was prespecified for the first operative eye. That avoids treating two eyes from the same participant as if they were unrelated observations in this endpoint summary. The registry does not report the detailed statistical handling of the eye-level observations, missing measurements, or protocol deviations. The primary population is described as the safety population; the record does not give a separate efficacy-population definition for the posted endpoint.

What does the design information support?

Randomized allocation, double masking, and a parallel-group structure are reported. In general, randomization is intended to make assigned groups comparable with respect to measured and unmeasured factors, while masking can reduce the influence of expectations on care or assessment. Those design features do not guarantee that bias is absent. The registry record does not detail the randomization method, allocation concealment, masking procedures, or how departures from assignment were handled. Statistical interpretation should therefore distinguish the design features that are reported from operational safeguards that are not described.

The calculations are not the trial's original design analysis. The registry record does not report the original sample-size justification, the statistical plan for the primary comparison, or an interim-analysis plan. Those details cannot be inferred from the observed group counts, p-values, or planning illustrations. The posted numbers support a transparent comparison of the reported summaries, while leaving important parts of the trial's prespecified inferential approach unreported.

10. Confidence Intervals and Precision

Precision concerns how tightly an estimate is determined by the data and method. For a mean difference, a confidence interval communicates uncertainty around the estimated group contrast. The recalculated 95% confidence interval for Model ZLB00 compared with Model ZFR00 extends from 0.079 to 0.164. For Model ZYR00 compared with Model ZFR00, it extends from 0.006 to 0.092. Both intervals are unadjusted and are calculated from the posted summary statistics.

The interval for Model ZLB00 versus Model ZFR00 is centered around the reported difference of 0.121; the interval for Model ZYR00 versus Model ZFR00 is centered around the reported difference of 0.049. In general, a narrower interval indicates greater precision under the method used, while a wider interval indicates more uncertainty about the estimate. The intervals do not represent the range of individual participants' visual-acuity values. Those values vary within each group, as reflected in the reported standard deviations of 0.115, 0.146, and 0.149.

Both intervals lie above zero, but this is not an adjusted assessment across the two comparisons. The registry record does not report a multiplicity adjustment or a sponsor analysis for the comparisons. The interval calculations should therefore be viewed as unadjusted summaries rather than as confirmation of an unreported prespecified inference. Their precision also applies only to the 1-month, first-operative-eye endpoint and should not be extended to other outcomes or visits.

Confidence intervals do not resolve questions about the clinical meaning of a difference. The registry record does not report a threshold for interpreting the size of a logMAR difference, nor does it report a minimally important difference for this endpoint. Thus, the statistical range can be described, but its implications for individual experience are not established by these data alone.

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 planning illustrations use participants per arm, not total events. They are based on a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect used for planning is a stated fraction of the observed effect. These are planning assumptions for illustration; the trial's own original sample-size assumptions and justification are not reported in the registry record.

The 80% power column gives the illustrated number of participants per arm for a design with an 80% chance of detecting the chosen effect under those assumptions, if the effect and model assumptions hold. The 90% power column gives the corresponding number per arm for a design with a 90% chance. These are prospective design quantities, not measures of the probability that the posted result is correct. This is not observed power.

For Model ZLB00 compared with Model ZFR00, planning for 100% of the observed effect gives 19 participants per arm for 80% power and 25 for 90% power. Planning for 75% of the observed effect gives 33 and 44 participants per arm, respectively; planning for 50% gives 74 and 99. For Model ZYR00 compared with Model ZFR00, the corresponding figures are 116 and 155 for 100% of the observed effect, 205 and 275 for 75%, and 461 and 617 for 50%.

The illustrations show the expected pattern: smaller effects require more participants to detect under the same assumptions. Because the observed effects are used as the reference for these scenarios, the calculations are not a report of the trial's planned design and should not be treated as evidence about whether the trial was adequately powered. The registry record does not report the original design target or the rationale for the enrollment field of 225.

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 = 0.121; pooled standard deviation σ = 0.131.
2. n = 2 × (1.96 + 0.842)² × 0.131² / 0.121² = 18.4, rounded up to 19 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 <- 0.121                      # observed difference in means
sigma <- 0.130994902128143                     # 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(3372434)
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 = 19 (80% power), 25 (90% power)
 75% of observed effect: n per arm = 33 (80% power), 44 (90% power)
 50% of observed effect: n per arm = 74 (80% power), 99 (90% power)
power.t.test: 19.4 
Simulated power at n = 19 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 posts one primary outcome measure: distance-corrected intermediate visual acuity at 1 month. It also posts two unadjusted comparisons, each using Model ZFR00 as the reference. When several comparisons are examined, the chance of a nominally unusual result can increase. A multiplicity procedure may adjust the interpretation of p-values or confidence intervals to account for the set of comparisons, but the registry record does not report whether such a procedure was planned or used. The recalculated comparisons and intervals are unadjusted.

The registry record does not report an analysis plan for missing endpoint measurements, the amount of missing outcome data, or reasons for missingness. It also does not describe imputation, complete-case analysis, or sensitivity analyses. The posted endpoint is identified as using the safety population, but a separate efficacy population definition and the handling of participants who did not follow the assigned treatment are not reported in the registry record.

The record describes randomization and double masking, but it does not provide the randomization sequence method, allocation concealment details, or procedures for maintaining masking. It also does not report an interim-analysis plan, stopping rules, subgroup analysis plan, or the original statistical plan for the primary endpoint. These details cannot be inferred from the observed means, standard deviations, p-values, or the planning illustrations.

The registry summary describes approximate targets for randomized and evaluable participants, whereas the enrollment field and posted outcome counts report different figures. The record does not explain the relationship among those numbers, nor does it state how many participants contributed data at each visit beyond the displayed outcome counts. This leaves uncertainty about missingness and analysis populations. As a result, interpretation should remain tied to the posted safety-population outcome summaries rather than assuming an unreported analysis population or missing-data strategy.

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.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: hospitalization (4.1%), cystoid macular edema (2.7%), macular hole (1.4%), bothersome visual symptom (1.4%), herpes zoster keratitis (1.4%).

The registry reports serious adverse events for 5 of 78 participants at risk in the Model ZFR00 group, 13 of 73 at risk in the Model ZLB00 group, and 4 of 74 at risk in the Model ZYR00 group. Other adverse events were reported for 6 of 78, 1 of 73, and 3 of 74 participants at risk, respectively. The record reports zero deaths in each group. These are posted counts and denominators; they are not inferential comparisons between device groups.

The registry also lists serious-event terms with reported percentages: Hospitalization, 4.1%; Cystoid Macular Edema, 2.7%; Macular Hole, 1.4%; Bothersome Visual Symptom, 1.4%; Herpes Zoster Keratitis, 1.4%; and Haptic anterior to capsule bag, 1.4%. The percentages describe the listed terms in the registry record; they do not by themselves establish that a device caused an event.

Counts of participants with events do not show event timing, duration, severity beyond the serious classification, or whether one participant experienced more than one event. Further detail on those matters is not reported in the registry record. The figures should be read as descriptive safety reporting, not as proof of equivalence or a causal safety difference.

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

The posted statistics describe mean distance-corrected intermediate visual acuity at 1 month in the first operative eye. The mean logMAR values were 0.098 for Model ZFR00, 0.219 for Model ZLB00, and 0.147 for Model ZYR00. The registry states that lower numeric values indicate better acuity. The recalculated unadjusted comparisons quantify differences between the group means, with confidence intervals that describe uncertainty under the calculation method.

These findings do not establish that a lens is suitable for a particular person, and they are not a recommendation about treatment or device choice. Group averages do not determine an individual's result. The record does not report a threshold for judging the clinical importance of the observed differences, nor does it report patient-reported outcomes that could help describe how the visual-acuity measurements correspond to participants' experience.

The results are specific to the assessment conditions, the first operative eye, and the 1-month visit. They do not establish comparisons for binocular vision, other visual tasks, outcomes not posted, or later visits. Although the study summary describes 6-month follow-up, the posted primary outcome addressed is at 1 month. Broader claims about the full follow-up period cannot be drawn from this endpoint alone.

The two recalculated comparisons are unadjusted, and the registry record does not report a multiplicity procedure or sponsor analysis for them. The p-values should therefore be understood as nominal, unadjusted summaries. The planning illustrations are not a retrospective measure of study power and do not establish that the trial was designed around the observed differences. Its original sample-size justification and detailed statistical plan are not reported in the registry record.

The safety counts are also descriptive. They identify reported serious and other adverse events and deaths by group, but do not provide causal attribution or a complete comparative safety analysis. Taken together, the posted information supports a focused description of one visual-acuity endpoint and selected safety counts. It does not answer every question about comparative benefit, risk, durability, or individual outcomes.

16. Why This Trial Matters Statistically

This trial illustrates how a continuous clinical endpoint can be reported as group means and standard deviations, then compared through mean differences and confidence intervals. Those quantities answer distinct questions: the means describe average measured acuity, standard deviations describe variation among measurements, and confidence intervals express uncertainty about the estimated differences. Reading them together is more informative than relying on a p-value alone.

The outcome definition also demonstrates why measurement context matters. The registry specifies monocular testing, photopic conditions, best distance correction, a high-contrast chart, and a fixed viewing distance. It identifies the first operative eye as the primary study eye and states that lower logMAR values represent better acuity. Without these details, a mean would be harder to interpret and could be confused with a different visual-acuity condition or a binocular result.

The comparisons show why multiplicity and analysis provenance matter. Two unadjusted comparisons share a reference group, yet the registry does not report an adjustment or sponsor analysis. Recalculated estimates can clarify the arithmetic in posted summaries, but they do not replace an analysis specified by the trial team. Similarly, planning calculations based on observed effects can illustrate how target effect size affects sample requirements, but they do not reveal the original design rationale.

Finally, the record juxtaposes a planned study summary, an enrollment field, and outcome-specific group counts without explaining their relationship. That makes transparent distinction between planned targets and posted analysis counts essential. The case is statistically instructive because it shows how to describe what the registry actually reports while preserving uncertainty about methods and clinical interpretation that are not documented.

17. Limitations

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

The registry record describes the study as bilateral, with the same lens in both eyes, but the primary outcome analysis is limited to the first operative eye. The reported endpoint therefore does not summarize both eyes or binocular performance. It also represents one visit, 1 month, even though the study summary describes 6-month follow-up. The record does not post primary-outcome results for another visit.

The study summary refers to up to 260 subjects, approximately 220 randomized and bilaterally implanted subjects, and approximately 195 evaluable subjects at 1 and 6 months. The enrollment field reports 225, and the posted outcome counts are 76, 72, and 73. The relationship among these planned and observed figures is not reported in the registry record. In particular, the record does not explain the difference between the approximate evaluable target and the displayed outcome counts.

The record states that the study was to be conducted at up to 14 sites in the United States, but it does not report the number of sites that actually enrolled participants. It does not provide details on recruitment, participant characteristics beyond the cataract condition, or the generalizability of the enrolled population. Randomization and double masking are listed, but the sequence generation, allocation concealment, and masking procedures are not described in detail.

Outcome-data completeness and the handling of missing measurements are not reported. The registry also does not explain protocol deviations, treatment discontinuations, or how such events entered the analysis. The endpoint is labelled as using the safety population, but the precise population definition is not given. These omissions constrain assessment of bias and of the precision that the posted counts alone suggest.

Finally, there is no posted sponsor analysis for the primary comparisons, no reported multiplicity approach, and no stated clinical-importance threshold for logMAR differences. The recalculated comparisons are unadjusted and rely on summary statistics. They should not be taken as a complete account of the trial's prespecified statistical analysis.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Clinical Investigation of the Next-Generation Intraocular Lenses — NCT03372434.
• Registry record last updated 2025-06-24; status last verified 2025-06.
• Results first posted 2021-07-27.
• 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

NCT03372434 is a completed randomized, double-masked, parallel clinical investigation of Model ZFR00 and Model ZYR00 compared with the TECNIS Multifocal control, Model ZLB00, in participants with cataract. The registry reports enrollment of 225 and describes a prospective, multicenter study with intended bilateral implantation and 6-month follow-up.

The posted primary outcome is distance-corrected intermediate visual acuity at 1 month, measured in logMAR in the first operative eye and summarized as a mean and standard deviation for the safety population. The recalculated unadjusted mean differences versus Model ZFR00 are 0.121 for Model ZLB00 and 0.049 for Model ZYR00. The registry also reports serious and other adverse-event counts and zero deaths in each group.

The registry record does not report the original sample-size justification, detailed statistical plan, missing-data methods, or multiplicity procedure. The posted comparison calculations and planning illustrations should be interpreted with those omissions in mind.