Study of the Femtosecond Laser System as Compared to Continuous Curvilinear Capsulorhexis for Cataract Surgery: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Study of the Femtosecond Laser System as Compared to Continuous Curvilinear Capsulorhexis for Cataract Surgery (NCT01069172), a randomized phase 3 study. The primary outcome is Deviation From Intended Capsulotomy Diameter.

2. Clinical Question

3. Trial Design

The registry describes NCT01069172 as a completed Phase 3, prospective, randomized study with no masking and a parallel model. Its official title identifies a comparison of cataract surgery assisted by the OptiMedica Femtosecond Laser System with standard continuous curvilinear capsulorhexis and ultrasonic phacoemulsification. Abbott Medical Optics is listed as the sponsor. The recorded start is 2010-02 and the primary completion is 2010-07.

The registry records an enrollment of 30 subjects. For the primary outcome, the population description states that 29 subjects had FS laser surgery in one eye and CCC with ultrasound surgery in the fellow eye. The result therefore concerns measurements from two eyes belonging to each subject in that reported analysis population. Although the registry lists the model as parallel, the fellow-eye description is important context when interpreting the comparison: measurements from the two eye groups are not necessarily independent of one another.

The intervention description allows ultrasound phacoemulsification in the FS laser group if needed, and describes ultrasound as part of the CCC procedure. The comparison is consequently between two surgical approaches, not simply between use and non-use of ultrasound. The registry lists two outcome measures: deviation from intended capsulotomy diameter as primary and cumulative dissipated energy as secondary.

The registry record does not report the original sample-size justification, the method used to generate or conceal randomization, the allocation of treatments to right or left eyes, or a detailed statistical analysis plan. It also does not report whether the comparison accounted for the relationship between fellow eyes. Those omissions limit what can be concluded about the intended design and analysis beyond the recorded study descriptors and outcome results.

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: 30 subjects were included in the study, but one subject withdrew prior to surgery on their second eye. Baseline and outcome measure analysis was performed on the 29 subjects with both eyes enrolled. Of these 29 subjects, all had FS laser surgery in one eye (29 FS surgery eyes) and CCC with U/S surgery in their fellow eye (29 CCC surgery eyes).

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: 29 subjects had FS laser surgery in one eye (29 FS surgery eyes) and CCC with U/S surgery in their fellow eye (29 CCC surgery eyes). Analysis of capsulotomy size was done by eye group.

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: Baseline analysis population consists of the 29 subjects that had both eyes enrolled. Of these 29 subjects, all had FS laser surgery in one eye (29 FS surgery eyes) and CCC with U/S surgery in their fellow eye (29 CCC surgery eyes).

6. Primary Endpoint

The registry lists the primary outcome as Deviation From Intended Capsulotomy Diameter, measured over Day of Surgery.

The primary endpoint, deviation from intended capsulotomy diameter, measures how far the capsulotomy diameter observed during surgery differed from the intended diameter. It is recorded in micrometers, with the measurement taken on the day of surgery. The registry describes it as a continuous outcome summarized by a mean and standard deviation for each eye group.

This measure is relevant to the procedural comparison because the laser-assisted approach includes a laser capsulotomy, while the CCC group receives the standard manual capsulorhexis procedure. Comparing deviations can describe the closeness of the measured diameter to the intended diameter across the two groups. A smaller mean deviation indicates measurements closer to the intended size on average; it does not, by itself, establish that every eye had a small deviation or that other aspects of surgery differed in the same way.

The endpoint is a surgical measurement, not a patient-reported outcome or a measure of long-term visual function. It is assessed on the day of surgery, so it describes an immediate procedural characteristic. The registry record does not state how the intended diameter was set, how measurements were obtained, or whether assessors were masked. Those details would help readers judge measurement consistency and possible assessment bias.

7. Results Posted in the Registry

• CCC Surgery: mean 339.10 versus 26.80 on control; difference 312.30 (95% CI 221.60 to 403.00), standardized effect d = 1.77; z-test p = <0.001.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Cumulative Dissipated Energy (CDE)

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • CCC Surgery: mean 18.54 versus 11.58 on control; difference 6.96 (95% CI 1.62 to 12.30), standardized effect d = 0.67; z-test p = 0.011.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for CCC Surgery than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The secondary outcome is cumulative dissipated energy, a measure recorded on the day of surgery. Its group means and comparison point in the same direction as the primary endpoint: the FS laser group has the lower reported mean than the CCC group. This shared direction provides a consistent descriptive pattern across the two posted continuous surgical measures, but the outcomes measure different features of surgery and should not be treated as interchangeable.

The secondary comparison is less confirmatory than the primary result. The registry reports an unadjusted p-value and does not report a multiplicity adjustment, a prespecified hierarchy among outcomes, or a statistical plan explaining how secondary results were to be interpreted. When several outcomes are examined, the chance of at least one apparently notable result can increase. General statistical practice may address this with prespecified testing order or adjustment, but the registry does not report such an approach.

The secondary outcome therefore adds descriptive context to the primary result, rather than independently establishing a broad or general effect. It does not show whether the primary result translates into other outcomes, and it cannot answer questions about longer-term vision or safety. The registry lists one secondary outcome and provides no additional reported analyses for it. Its uncertainty should be considered alongside the missing detail on the fellow-eye analysis structure and any unreported analysis choices.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Cumulative Dissipated Energy (CDE)

9. Statistical Interpretation

10. Statistical Methods Explained

The primary outcome is continuous: each eye has a measured deviation in micrometers, and the registry summarizes each group with a mean and standard deviation. A mean is the arithmetic average of the recorded measurements. A standard deviation describes how spread out observations are around that average. When the spread is large relative to the mean, individual observations may differ substantially from the group average; the mean alone does not reveal their shape or range.

What does the mean difference represent?

The posted comparison expresses the difference as CCC surgery minus FS laser surgery. The reported group means are 339.1 μm for CCC surgery and 26.8 μm for FS laser surgery, and the reported mean difference is 312.3 μm. A positive value therefore indicates a higher average deviation in the CCC group. This contrast is measured in the same units as the endpoint, which makes its direction and scale directly interpretable. It is a contrast between averages, not a claim that every CCC eye differed from every FS laser eye by that amount.

How should a confidence interval be understood?

A confidence interval describes uncertainty around an estimated effect under the statistical method used. The interval for the primary mean difference runs from 221.6 to 403.0 μm. It conveys a range of values compatible with the estimate under that method; it is not a range containing a stated proportion of individual eye measurements. The interval also gives information about precision: narrower intervals indicate more precise estimates than wider intervals, assuming comparable methods and scales. The posted interval does not account for analysis features that are not reported in the registry.

What does the p-value add?

The primary unadjusted p-value is <0.001. In general, a p-value describes how surprising data at least as incompatible with a specified null hypothesis would be if that hypothesis and the statistical model were correct. It is not the probability that the null hypothesis is true, and it does not measure the size or practical importance of an effect. The registry does not report whether the p-value was adjusted for the fellow-eye structure or for any other analysis choices.

Why does the fellow-eye structure matter?

As a general statistical principle, observations from two eyes of the same subject can be correlated because they share characteristics. An analysis that treats correlated observations as independent may represent uncertainty differently from an analysis that accounts for the within-subject relationship. Conversely, a paired analysis uses the within-subject contrast and depends on the variability of those paired differences. The registry describes fellow eyes but does not report the model or test used for the posted comparison. It is therefore not possible to determine from the record whether the reported uncertainty reflects a paired analysis.

Why is unequal variability relevant?

The standard deviations are 24.6 μm in the FS laser group and 248.0 μm in the CCC group. As a general matter, over-dispersion or substantially unequal variability can affect how well methods that assume similar spread perform. The marked difference in the reported standard deviations makes the distribution of measurements and the variance assumptions relevant to interpretation. The registry does not report distributional diagnostics, transformations, robust methods, or a variance model, so those details are not available for assessment.

The secondary CDE outcome is also continuous and is summarized using means and standard deviations. Its reported comparison has a 95% confidence interval and an unadjusted p-value, but the registry does not list reported analysis details for either endpoint. The general explanations above describe what these statistics mean; they do not establish which specific test, model, or assumptions generated the posted results. The registry record does not report the detailed analysis plan, handling of missing measurements, or adjustments for the study's multiple outcomes.

11. Confidence Intervals and Precision

The primary mean difference is 312.3 μm, with a 95% confidence interval from 221.6 to 403.0 μm. The interval excludes zero and is on the positive side, consistent with the higher mean deviation in the CCC group. It also shows that the estimated contrast is not a single precisely known value: a range of effect sizes remains compatible with the statistical method used. The interval is more informative about the estimate's uncertainty than the p-value alone.

The confidence interval should not be mistaken for the range of individual eye outcomes. The group standard deviations are 24.6 μm and 248.0 μm, and they describe variability among measurements, whereas the confidence interval describes uncertainty in the estimated difference in means. The large contrast between the group standard deviations also cautions against assuming that the outcome distributions have similar spread.

The secondary CDE mean difference is 6.96, with a 95% confidence interval from 1.618 to 12.3. This interval also excludes zero, but the result is secondary and unadjusted. The confidence intervals and p-values are only as reliable as the analysis assumptions used to calculate them. In particular, the registry does not report whether the fellow-eye relationship was incorporated into the analysis, or how any missing outcome measurements were handled.

Precision is also limited by the scale of the study population: the primary outcome description records 29 subjects, each contributing two eyes. The record does not provide an interval for the separate group means, a distribution of individual paired differences, or further precision measures. Accordingly, the posted confidence interval offers a useful summary of uncertainty for the reported mean contrast, but not a complete account of measurement variability or analytic uncertainty.

12. 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 for 80% power and participants per arm for 90% power. They are based on a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is set as a stated fraction of the observed effect. These are planning illustrations based on the observed results, not the original trial's design calculations; the registry record does not report the original sample-size assumptions. This is not observed power.

The 80% power column gives the number of participants per arm that the planning calculation associates with an 80% chance of detecting the specified effect under its assumptions, if that effect and the calculation model were correct. The 90% column uses a higher target chance of detection and therefore generally calls for more participants per arm for the same assumed effect. The figures are not the number enrolled in the completed study and do not describe the probability that the posted result is true.

The planning rows vary the target effect relative to the observed effect: 100%, 75%, and 50%. Smaller effects need more participants because weaker contrasts are harder to distinguish from random variation. The figures apply separately to each arm, not to the total study population. The record's planning note distinguishes these calculations from time-to-event calculations, which would report total events; the outcomes in this study are not time-to-event outcomes.

The original trial design assumptions, including its intended effect size and power target, are not reported in the registry record. The planning illustrations should therefore be treated as a way to understand how sample requirements change with assumed effect size and target power, rather than as evidence that the trial was designed around those numbers.

13. 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 = 312.300; pooled standard deviation σ = 176.223.
2. n = 2 × (1.96 + 0.842)² × 176.223² / 312.300² = 5.0, rounded up to 5 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 <- 312.3                      # observed difference in means
sigma <- 176.223097237564                     # 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(1069172)
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 = 5 (80% power), 7 (90% power)
 75% of observed effect: n per arm = 9 (80% power), 12 (90% power)
 50% of observed effect: n per arm = 20 (80% power), 27 (90% power)
power.t.test: 6.1 
Simulated power at n = 5 per arm: 0.693 (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.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary outcome and a secondary outcome, but does not report a multiplicity plan. It does not state whether there was a hierarchy of hypotheses, whether secondary outcomes were exploratory, or whether any adjustment was intended. The primary p-value is reported as unadjusted, and the secondary p-value is also unadjusted. Without a stated plan, the findings should not be read as though the probability of false-positive results across all analyses had been controlled.

The registry reports no analyses in its analysis listing, while outcome results are posted. It does not report the detailed statistical analysis plan, the tests or models used, or whether the fellow-eye relationship was incorporated. This matters because two eyes from the same subject may not be statistically independent. The record also does not report whether the analysis was intention-to-treat, per-protocol, or based on another analysis population definition.

The primary outcome population description specifies 29 subjects with an FS laser eye and a CCC fellow eye. The overall enrollment is 30. The registry does not explain the difference between enrollment and the described outcome population, identify why measurements are absent for any enrolled subject, or describe how missing data were handled. No imputation, exclusion, or sensitivity-analysis strategy is reported. These omissions prevent a fuller assessment of potential selection or missing-data effects.

The record does not report interim analyses, stopping rules, or a detailed account of protocol deviations. It also does not report whether the outcome measurement was assessed by masked personnel. These design and analysis details could affect how confidently the posted estimates can be interpreted, but no conclusion about the methods used should be inferred from their absence in the registry record.

15. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: secondary surgical intervention to reposition lens haptic (3.4%), zonular dehiscence requiring anterior vitrectomy (3.4%), elevated iop requiring treatment (3.4%).

The adverse-event figures are reported for 29 subjects at risk in each surgery group. Serious adverse events affected 2 subjects in the FS laser surgery group and 1 in the CCC surgery group. Other adverse events affected 0 subjects in the FS laser group and 6 in the CCC group. These counts describe the registry's reported affected-subject figures; they do not by themselves establish whether an event was caused by a procedure.

The registry lists three serious-event terms, each with a reported frequency of 3.4%: secondary surgical intervention to reposition lens haptic, zonular dehiscence requiring anterior vitrectomy, and elevated IOP requiring treatment. The listed terms should not be assigned to a particular group because the registry information does not give that attribution in the term list. Death counts are not reported in the registry record.

These safety figures are descriptive and come from a small study population. The registry does not provide enough detail to compare event timing, severity beyond the serious/non-serious classification, or causal attribution. Counts should therefore be read as the events recorded, not as a complete estimate of comparative safety.

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

The posted primary result describes a difference in the mean deviation from intended capsulotomy diameter between the two eye groups on the day of surgery. The mean was lower in the FS laser surgery group than in the CCC surgery group, and the reported mean difference and confidence interval indicate a substantial separation in the recorded group averages. The CDE secondary result points in the same direction for that separate surgical measure.

These findings do not establish that all individuals had the same result, because group averages do not describe every eye. The different standard deviations also show that the spread of observations varied between groups. Nor do the findings establish how the procedures compare on outcomes that were not reported, such as longer-term visual function. The registry record does not report such outcomes in the posted results.

The results should also be interpreted in light of the fellow-eye population and the lack of a reported statistical method accounting for within-subject correlation. A p-value below a conventional threshold does not resolve uncertainty about model assumptions, measurement procedures, or analysis populations. The registry does not report enough detail to assess those issues fully.

Safety counts are descriptive and cannot establish causal relationships. The event numbers and the small recorded outcome population also limit how much can be learned about uncommon events. The posted data support statements about the measurements and adverse-event counts recorded in this study; they do not support medical advice or a broad claim about which approach should be used for an individual. Applicability beyond the studied setting and participants is not established by these results alone.

17. Why This Trial Matters Statistically

This study illustrates why the design structure behind a clinical measurement matters. The primary outcome population includes fellow eyes from the same subjects, so the data have a within-subject structure even though the registry lists a parallel model. The statistical treatment of that dependence can affect uncertainty estimates. Because the analysis method is not reported, readers should separate the observed group contrast from assumptions about how precisely it has been estimated.

It also demonstrates the difference between statistical evidence and a complete clinical interpretation. The primary mean difference is expressed in the endpoint's physical units, and its confidence interval communicates uncertainty in that average contrast. Neither the p-value nor the interval describes every eye or answers questions about unmeasured outcomes. The secondary measure provides additional procedural context, but unadjusted secondary evidence is not equivalent to a prespecified confirmatory result.

Finally, the registry distinguishes the completed study population from planning illustrations based on observed effects. Sample-size calculations can help readers understand how assumed effect size and target power relate to participant requirements, but they do not reveal the original design rationale when that rationale is not reported. Keeping these distinctions clear helps prevent retrospective planning figures from being mistaken for evidence of the study's original statistical design or for observed power.

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 main trial-specific limitation is incomplete reporting of the analysis for a fellow-eye comparison. The primary population description states that each of 29 subjects contributed an FS laser surgery eye and a CCC surgery fellow eye, but the registry does not state whether the comparison used paired methods or otherwise accounted for within-subject correlation. The registry's parallel-model label does not resolve that question.

The registry does not explain why the primary outcome population includes 29 subjects when enrollment was 30, or how any missing measurements were handled. It does not report the intended diameter-setting procedure, measurement method, assessor masking, or a detailed protocol for obtaining the capsulotomy measurement. Those details are relevant because the primary endpoint depends on a measurement made during surgery.

The reported standard deviations differ considerably between the groups, but the registry does not report distributional checks, variance assumptions, or methods intended to address unequal spread. It also does not report a detailed analysis plan or a multiplicity strategy for the primary and secondary outcomes. These gaps make it difficult to assess the assumptions behind the posted confidence intervals and p-values.

Finally, the outcomes described are procedural measures recorded on the day of surgery, and the registry's safety summaries provide limited detail on event attribution and timing. The record does not report longer-term outcome results in the information described. These limitations restrict interpretation to the posted measures and do not support conclusions about unreported outcomes or broader populations.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Study of the Femtosecond Laser System as Compared to Continuous Curvilinear Capsulorhexis for Cataract Surgery — NCT01069172.
• Registry record last updated 2014-09-04; status last verified 2014-08.
• Results first posted 2014-09-04.
• 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

NCT01069172 is recorded as a completed, randomized Phase 3 cataract-surgery study sponsored by Abbott Medical Optics. The registry describes a comparison of femtosecond laser-assisted surgery with CCC and ultrasonic phacoemulsification. Although the design is labeled parallel, the primary outcome population is described as fellow eyes from 29 subjects.

The primary outcome was deviation from intended capsulotomy diameter on the day of surgery. The reported mean was 26.8 μm for FS laser surgery and 339.1 μm for CCC surgery, with a mean difference of 312.3 μm and a 95% confidence interval from 221.6 to 403.0 μm. Cumulative dissipated energy was reported as a secondary outcome, with an unadjusted comparison.

The registry does not report the detailed statistical analysis plan, the handling of missing data, or whether the analysis accounted for fellow-eye correlation. Those omissions are important qualifications when interpreting the posted estimates.