Tutorial on Biostatistics: Linear Regression Analysis of Continuous Correlated Eye Data

ABSTRACT

Purpose: To describe and demonstrate appropriate linear regression methods for analyzing correlated continuous eye data.

Methods: We describe several approaches to regression analysis involving both eyes, including mixed effects and marginal models under various covariance structures to account for inter-eye correlation. We demonstrate, with SAS statistical software, applications in a study comparing baseline refractive error between one eye with choroidal neovascularization (CNV) and the unaffected fellow eye, and in a study determining factors associated with visual field in the elderly.

Results: When refractive error from both eyes were analyzed with standard linear regression without accounting for inter-eye correlation (adjusting for demographic and ocular covariates), the difference between eyes with CNV and fellow eyes was 0.15 diopters (D; 95% confidence interval, CI −0.03 to 0.32D, p = 0.10). Using a mixed effects model or a marginal model, the estimated difference was the same but with narrower 95% CI (0.01 to 0.28D, p = 0.03). Standard regression for visual field data from both eyes provided biased estimates of standard error (generally underestimated) and smaller p-values, while analysis of the worse eye provided larger p-values than mixed effects models and marginal models.

Conclusion: In research involving both eyes, ignoring inter-eye correlation can lead to invalid inferences. Analysis using only right or left eyes is valid, but decreases power. Worse-eye analysis can provide less power and biased estimates of effect. Mixed effects or marginal models using the eye as the unit of analysis should be used to appropriately account for inter-eye correlation and maximize power and precision.

KEYWORDS:

• Correlated data
• generalized estimating equations
• inter-eye correlation
• linear regression models
• marginal model
• mixed effects model

Acknowledgments

Part of this paper has been in an eNewsletter that was sent to grant awardees (P30, U10, K) from the National Eye Institute. Permission was obtained from the owners of eNewsletter (Drs Ying, Maguire, Glynn and Rosner).

Declaration of interest

The authors report no conflict of interest. The authors alone are responsible for the writing and content of this article.

Funding

Supported by grants R01EY022445 and P30 EY01583-26 from the National Eye Institute, National Institutes of Health, Department of Health and Human Services and an unrestricted grant from Research to Prevent Blindness to the University of Pennsylvania.

Additional information

Funding

Supported by grants R01EY022445 and P30 EY01583-26 from the National Eye Institute, National Institutes of Health, Department of Health and Human Services and an unrestricted grant from Research to Prevent Blindness to the University of Pennsylvania.