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Updated: Jan 20, 2026

Statistical Methods for Analyzing Epidemiological Data
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Evaluation of Statistical Methods for Clustered Eye Data with Skewed Distribution.

Sifan Zhang1, Ziyi You2, Bernard Rosner3

  • 1New York University, New York, New York.

Ophthalmology Science
|January 19, 2026
PubMed
Summary

For skewed correlated eye data, clustered Wilcoxon methods are recommended. Alternatively, normalizing data and using generalized estimating equations (GEE) score or linear mixed-effects models (LMM) can increase statistical power.

Keywords:
Clustered Wilcoxon testCorrelated eye dataGeneralized estimating equationsNonparametric testStatistical analysis

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Area of Science:

  • Ophthalmology and vision research
  • Biostatistics
  • Statistical modeling

Background:

  • Ophthalmology and vision research frequently involve analyzing skewed, correlated data from a subject's two eyes within the same group.
  • Evaluating the performance of different statistical methods for such data is crucial for accurate analysis.

Purpose of the Study:

  • To assess the effectiveness of various analytical approaches for skewed, correlated ocular data.
  • To compare the type 1 error rate and statistical power of different statistical tests under various simulation conditions.

Main Methods:

  • A simulation study was conducted using skewed correlated data with varying intereye correlation, sample sizes, and mean differences.
  • Nine different analysis methods were evaluated, including t-tests, generalized estimating equations (GEE), and linear mixed-effects models (LMM), with and without rank-based normalization.
  • Real data from the Dry Eye Assessment and Management (DREAM) study, specifically tear break-up time (TBUT) data, were analyzed to validate simulation findings.

Main Results:

  • Standard t-tests and Wilcoxon tests ignoring intereye correlation inflated the type 1 error rate.
  • Generalized estimating equations (GEE) Wald test also showed inflated type 1 error rates with small sample sizes.
  • For skewed data without normalization, GEE score and LMM demonstrated lower statistical power compared to clustered Wilcoxon methods.
  • After normalization, GEE score and LMM achieved comparable or slightly superior statistical power to clustered Wilcoxon methods.
  • Analysis of TBUT data from the DREAM study corroborated the simulation results.

Conclusions:

  • Clustered Wilcoxon methods are suitable for comparing skewed correlated eye measures between groups.
  • Normalizing skewed data followed by GEE score or LMM analysis offers an alternative approach.
  • Normalization with GEE score or LMM may provide slightly higher statistical power and greater flexibility for adjusting covariates.