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Correlation and Regression00:53

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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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Related Experiment Video

Updated: Mar 8, 2026

In vivo Structural Assessments of Ocular Disease in Rodent Models using Optical Coherence Tomography
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Tutorial on Biostatistics: Linear Regression Analysis of Continuous Correlated Eye Data.

Gui-Shuang Ying1, Maureen G Maguire1, Robert Glynn2

  • 1a Center for Preventive Ophthalmology and Biostatistics, Department of Ophthalmology , Perelman School of Medicine, University of Pennsylvania , Philadelphia , PA , USA.

Ophthalmic Epidemiology
|January 20, 2017
PubMed
Summary

Properly analyzing correlated eye data requires accounting for inter-eye correlation. Mixed effects or marginal models are recommended for accurate inferences and increased statistical power in eye research.

Keywords:
Correlated datageneralized estimating equationsinter-eye correlationlinear regression modelsmarginal modelmixed effects model

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Area of Science:

  • Ophthalmology
  • Biostatistics
  • Statistical Modeling

Background:

  • Ocular data often involves correlated measurements from both eyes.
  • Ignoring this inter-eye correlation can lead to inaccurate statistical inferences in research.

Purpose of the Study:

  • To describe and demonstrate appropriate linear regression methods for analyzing correlated continuous eye data.
  • To highlight the importance of accounting for inter-eye correlation in statistical analyses.

Main Methods:

  • Described mixed effects and marginal models to account for inter-eye correlation.
  • Applied these models using SAS statistical software.
  • Demonstrated applications in refractive error and visual field studies.

Main Results:

  • Standard linear regression without accounting for correlation yielded different results (p=0.10) compared to mixed effects/marginal models (p=0.03) for refractive error.
  • Standard regression for visual field data produced biased standard errors and smaller p-values.
  • Analysis of only the worse eye resulted in less power and biased effect estimates.

Conclusions:

  • Ignoring inter-eye correlation in research involving both eyes can lead to invalid inferences.
  • Using mixed effects or marginal models appropriately accounts for inter-eye correlation.
  • These models maximize statistical power and precision in eye research.