Visual Function After Bilateral Implantation of AcrySof® Toric: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Visual Function After Bilateral Implantation of AcrySof® Toric (NCT00758550), a randomized phase 4 study. The primary outcome is Uncorrected Visual Acuity (UCVA).

2. Clinical Question

3. Trial Design

This was a Phase 4, randomized, parallel-group study with no masking. Its stated objective was to evaluate visual function after implantation of AcrySof Toric and AcrySof Natural intraocular lenses for cataract replacement. Alcon Research is listed as the sponsor. The study record lists an enrollment of 60 and a completed status.

The record lists the study start as 2007-04 and primary completion as 2008-06. It assigns 30 participants to each lens group in the posted primary outcome results. Random allocation is recorded, but the method used to generate the allocation sequence, how assignments were concealed, and whether any additional safeguards were used are not reported in the registry record. Masking is recorded as none, so the study is described as open-label rather than masked.

The primary outcome was uncorrected visual acuity at 6 months after surgery, expressed as a mean in logMAR with standard deviations. The registry record also lists questionnaire results as a secondary outcome, measured at 6 months. It does not report a fuller protocol description, eligibility criteria, participant demographics, or the intended analysis population. The record contains no reported analyses for the secondary outcome and lists no reported analyses overall. Therefore, interpretation can describe the posted group summaries and comparison estimates, but cannot establish whether they represent a prespecified analysis population or whether the recorded analysis followed a complete statistical plan.

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: Randomized

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 Uncorrected Visual Acuity (UCVA), measured over 6 Months after surgery.

The primary endpoint is uncorrected visual acuity (UCVA) measured in logMAR at 6 months after surgery. UCVA assesses vision without corrective lenses at the time of measurement. The logMAR scale expresses visual acuity using the logarithm of the minimum angle of resolution; as specified in the registry record, lower values indicate better visual acuity.

Using a continuous scale retains distinctions among measured values rather than reducing vision to a simple category. Reporting a group mean describes the central value, while a standard deviation describes the spread of individual observations around that mean. These summaries are useful for comparing groups, but they do not show the full distribution or how many participants had particular levels of acuity. No distributional plots or participant-level results are reported in the registry record.

The reported time point is 6 months after surgery, so the endpoint concerns visual acuity at that follow-up, not a trajectory of change over time. Although the endpoint description says UCVA was measured from surgery, the registry record does not provide further detail about the measurement procedure or any baseline-adjusted analysis. The primary endpoint is therefore interpreted as the posted comparison of mean UCVA at the stated follow-up.

7. Results Posted in the Registry

• AcrySof Natural IOL: mean 0.14 versus 0.06 on control; difference 0.08 (95% CI 0.02 to 0.14), standardized effect d = 0.64; z-test p = 0.014.

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.

Questionnaire Results

• 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 errors.
• Result:
  • AcrySof Natural IOL: mean 4.50 versus 5.60 on control; difference -1.10 (95% CI -3.04 to 0.84), standardized effect d = -0.29; z-test p = 0.266.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between AcrySof Natural IOL and the control. The interval gives the range of effects that remain compatible with the data.

The registry record lists questionnaire results as a secondary outcome at 6 months. Its posted group means are 5.6 for AcrySof Toric and 4.5 for AcrySof Natural, with a reported mean difference of -1.1 for Natural minus Toric. The confidence interval extends across zero, and the reported unadjusted p-value is 0.266. The questionnaire scale is described only as units on a scale; no interpretation of the score direction or clinically meaningful difference is reported. The registry record lists no reported analyses for this secondary outcome.

The secondary result does not provide the same pattern of statistical evidence as the primary UCVA comparison: the secondary confidence interval includes zero, whereas the primary interval excludes zero. The outcomes measure different constructs, however, so the secondary result is not a direct confirmation or refutation of the visual acuity finding. The questionnaire score's meaning, including whether higher scores are better, is not reported, limiting directional interpretation.

Secondary outcomes are often considered alongside a primary outcome, but testing multiple outcomes can raise the chance of finding an apparently notable result by chance. The registry record does not report a multiplicity plan or indicate whether the questionnaire comparison was prespecified for confirmatory inference. Its unadjusted p-value should therefore be treated as exploratory evidence rather than as an independent definitive finding. The lack of reported analysis details further limits assessment of the intended role of this endpoint.

The overall secondary-outcome picture is therefore limited: one questionnaire outcome is listed, and its posted comparison is uncertain, with an interval spanning both negative and positive values. It should be considered as supplementary context rather than as a substitute for the primary endpoint or as a basis for a broad conclusion about visual function.

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

• Questionnaire Results

9. Statistical Interpretation

10. Statistical Methods Explained

The primary outcome is continuous, and the registry record reports a mean and standard deviation for each group. A mean summarizes the central value of observations; a standard deviation describes how dispersed those observations are around the mean. These are distinct quantities: the standard deviation is not the uncertainty in the mean difference. The latter depends on the variability and the amount of information in both groups.

What does the group comparison represent?

The reported comparison is a mean difference between AcrySof Natural and AcrySof Toric. The group means are 0.14 and 0.06 logMAR, and the reported difference is 0.08. The subtraction direction matters: a positive difference means the Natural group has the higher mean on the logMAR scale. Since lower logMAR indicates better visual acuity, the group means are ordered toward lower values in the Toric group. This is a comparison of averages, not a count of participants who improved or a comparison of individual responses.

Because the study is described as randomized, the intended design is to compare groups formed by random allocation. Randomization can support a causal interpretation when allocation is implemented as planned and outcomes are handled appropriately. The registry record does not report details of sequence generation, concealment, baseline comparability, exclusions, or analysis population, so those aspects cannot be assessed from the record.

How should the p-value be read?

The primary comparison has an unadjusted p-value of 0.014. In general, a p-value measures how incompatible the observed data are with a specified null model, under the assumptions of the analysis. It is not the probability that the null hypothesis is true, nor is it a measure of the size or clinical importance of a difference. The reported value is unadjusted, and the registry record does not specify the complete analysis model or a multiplicity procedure. It should therefore be read as the reported evidence for this comparison, not as a definitive summary of every uncertainty around the study.

The confidence interval gives a range of effect values compatible with the data and the method used to form the interval. For the primary mean difference, the posted interval excludes zero. That is consistent with the reported p-value indicating evidence against a zero mean difference under the unadjusted comparison. Confidence intervals and p-values answer related but different questions: the interval describes precision and plausible effect magnitudes, while the p-value summarizes evidence relative to a null value.

Why do standard deviations and standard errors differ?

The primary endpoint reports standard deviations, which describe participant-level spread. The secondary questionnaire outcome is reported with standard errors, which describe uncertainty in the estimated group means. A standard error should not be read as the typical amount by which individual questionnaire scores vary. For the primary endpoint, the reported standard deviations are 0.14 for AcrySof Toric and 0.11 for AcrySof Natural.

General statistical principle: the standard error of a mean generally becomes smaller as the amount of information increases, assuming comparable variability and sampling conditions. A standard deviation, by contrast, describes variability among observations and does not serve as a direct measure of uncertainty in a treatment contrast. The record's distinction between these measures is important when comparing how precisely outcomes are summarized.

What does over-dispersion mean in general?

General explanation: over-dispersion occurs when observed variability is greater than a statistical model expects. It matters because a model that underestimates variability can produce uncertainty intervals that are too narrow and p-values that overstate evidence. The posted primary outcome is a continuous measure summarized with means and standard deviations; the registry record does not report an over-dispersion assessment or a model-based diagnostic. No conclusion about over-dispersion can be drawn from the available summaries alone.

What can be inferred from the analysis record?

The registry record reports the primary group summaries and comparison, but does not report the detailed statistical plan, assumptions used for the primary test, or whether adjustment for baseline variables was intended. It also lists no reported analyses overall. Thus the posted comparison can be described, but its full implementation cannot be independently evaluated from the registry record. The secondary endpoint has posted group summaries and a comparison estimate, but no reported analyses are listed for it. As with the primary endpoint, the record does not state how missing observations or multiple outcomes were handled.

These limits matter because the same numerical contrast may be analyzed using different methods depending on the design details, distributional properties, and analysis population. General statistical concepts can explain what a mean difference, standard deviation, p-value, or confidence interval represents; they cannot fill in undocumented choices in this study. Interpretations should remain anchored to the posted estimates and clearly distinguish them from methodological details that are not reported in the registry record.

11. Confidence Intervals and Precision

The primary estimate is a mean difference of 0.08 logMAR, with a reported confidence interval that runs from 0.016 to 0.144. This interval does not include zero, indicating that the posted interval is compatible with positive mean differences under the method used, rather than with no difference. The reported unadjusted p-value is 0.014. The interval conveys more information than a significance decision alone because it describes a range of effect sizes compatible with the data and the interval procedure.

The range also indicates that the estimate is not exact. Its lower and upper bounds are separated, so the true group-average difference is uncertain. A confidence interval does not mean that there is a specified probability that the true effect lies inside this particular realized interval. In general, the confidence level describes the long-run performance of the procedure under its assumptions. The registry record does not report the confidence level or full method used, so those details are not inferred.

The primary outcome summaries include 30 participants per group, with standard deviations of 0.14 for AcrySof Toric and 0.11 for AcrySof Natural. The amount of uncertainty in a comparison depends on both within-group variability and the information available. The registry record does not explain whether there were missing observations or whether the participant counts in the summaries match a prespecified analysis population.

Precision is separate from clinical importance. A confidence interval can characterize statistical uncertainty without defining what size of difference matters to patients or clinicians. No threshold for a clinically important difference is reported in the registry record. Nor does the interval capture every source of uncertainty, such as possible bias from study conduct, outcome measurement, missing data, or analysis choices that are not described.

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 sample-size figures are planning illustrations based on the observed effect, not the trial's original design calculation. For this continuous outcome, the figures are participants per arm, rather than a total number of events. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is specified as a fraction of the observed effect. The registry record does not report the assumptions used for the trial's original design or a sample-size justification.

The 80% power column gives the planned number of participants per arm for a hypothetical study designed to have an 80% chance of detecting the chosen effect under the stated assumptions, if that effect and those assumptions were correct. The 90% column uses the corresponding higher target chance of detection. These are design targets, not probabilities that the reported finding is true or that a treatment works.

The planning scenarios consider 100%, 75%, and 50% of the observed effect. For 100% of the observed effect, the illustration gives 39 participants per arm for 80% power and 53 for 90% power. For 75% of the observed effect, it gives 70 and 93 participants per arm, respectively. For 50% of the observed effect, it gives 156 and 209 participants per arm, respectively. Smaller effects need more participants to detect under the same assumptions, which is why the projected requirements increase as the target effect becomes a smaller fraction of the observed effect.

These calculations are not observed power. They are prospective planning illustrations derived from the observed effect and do not describe the probability that the completed study detected a real effect. They also do not show that the original study was designed using these assumptions.

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 = 0.080; pooled standard deviation σ = 0.126.
2. n = 2 × (1.96 + 0.842)² × 0.126² / 0.080² = 38.9, rounded up to 39 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 <- 0.08                      # observed difference in means
sigma <- 0.125896783120142                     # 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(758550)
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 = 39 (80% power), 53 (90% power)
 75% of observed effect: n per arm = 70 (80% power), 93 (90% power)
 50% of observed effect: n per arm = 156 (80% power), 209 (90% power)
power.t.test: 39.9 
Simulated power at n = 39 per arm: 0.794 (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 record does not report whether the study prespecified a strategy for handling multiple statistical tests. The posted primary outcome is uncorrected visual acuity, and questionnaire results are listed as a secondary outcome. If more than one outcome is tested, interpreting each unadjusted p-value as if it were the only test can increase the chance of at least one apparently unusual result arising by chance. A multiplicity procedure can address that issue, but no such procedure is reported in the registry record.

The primary comparison is reported with an unadjusted p-value of 0.014. The questionnaire comparison also has an unadjusted p-value, but the registry record lists no reported analyses for that endpoint. Without a prespecified hierarchy, adjustment, or clear statement that secondary outcomes are descriptive, the strength of evidence across outcomes is difficult to judge. This does not change the posted estimates; it affects how confidently findings across several outcomes can be interpreted together.

Missing-data handling is also not reported in the registry record. The posted primary summaries list 30 participants in each group, but the record does not say whether those numbers reflect all randomized participants, participants with observed outcome data, or another analysis population. It does not describe missing measurements, reasons for missingness, exclusions, imputation, or sensitivity analyses. No assumptions about these procedures should be inferred from the group counts alone.

The analysis population is not specified beyond the posted group summaries. The record does not state whether participants were analyzed according to randomized assignment, whether any participants were excluded after randomization, or whether a per-protocol population was used. These omissions matter because analysis-population choices can affect estimates and their uncertainty. The registry record also does not provide a complete statistical analysis plan, so prespecification and deviations from plan cannot be assessed.

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 0% reporting threshold.

The adverse-event record lists 30 participants at risk for serious adverse events in each group. It reports zero participants affected by serious adverse events in both the AcrySof Toric and AcrySof Natural groups. The record also lists 30 participants at risk for other adverse events in each group and zero affected in either group. No serious adverse-event terms are listed.

These figures describe what was recorded for the stated groups and do not establish that no events occurred outside the registry's reporting scope or observation period. The duration and method of safety surveillance are not reported in the registry record. The death counts are not reported in the registry record, so they cannot be interpreted as zero. With the available safety information, the appropriate reading is limited to the posted counts and the absence of listed serious adverse-event terms, not a general conclusion about comparative safety.

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

The primary result describes a difference in average uncorrected visual acuity at 6 months after surgery between the two randomized groups. The AcrySof Toric group had a mean of 0.06 logMAR, compared with 0.14 for the AcrySof Natural group. Since lower logMAR indicates better visual acuity, the direction of the observed group means favors lower values in the Toric group. The reported mean difference was 0.08, and its confidence interval excludes zero.

This is a result about group averages at a specific follow-up, not a statement about every participant. It does not indicate how many participants had a particular level of vision, whether individual participants experienced a change, or how outcomes varied over time. The standard deviations describe variability within groups but do not give the full distribution. The registry record does not report an analysis of change from baseline or a clinically important threshold for the scale.

A statistically distinguishable group difference is not automatically a clinically important difference. The record does not state what size of logMAR difference would be meaningful to participants or clinicians. The endpoint is one measure of visual function; it does not encompass every aspect of vision, satisfaction, or daily functioning. The questionnaire result provides additional information but its scale interpretation is not reported, and its unadjusted comparison is uncertain.

The randomized design is relevant to interpretation, but the registry record does not describe allocation procedures, participant characteristics, missing-data handling, or the analysis population. It also does not report the full analysis plan. Those gaps make it difficult to evaluate potential bias or determine precisely which participants contributed to the estimates. The posted result should therefore be read as a comparison of the recorded group summaries, not as a complete assessment of all design and analysis choices.

The finding does not establish persistence beyond the reported 6-month time point, nor does it establish effects on outcomes not included in the record. The posted safety counts are limited to the reported adverse-event categories and do not provide a full account of surveillance. The result is best understood as evidence about the recorded primary endpoint and follow-up, with uncertainty about its clinical importance and broader applicability.

17. Why This Trial Matters Statistically

This trial offers a useful statistical example of how a continuous clinical outcome is reported: group means, standard deviations, a mean difference, a confidence interval, and an unadjusted p-value. The values have different roles. The means describe observed group averages, the standard deviations describe participant-level spread, the confidence interval characterizes uncertainty in the contrast, and the p-value summarizes evidence relative to a null comparison under the analysis assumptions.

The direction of a contrast depends on the scale and subtraction order. Here, the mean difference is defined as AcrySof Natural minus AcrySof Toric, while lower logMAR values indicate better acuity. Reading the sign together with the scale definition avoids treating a positive difference as inherently favorable or unfavorable. This is a general lesson for interpreting outcomes where higher or lower values have different meanings.

The record also illustrates why statistical evidence and practical importance are separate. The primary interval excludes zero, but the registry record does not report a threshold for a clinically meaningful difference. The result can indicate a group-average contrast without resolving whether its size matters in practice. Similarly, the secondary outcome is a distinct measure and has no reported scale interpretation that would permit a clear directional judgment.

Finally, planning illustrations based on an observed effect should not be confused with the original design or with observed power. Their assumptions are stated, but the trial's own sample-size rationale and detailed statistical plan are not reported. Distinguishing recorded findings from undocumented methods is central to sound evidence interpretation.

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 record provides limited information for evaluating how representative the participants were. It does not report eligibility criteria, demographic characteristics, baseline visual acuity, or other clinical features. The outcome summaries list 30 participants per group, but the record does not clarify how these counts relate to all randomized participants or whether any observations were missing.

Although allocation is recorded as randomized, details of sequence generation and allocation concealment are not reported. Masking is listed as none, and the record does not describe whether outcome assessment was standardized or whether the assessor knew the assigned lens. The absence of masking may be relevant to outcomes involving measurement or participant reporting, but the record does not provide enough detail to assess its impact.

The primary endpoint is reported at 6 months after surgery. No additional follow-up results are described, so the record cannot address durability or changes over time. The measurement protocol and any baseline-adjusted analysis are not reported. A clinical threshold for interpreting the size of the mean difference is also absent, leaving clinical importance unresolved.

One secondary questionnaire outcome is listed, but its scale interpretation is not reported. Multiplicity handling, missing-data methods, analysis populations, and the full statistical analysis plan are not reported in the registry record. The number and nature of outcome analyses therefore cannot be fully evaluated. Finally, the adverse-event counts do not include reported death counts or details of safety follow-up. These limitations constrain interpretation of the posted results without negating the descriptive group comparison.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Visual Function After Bilateral Implantation of AcrySof® Toric — NCT00758550.
• Registry record last updated 2010-03-16; status last verified 2010-03.
• Results first posted 2010-03-16.
• 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

NCT00758550 is a completed Phase 4 randomized, open-label, parallel-group study sponsored by Alcon Research. It enrolled 60 participants and compared AcrySof Toric with AcrySof Natural intraocular lenses for visual function after cataract replacement. The primary endpoint was mean uncorrected visual acuity in logMAR at 6 months after surgery.

The posted primary group means were 0.06 for AcrySof Toric and 0.14 for AcrySof Natural, with a reported mean difference of 0.08 and an unadjusted p-value of 0.014. The registry record also lists questionnaire results at 6 months as a secondary outcome. It does not report the full statistical plan, missing-data handling, analysis populations, or multiplicity procedures.