Cataract Surgery: Femto LDV Z8 Versus Conventional: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Cataract Surgery: Femto LDV Z8 Versus Conventional (NCT02351271), a randomized na study. The primary outcome is Effective Phaco Time (EPT).

2. Clinical Question

3. Trial Design

The registry identifies this as a randomized, parallel-group, single-centre eye study. It compares femtosecond laser-assisted cataract pretreatment using the Femto LDV Z8 with a conventional procedure. The record lists the masking as none, so the trial is recorded as unmasked. The enrollment field states 130, and the arm-level outcome records report 68 eyes in the Femto LDV Z8 group and 62 in the manual capsulorhexis and lens fragmentation group. These are the counts attached to the posted primary outcome, rather than a description of every analysis population.

In the laser-assisted arm, capsulotomy and lens fragmentation were performed with the femtosecond laser before ultrasound phacoemulsification. In the conventional arm, capsulorhexis and lens fragmentation were manual, with ultrasound phacoemulsification. This design therefore compares two treatment approaches that both include ultrasound phacoemulsification, while the pretreatment steps differ.

The registry lists the study as completed. Its start is recorded as 2015-02 and its primary completion as 2016-12-28. The sponsor is Ziemer Ophthalmic Systems AG. The study phase is listed as NA, a designation that should be read as the registry entry rather than as a clinical interpretation.

Further design details—including the randomization sequence, allocation concealment, eligibility criteria, and the rules for assigning eyes to groups—are not reported in the registry record. The registry also does not report the trial's original sample-size justification or the detailed analysis plan. The posted outcome counts and summaries describe the available registry results; they should not be treated as a substitute for those missing protocol 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.

Overall Study

Analysis population for the primary outcome, as defined in the registry: effective phaco time

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 Effective Phaco Time (EPT), measured over day of surgery.

The primary endpoint is effective phaco time (EPT), recorded on the day of surgery. The registry describes EPT as a measure of phaco energy during cataract surgery, expressed as the total phaco time at 100 percent phaco power. It notes that this value can be less than total foot-pedal time and describes EPT as a commonly used way to characterize phaco energy across manufactured phaco devices.

The endpoint is continuous, and the posted results summarize it with a mean and standard deviation for each group. A lower EPT indicates less energy delivered through phaco power, according to the registry's endpoint description. That is the measure's intended interpretation; an EPT result alone does not establish effects on every aspect of the procedure, patient experience, or later clinical outcome.

The registry's stated criterion for superior efficacy was that EPT in the Femto LDV Z8 arm be statistically the same as or lower than EPT in the manual arm at p < 0.05. The posted group means are 1.48 for Femto LDV Z8 and 2.3 for manual capsulorhexis and lens fragmentation. The timeframe is the day of surgery; later EPT measurements are not described. Other details about endpoint assessment and handling of measurements are not reported in the registry record.

7. Results Posted in the Registry

• Manual Capsulorhexis&Lens Fragmentation: mean 2.30 versus 1.48 on control; difference 0.82 (95% CI 0.08 to 1.56), standardized effect d = 0.39; z-test p = 0.029.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is a continuous measurement, so the registry summarizes each arm with a mean and standard deviation. The posted mean is the arithmetic average of observed EPT values in that arm. A standard deviation describes the spread of those values around the mean. These summaries answer different questions: the mean locates the group average, while the standard deviation describes variation among observations. Neither statistic alone gives the uncertainty in the difference between the two group means.

What does the mean difference represent?

The posted comparison reports a mean difference of 0.82, with the manual arm represented relative to the Femto LDV Z8 arm. The group means underlying this comparison are 2.3 and 1.48, respectively. A mean difference expresses the contrast between group averages in the measurement's units. It is not the difference for every eye, and it does not describe how much each individual value changes. A group-level contrast can coexist with considerable variation among observations.

In general, an unadjusted comparison uses the observed group summaries without controlling for other variables. The posted comparison is identified as an unadjusted re-calculation from the summary statistics. It should not be confused with a model that adjusts for baseline characteristics, site effects, or other covariates. The registry does not report an adjusted analysis of the primary endpoint.

How should the p-value be understood?

The unadjusted p-value is 0.029. In general, a p-value describes how compatible the observed data, or more extreme data, are with a specified null model, assuming the model's conditions hold. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of a difference. The registry's endpoint description uses p < 0.05 as part of its stated efficacy criterion. The reported p-value is below that threshold, but the p-value alone does not establish the validity of the trial's design, the completeness of the data, or the practical importance of the mean contrast.

The registry lists zero analyses. The p-value and comparison shown in the posted result are therefore best understood as a calculation from the available summaries, not as a separately documented sponsor analysis. The record does not describe the test procedure, model checks, or whether other statistical methods were prespecified. Those details are not reported in the registry record.

What does the confidence interval add?

In general, a confidence interval gives a range of values compatible with the data and the method used to calculate it, reflecting sampling uncertainty. For this comparison, the interval has a positive lower bound and an upper bound of 1.557 around the reported mean difference of 0.82. Because zero is below the reported lower bound, the interval does not include a no-difference value. The interval also shows that the estimate is not a single exact value: uncertainty remains about the size of the mean difference.

A confidence interval is not a guarantee that the true value lies within the particular interval, nor does it account automatically for design limitations, missing observations, measurement error, or multiple comparisons. Its interpretation depends on the analysis assumptions and the way the data were collected. The registry does not provide the additional details needed to evaluate all of those assumptions.

Why can variation matter?

The standard deviations are 1.8 and 2.41 in the two arms. In general, variation affects how precisely a group mean and the difference between means can be estimated. More variability can make a comparison less precise when other aspects of a study are unchanged. The balance of the group counts, the sample sizes, and the variability all contribute to the uncertainty represented by the comparison interval. These summaries do not, however, reveal the shape of the underlying distributions or whether unusual observations affected the means.

In general, over-dispersion means that observed variability is greater than a statistical model expects. A model that ignores such excess variability may report uncertainty that is too small. The registry does not report a model-based over-dispersion assessment, and the posted primary outcome is presented as a continuous measure summarized by means and standard deviations. No conclusion about over-dispersion can be drawn from the registry record.

What cannot be recovered from summary statistics?

Group-level means and standard deviations do not show the individual EPT values, their distribution, or the presence of influential observations. They also do not describe baseline comparability, protocol deviations, or missing endpoint data. Without participant-level data and a fuller statistical plan, it is not possible to independently assess those features or reproduce analyses beyond simple calculations from the posted summaries. The registry record does not report the original design assumptions, the chosen analysis population, handling of missing data, or details of any interim analyses.

The distinction between a statistical result and a planning calculation is important. The confidence interval and p-value describe the posted comparison. The separate sample-size illustrations are hypothetical planning calculations based on fractions of the observed effect. They do not describe the trial's achieved statistical power and cannot recover its original design rationale. In general, planning calculations depend on assumptions about the effect to detect, variability, allocation, significance threshold, and analysis method; only the assumptions explicitly stated for the illustrations can be attached to those figures.

10. Confidence Intervals and Precision

The mean difference is reported as 0.82, with a confidence interval whose lower bound is positive and whose upper bound is 1.557. The interval therefore excludes zero, but it extends from a value close to zero to a value above the point estimate. The posted result supports a direction for the mean contrast under the calculation used, while leaving uncertainty about its size. The interval is more informative about precision than the p-value alone because it displays a range of estimates compatible with the data and method.

In general, a narrower confidence interval indicates greater precision than a wider interval, when the same quantity and method are being considered. Precision is not the same as accuracy: an estimate can be precise but affected by bias, measurement limitations, or incomplete data. Nor does a confidence interval determine whether the difference is clinically important. The registry does not provide a threshold for a meaningful EPT difference, so that question remains unresolved.

The arm-level standard deviations, 1.8 and 2.41, show the spread of EPT observations around their respective means. The posted comparison also reports its own confidence interval for the difference, which should not be confused with either arm's standard deviation. The registry does not provide participant-level values or additional distribution summaries, so the extent to which the means reflect the full pattern of observations cannot be assessed from the record.

The lower confidence bound is positive, but the registry does not report adjustment for multiple outcomes or a prespecified multiplicity strategy. If multiple hypotheses were assessed, that could affect how a single unadjusted interval or p-value should be interpreted; whether and how such adjustment was planned is not reported in the registry record. The interval quantifies uncertainty under its calculation, not uncertainty from every possible design or reporting limitation.

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. They use the observed effect as a reference and illustrate planning for 100%, 75%, and 50% of that effect. For planning for 100% of the observed effect, the figures are 105 participants per arm for 80% power and 140 participants per arm for 90% power. For planning for 75% of the observed effect, they are 186 participants per arm for 80% power and 249 participants per arm for 90% power. For planning for 50% of the observed effect, they are 417 participants per arm for 80% power and 559 participants per arm for 90% power.

The calculation assumptions stated in the registry material are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. In plain terms, the 80% power column gives the planned number per arm under which a study would have an 80% chance of detecting the target effect at the stated threshold if the assumptions and effect were true. The 90% column uses a higher chance of detection under those same planning conditions.

Smaller target effects require more participants per arm in these illustrations. The original trial's own sample-size justification and design assumptions are not reported in the registry record. These figures are planning illustrations, not observed power.

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 = 0.820; pooled standard deviation σ = 2.113.
2. n = 2 × (1.96 + 0.842)² × 2.113² / 0.820² = 104.2, rounded up to 105 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 <- 0.82                      # observed difference in means
sigma <- 2.11278492900958                     # 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(2351271)
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 = 105 (80% power), 140 (90% power)
 75% of observed effect: n per arm = 186 (80% power), 249 (90% power)
 50% of observed effect: n per arm = 417 (80% power), 559 (90% power)
power.t.test: 105.2 
Simulated power at n = 105 per arm: 0.802 (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 two secondary outcomes: ease of phacoemulsification and number of participants with a complete treatment pattern. It lists four outcome measures and zero analyses. The primary endpoint is EPT, measured on the day of surgery. The record does not provide numerical results for the secondary outcomes or identify which outcome measures, beyond the primary endpoint, have posted results.

When several outcomes or statistical comparisons are examined, multiplicity can arise. In general, considering multiple hypotheses can increase the chance that at least one result appears statistically notable by chance. Researchers may address this with prespecified testing sequences or adjustment methods, but the registry record does not report whether a multiplicity strategy was planned or used. The unadjusted primary comparison should therefore not be interpreted as if a documented multiplicity procedure had been applied.

The handling of missing endpoint data is also not reported in the registry record. The arm-level outcome counts are 68 for Femto LDV Z8 and 62 for manual capsulorhexis and lens fragmentation, but the record does not explain whether these are all randomized eyes, all eyes with an available EPT measurement, or an analysis subset. It does not describe imputation, exclusions, protocol deviations, or sensitivity analyses. Those omissions prevent a full assessment of whether missing observations could affect the comparison.

The analysis population is not reported in the registry record. In general, an intention-to-treat analysis retains randomized participants in their assigned groups, while other analysis populations may apply additional inclusion rules. The registry does not state which approach was used or how crossovers and deviations were handled. Randomization is recorded, but details about allocation concealment and the analysis set are not present. The p-value and confidence interval should therefore be read as the posted unadjusted comparison rather than as a fully documented confirmatory analysis.

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 non-serious adverse event terms

The serious adverse event summary reports zero affected in the Femto LDV Z8 arm among 68 at risk and zero affected in the manual arm among 62 at risk. The death count is zero in each arm. No serious adverse event terms are listed in the registry record.

These are counts in the posted safety summary. A zero count means no serious adverse event is recorded as affecting an eye in that arm in this entry; it does not establish that the risk is absent. In general, event counts are interpreted in relation to how many were observed, the period of observation, and how events were collected and classified. The record gives the at-risk counts but does not provide detailed event definitions, surveillance procedures, or a fuller account of follow-up for safety.

The separate other-adverse-event counts are one in the Femto LDV Z8 arm and two in the manual arm. The registry does not list their terms in the registry record recorded for this comparison. Counts alone do not establish a causal relationship to the intervention, and they do not support a broader safety comparison. The safety figures should be read as registry-reported event counts, not as proof that either procedure is risk-free.

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

The posted primary results show a mean EPT of 1.48 for Femto LDV Z8 and 2.3 for manual capsulorhexis and lens fragmentation. The reported mean difference is 0.82 in the manual-relative-to-laser direction, with a confidence interval that has a positive lower bound and an upper bound of 1.557. The unadjusted p-value is 0.029. These statistics describe a lower average EPT in the laser-assisted arm in the posted summary data.

The result is limited to EPT on the day of surgery. The endpoint is a measure of phaco energy as defined in the registry, not a direct summary of every surgical outcome or of later health outcomes. The registry's stated criterion links a statistically same-or-lower EPT in the laser-assisted arm with superior efficacy, but the posted comparison alone does not establish a comprehensive efficacy or safety conclusion. The record does not state what size of EPT difference would be clinically important.

The result does not show that every eye in one arm had a lower EPT than every eye in the other arm. The group means and standard deviations summarize distributions, and the individual observations are not reported. The comparison also cannot establish what would happen in settings beyond this single-centre study. Details of eligibility, participant characteristics, and procedural implementation are not available in the registry record.

The randomized design is relevant to interpretation, but the registry does not provide allocation procedures, the analysis population, missing-data handling, or a complete statistical plan. These gaps matter when judging how robustly the posted comparison represents the randomized study. The registry lists secondary outcomes but does not post their numerical analyses, and the record reports zero analyses. The primary result should consequently be considered alongside those limitations rather than as a stand-alone answer to every question about the procedures.

Overall, the posted summaries support a statistical contrast in mean EPT for this registry comparison. They do not, on their own, determine clinical importance, demonstrate effects on unreported outcomes, or resolve the limitations in the available design and analysis information.

16. Why This Trial Matters Statistically

This trial is statistically informative because its primary endpoint is continuous and is reported with a mean, standard deviation, confidence interval, and unadjusted p-value. These quantities illustrate distinct aspects of the result: the group averages describe the observed endpoint levels, the standard deviations describe within-arm variation, the mean difference expresses the group contrast, and the confidence interval conveys uncertainty around that contrast. Reading them together is more informative than relying on a p-value alone.

The registry also makes the distinction between a result and a design calculation important. The primary comparison uses the posted outcome summaries, while the planning illustrations are based on fractions of the observed effect. They show how planning targets change when a smaller effect is considered, under stated assumptions. They do not document why the original trial enrolled its stated number, and they are not evidence of observed power.

At the same time, the record illustrates the limits of registry-level statistical interpretation. The trial is marked randomized and unmasked, but allocation details, analysis population, missing-data procedures, multiplicity handling, and the full statistical plan are not reported. The secondary outcomes are named without posted numerical analyses. These omissions prevent readers from determining how the primary comparison fits within the complete analysis strategy.

The safety summary is also a reminder that sparse event counts require careful description. Zero serious events are recorded in each arm, but those counts do not prove the absence of risk. The observed counts and the available follow-up details are not enough to support broad conclusions about safety.

For clinical researchers and biostatisticians, the central lesson is to distinguish the endpoint-specific estimate from broader claims, to attend to the confidence interval as well as the p-value, and to identify where registry reporting does not allow methods to be evaluated. That separation keeps the statistical result proportionate to the information recorded.

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.

Several limitations are specific to the information recorded for this trial. It is a single-centre study, so the registry result documents experience at one centre; details needed to assess how closely its participants and procedures resemble other settings are not reported. The registry also records no masking. It does not explain how knowledge of treatment assignment may have been handled during endpoint measurement or other study procedures.

The primary comparison is based on posted group summaries and is an unadjusted re-calculation. The registry lists zero analyses and does not describe an adjusted analysis, the statistical test, model checks, or the analysis population. It also does not report whether all randomized eyes had an EPT measurement, how missing values were handled, or whether protocol deviations and exclusions occurred. These omissions limit independent assessment of the estimate.

The record names two secondary outcomes but does not provide their numerical results. It does not report a multiplicity strategy, so the relationship between the primary comparison and any other planned testing cannot be evaluated. The original sample-size justification is not reported; the available planning illustrations are based on the observed effect and stated assumptions rather than on the trial's documented design rationale.

The registry's arm-level counts and safety summaries provide limited detail. Individual EPT values, distributions, baseline characteristics, event terms for other adverse events, and detailed safety follow-up are not reported in the registry record. The endpoint is measured on the day of surgery, and the record does not describe later outcome assessment. Consequently, the primary result should not be extended to unreported outcomes or interpreted as a complete account of procedural performance and safety.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Cataract Surgery: Femto LDV Z8 Versus Conventional — NCT02351271.
• Registry record last updated 2019-10-23; status last verified 2019-09.
• Results first posted 2019-10-23.
• 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 describes a completed, randomized, parallel, single-centre eye study comparing Femto LDV Z8 laser-assisted cataract pretreatment with conventional manual capsulorhexis and lens fragmentation. Both arms include ultrasound phacoemulsification, and masking is recorded as none. The stated enrollment is 130.

The primary endpoint is effective phaco time on the day of surgery. The posted means are 1.48 for the Femto LDV Z8 arm and 2.3 for the manual arm. The unadjusted comparison reports a mean difference of 0.82, a confidence interval with a positive lower bound and upper bound of 1.557, and p = 0.029.

The record lists two secondary outcomes and zero analyses. It does not report the trial's original sample-size justification, detailed statistical plan, missing-data handling, or analysis population. The serious adverse event summary records zero affected in each arm.