Comparison of Cross-cylinder and Conventional Photorefractive Keratectomy(PRK) in Correcting Medium-high Astigmatism: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Comparison of Cross-cylinder and Conventional Photorefractive Keratectomy(PRK) in Correcting Medium-high Astigmatism (NCT00663923), a randomized phase 3 study. The primary outcome is Correction of Astigmatism.

2. Clinical Question

3. Trial Design

This was a completed, phase 3, randomized, single-masked, parallel-group clinical trial sponsored by Tabriz University. The registry reports enrollment of 50 participants and lists astigmatism as the condition. The two intervention descriptions are Cross-cylinder PRK and Single PRK, both forms of photorefractive keratectomy. The listed start was 2007-11, and primary completion was 2009-06.

The trial compared the approaches as assigned to separate groups. The record describes the cross-cylinder method as applying ablation centrally and paracentrally according to the cylinder axis and amount. The single-meridian approach uses an elliptical ablation to flatten the steeper meridian. The registry identifies single masking but does not report who was masked in the registry record. Further details about random-sequence generation, allocation concealment, or masking procedures are not reported in the registry record.

The primary endpoint was correction of astigmatism, measured by refraction using an autorefractor at six months after surgery. The primary outcome analysis is described as per protocol. The posted group summaries include 48 observations in each arm. The relation between the enrollment figure and the analyzed observations, and the reasons for any participants not appearing in the primary summaries, are not reported in the registry record.

Secondary outcomes included higher order aberrations, corrected distance visual acuity, uncorrected distance visual acuity, and surgically induced astigmatism. Results are posted for three of these outcomes; results for surgically induced astigmatism are not reported in the registry record. The registry lists five outcome measures overall, but does not provide further detail about the fifth measure in the information.

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: All enrolled patients having inclusion criteria accepted both available techniques for correction of astigmatism.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: The sample size was determined by the one proportion formula where power = 0.8, d=0.02 , p= 0.5(primary outcome) and type I error probability associated with this test of null hypothesis is 0.05. The analysis was per protocol

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 Correction of Astigmatism, measured over six months after surgery.

The primary endpoint, Correction of Astigmatism, is a continuous measure reported in diopters. The registry describes it as the result of astigmatism correction and says it was measured by refraction using an autorefractor six months after surgery. A diopter expresses optical power and is defined in the record as the reciprocal of focal length measured in meters.

The endpoint is used to quantify the remaining refractive astigmatism after the procedure. In the registry’s description of compound myopic astigmatism, the meridians with maximum and minimum power are both too strong, so both line images fall short of the retina. Measuring refraction therefore gives a numerical way to assess the refractive result rather than relying only on a categorical judgment.

The posted outcome is summarized as a group mean with a standard deviation. A mean conveys the group’s average value, while the standard deviation describes how spread out individual measurements are around that average. Neither measure alone describes every participant’s result. The endpoint’s interpretation also depends on the direction and scale of the measurement and on the analysis used to compare groups. The registry does not define a threshold for a clinically important difference in diopters, so the statistical comparison should not be treated as establishing the practical importance of any difference.

7. Results Posted in the Registry

• Single PRK: mean -0.59 versus -0.54 on control; difference -0.05 (95% CI -0.20 to 0.10), standardized effect d = -0.13; z-test p = 0.523.

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.

Higher Order Aberrations

• 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:
  • Single PRK: mean 0.51 versus 0.51 on control; difference 0.00 (95% CI -0.09 to 0.09), standardized effect d = 0.00; z-test p = 1.000.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Single PRK and the control. The interval gives the range of effects that remain compatible with the data.

Corrected Distance Visual Acuity(CDVA)

• 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:
  • Single PRK: mean 0.03 versus 0.02 on control; difference 0.01 (95% CI -0.00 to 0.02), standardized effect d = 0.39; z-test p = 0.055.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Single PRK and the control. The interval gives the range of effects that remain compatible with the data.

Uncorrected Distance Visual Acuity (UCDVA)

• 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:
  • Single PRK: mean 0.10 versus 0.08 on control; difference 0.02 (95% CI -0.04 to 0.08), standardized effect d = 0.13; z-test p = 0.528.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Single PRK and the control. The interval gives the range of effects that remain compatible with the data.

The secondary outcomes provide a broader view of the recorded results beyond the primary refractive endpoint. They include higher order aberrations and corrected and uncorrected distance visual acuity. The posted group summaries and unadjusted comparisons do not form a uniform pattern of clear separation across these outcomes. Some estimates are close to zero, while others have intervals that include zero; the measurements also use different units and scales.

These outcomes are related to the primary question in that they describe other optical or visual measurements after surgery, but they are not interchangeable with the primary diopter-based measure of astigmatism correction. A difference in one secondary measure would not by itself establish a difference in the primary endpoint, nor would a lack of a clear difference in a secondary measure settle the primary comparison. The registry does not report sponsor analyses for these secondary outcomes.

Unadjusted secondary results carry less weight because several outcomes are considered and the registry does not report how multiplicity was handled. When many comparisons are made, nominal statistical signals can occur by chance more often than when a single prespecified test is considered. This is a general statistical concern; the record does not provide a multiplicity-adjusted result or enough information to determine which secondary comparisons were planned as confirmatory.

One listed secondary outcome, surgically induced astigmatism, has no results in the registry record. Therefore, the secondary evidence is incomplete as well as exploratory in its statistical interpretation. It should be read as descriptive context for the primary comparison, not as a separate basis for a definitive overall judgment.

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

• Higher Order Aberrations
• Corrected Distance Visual Acuity(CDVA)
• Uncorrected Distance Visual Acuity (UCDVA)
• Surgically Induced Astigmatism

9. Statistical Interpretation

10. Statistical Methods Explained

The primary endpoint is continuous, so the registry reports means and standard deviations for the two groups. A mean is the arithmetic average of the recorded measurements. A standard deviation describes the dispersion of observations around the mean; it is not the uncertainty of the mean itself. The sample size and spread together determine how precisely a group mean, and a difference between group means, can be estimated.

What does a mean difference represent?

A mean difference compares the group averages on their original measurement scale. For the primary outcome, that scale is diopters. The posted summaries list Cross-cylinder PRK first and Single PRK second, and the recalculated comparison is expressed as Single PRK relative to Cross-cylinder PRK. The sign indicates the direction of the numerical contrast under that ordering. It does not by itself tell whether a difference is important to patients or clinically meaningful; the registry does not report a threshold for that judgment.

The recalculated comparisons are simple unadjusted calculations from the posted summary statistics. They do not reproduce an analysis that might have used participant-level data, covariates, exclusions, or other adjustments. The primary endpoint description identifies the analysis as per protocol, but details of that analysis are not reported in the registry record. Thus, the recalculation is a way to inspect the posted group means and variability, not a replacement for the sponsor’s analysis.

How should a p-value be read?

A p-value describes how compatible the observed data are with a specified null model, under the assumptions of the test. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. The registry identifies the sponsor’s primary test as two-sided. The recalculated p-value of 0.523 and the sponsor-reported p-value of <0.05 produce different conclusions about statistical evidence. Since the discrepancy is flagged, the sponsor’s analysis takes precedence as the trial’s reported analysis, while the recalculation remains a transparent check based on the posted summaries.

What does a confidence interval add?

A confidence interval gives a range of effect values compatible with the data and analysis under the method’s assumptions. Its width conveys precision: a narrower interval indicates more precise estimation than a wider one. A 95% confidence interval is not a probability statement about a fixed parameter after the data have been observed. The sponsor reports a 95% interval from -.62 to -.001. The unadjusted recalculation has a different interval; its exact bounds are not needed to see that its inference differs from the sponsor’s reported result.

Why can reported and recalculated results differ?

A calculation from group means and standard deviations assumes the summaries correspond to the same population and comparison being tested. Differences can arise when the analysis uses a different analysis set, model, variance estimate, or data handling. These are general possibilities, not explanations established for this trial. The registry does not report enough detail to identify the reason for the discrepancy. It also does not report whether any covariate adjustment or other analytical feature was used in the sponsor’s analysis.

Over-dispersion is a general concern when count data vary more than a model assumes. It is not the central issue for these continuous mean comparisons, and the registry does not report a count-based primary endpoint. For continuous outcomes, the reported standard deviations matter because greater variability generally makes a mean difference less precise when other conditions are unchanged. The observed group spreads are part of the uncertainty reflected in the calculations.

What is the role of the secondary comparisons?

Each secondary continuous outcome has its own scale, means, variability, and comparison. A value in LogMAR is not directly interchangeable with a value in diopters or microns. The unadjusted recalculations are exploratory descriptions unless a prespecified analysis plan establishes otherwise. The registry record does not report a multiplicity strategy, so the chance of false-positive findings across multiple comparisons cannot be assessed from the record. A single nominal p-value among several outcomes therefore deserves less weight than a primary result that was specified in advance, particularly when the secondary analyses are not reported by the sponsor.

Statistical methods answer questions about estimates and uncertainty under stated assumptions. They do not resolve missing design details, define clinical importance, or turn a registry summary into a complete clinical interpretation. The key methodological caution in this trial is the conflict between the sponsor-reported primary result and the simple unadjusted recalculation, alongside limited reporting about the underlying analysis choices.

11. Confidence Intervals and Precision

The sponsor’s primary analysis reports a 95% confidence interval from -.62 to -.001 around the mean difference of -0.05. This interval is the registry’s stated uncertainty range for the sponsor’s analysis. It lies on one side of zero as reported, consistent with the reported p-value of <0.05. That statistical conclusion should be kept distinct from the size or practical importance of the difference, which the registry does not define.

The unadjusted recalculation from the posted group means and standard deviations gives a different assessment: its p-value is 0.523, and its interval includes values on both sides of zero. The primary group means are -0.54 and -0.59, with standard deviations of 0.43 and 0.33. The recalculated interval is not reproduced numerically because the key issue is its disagreement with the sponsor-reported interval. In particular, the same displayed mean difference does not guarantee the same precision estimate or inferential result when the analysis basis differs.

Precision is not the same as accuracy. A narrow interval can still be affected by limitations in study conduct, measurement, or analysis, and a wide interval indicates uncertainty about the range of plausible differences rather than proof of no difference. The posted data do not resolve why the two analyses differ. The sponsor’s analysis takes precedence as the trial’s own reported analysis, while the disagreement limits confidence in any interpretation based solely on the posted summary statistics.

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 illustrations report 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. For each row, the assumed effect is the stated fraction of the observed effect. The planning entries show the number of participants per arm for 80% power and for 90% power under those assumptions.

In plain language, the 80% power column gives the planned number per arm for a design with an 80% chance of detecting the specified effect if that effect is real and the assumptions hold. The 90% power column applies the same idea at a higher target chance of detection, and therefore calls for more participants per arm. These are planning illustrations based on the observed effect, not observed power. Smaller assumed effects require more participants because they are harder to distinguish from random variation.

The illustrations are not the trial’s enrollment target and should not be read as evidence that the trial was adequately or inadequately powered. The registry’s primary outcome description separately says sample size was determined by a one proportion formula, with power = 0.8, d=0.02, p= 0.5 and type I error probability 0.05. How that original calculation relates to the two-group continuous outcome is not reported in the registry record. The planning illustrations use different stated assumptions and should be kept separate from the trial’s original design calculation.

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 = -0.050; pooled standard deviation σ = 0.383.
2. n = 2 × (1.96 + 0.842)² × 0.383² / -0.050² = 922.4, rounded up to 923 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 <- -0.0499999999999999                      # observed difference in means
sigma <- 0.383275357934736                     # 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(663923)
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 = 923 (80% power), 1,235 (90% power)
 75% of observed effect: n per arm = 1,640 (80% power), 2,196 (90% power)
 50% of observed effect: n per arm = 3,690 (80% power), 4,940 (90% power)
power.t.test: 923.4 
Simulated power at n = 923 per arm: 0.800 (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. Analyses Reported by the Sponsor

The registry reports a sponsor analysis using a two-sided t-test of the mean difference in final values. It gives a mean difference of -0.05, a 95% confidence interval from -.62 to -.001, and p <0.05. This is the trial’s own reported analysis and is the primary source for describing the sponsor’s inferential conclusion.

An unadjusted recalculation from the posted group summaries also gives a mean difference of -0.05, but its p-value is 0.523 and its confidence interval includes zero. This is a material discrepancy in the inferential result, even though the displayed mean differences match. The record does not explain the different uncertainty estimates or test results. Possible methodological explanations cannot be confirmed from the information in the registry.

Accordingly, the sponsor’s analysis takes precedence when reporting what the trial concluded statistically. The recalculation is useful as a check on how the posted means and standard deviations compare under a simple unadjusted approach, but it should not be substituted for the sponsor’s analysis. The distinction between the two results should remain explicit rather than combining them into a single conclusion.

15. Multiplicity, Missing Data and Analysis Populations

The primary outcome description says the analysis was per protocol. The registry record does not provide a fuller definition of that population, an intention-to-treat analysis, or an explanation of how participants without outcome data were handled. Although enrollment was 50 and the primary summaries include 48 participants in each group, the reasons for that difference and the disposition of each participant are not reported in the registry record. It is therefore not possible to determine from the posted information whether exclusions, missing measurements, or another analysis-population rule explains the displayed numbers.

The record lists multiple secondary outcomes, but does not report a multiplicity adjustment, a hierarchy among the secondary tests, or which outcomes were designated confirmatory. Without that information, individual unadjusted secondary p-values should be interpreted cautiously. Considering several outcomes raises the general possibility of chance findings, but the record does not quantify that possibility or show an adjusted analysis.

The registry does not report a missing-data method, sensitivity analyses, imputation, or a detailed statistical analysis plan. The primary outcome description includes a sample-size statement using a one proportion formula, with power = 0.8, d=0.02, p= 0.5 and type I error probability 0.05, and separately says the analysis was per protocol. The rationale connecting that calculation to the reported continuous two-group endpoint is not reported in the registry record. Details of interim analyses or stopping rules are also not reported in the registry record.

These omissions do not demonstrate that a particular procedure was or was not followed. They mark limits on what can be assessed from the posted registry information, especially regarding the analysis population, missing outcomes, and the interpretation of multiple secondary comparisons.

16. 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 48 participants at risk in each group. It reports zero serious adverse events in Cross-cylinder PRK and zero in Single PRK. It also reports zero other adverse events in each group. These figures describe the recorded events for the groups and denominators shown in the registry.

A zero count in a posted record does not establish that no event could occur, nor does it establish equal safety between procedures. The registry does not provide additional detail about event definitions, ascertainment, follow-up completeness, or the duration over which these counts were collected. Death counts are not reported in the registry record. The serious adverse event figures should therefore be read as the events recorded in these group summaries, not as a complete assessment of all possible risks.

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

The posted information describes a randomized comparison of two PRK approaches and reports the groups’ six-month mean correction-of-astigmatism values. The sponsor’s analysis reports a statistically significant mean difference, while the unadjusted recalculation from posted summary statistics does not. Because the registry flags a discrepancy, the sponsor’s own analysis takes precedence as the trial’s reported result; the disagreement should nevertheless remain part of the interpretation.

The statistical evidence does not by itself establish the clinical importance of the reported difference. The registry does not give a threshold for a meaningful difference in diopters, nor does it explain the discrepancy between the sponsor’s analysis and the summary-based recalculation. The estimates are group averages and do not describe every participant’s outcome. Variation is present within both groups, as reflected by the posted standard deviations.

The results also do not establish that one procedure is universally preferable, or that either procedure does or does not work. They are evidence from one registry-recorded trial with its stated population, measures, and analysis. The secondary results offer additional descriptive information, but are limited by unadjusted comparisons, absent sponsor analyses, and the lack of reported multiplicity handling. Surgically induced astigmatism is listed as an outcome without results in the registry record.

Finally, the primary analysis is described as per protocol, while further details about exclusions, missing data, and analysis choices are not reported. Those limitations matter when interpreting both the precision and generalizability of the comparison. The conclusions should remain tied to the posted trial results and the reporting limitations, rather than extending to unreported populations or outcomes.

18. Why This Trial Matters Statistically

This trial illustrates why a reported effect estimate should be considered alongside its uncertainty and the analysis that produced it. The sponsor-reported mean difference is -0.05, and the posted group means are -0.54 and -0.59. Yet the sponsor’s confidence interval and p-value lead to a different inferential conclusion from an unadjusted recalculation based on the posted group summaries. Matching displayed point estimates do not ensure that the underlying standard errors, confidence intervals, or tests match.

It also demonstrates the value of distinguishing a trial’s own analysis from a summary-based check. A simple recalculation can help readers understand how posted means and standard deviations behave under an unadjusted comparison, but it does not recreate undocumented analysis decisions. In this case the registry record does not explain the discrepancy, making careful attribution especially important.

Other statistical issues are visible in the reporting: the primary analysis is per protocol, while details on missing outcomes and participant disposition are not reported; several secondary outcomes are listed without a reported multiplicity strategy; and a planning illustration based on an observed effect is distinct from the trial’s original sizing. These are general lessons in reading clinical trial records: identify the endpoint, analysis population, uncertainty, and planning assumptions separately, and do not infer more than the record supports.

19. 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 trial-specific limitations restrict interpretation. The registry reports 50 enrolled participants, while the primary group summaries contain 48 participants in each arm. The record does not explain this difference or report participant flow, reasons for exclusion, or missing-outcome handling. Since the primary analysis is described as per protocol, the exact analysis population and its relationship to randomization are particularly relevant but not reported in the registry record.

The sponsor-reported primary result and the unadjusted recalculation disagree in their statistical conclusions. The record does not provide the analysis details needed to explain the difference. This uncertainty affects interpretation of the reported precision and means that the recalculation should remain a secondary check rather than a substitute for the sponsor’s analysis.

The registry does not report a threshold for clinical importance, a multiplicity adjustment for secondary outcomes, or sponsor analyses of those outcomes. Surgically induced astigmatism is listed but has no result posted. Details on randomization methods, allocation concealment, the identity of the masked party, and the full statistical analysis plan are not reported in the registry record. Death counts are also not reported in the registry record.

These reporting gaps do not establish that the trial lacked appropriate procedures; they mean the relevant details cannot be assessed from the registry information. The findings should be understood within these limits and should not be extended beyond the measured outcomes and the trial population described in the record.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Comparison of Cross-cylinder and Conventional Photorefractive Keratectomy(PRK) in Correcting Medium-high Astigmatism — NCT00663923.
• Registry record last updated 2012-03-13; status last verified 2012-03.
• Results first posted 2011-12-30.
• 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.

23. Record Summary

The registry describes a completed, phase 3, randomized, single-masked, parallel-group comparison of Cross-cylinder PRK and Single PRK for astigmatism. Enrollment was 50. The primary endpoint was correction of astigmatism in diopters at six months after surgery, analyzed per protocol.

The sponsor reports a two-sided t-test with a mean difference of -0.05, a 95% confidence interval from -.62 to -.001, and p <0.05. An unadjusted recalculation from the posted group summaries gives p = 0.523, so the inferential results differ; the sponsor’s analysis takes precedence. Secondary results are available for three listed outcomes, with no posted result for surgically induced astigmatism. The registry does not explain the primary-analysis discrepancy or report details of missing-data handling and multiplicity adjustment.