Tutorial on Biostatistics: Statistical Analysis for Correlated Binary Eye Data

ABSTRACT

Purpose: To describe and demonstrate methods for analyzing correlated binary eye data.

Methods: We describe non-model based (McNemar’s test, Cochran-Mantel-Haenszel test) and model-based methods (generalized linear mixed effects model, marginal model) for analyses involving both eyes. These methods were applied to: (1) CAPT (Complications of Age-related Macular Degeneration Prevention Trial) where one eye was treated and the other observed (paired design); (2) ETROP (Early Treatment for Retinopathy of Prematurity) where bilaterally affected infants had one eye treated conventionally and the other treated early and unilaterally affected infants had treatment assigned randomly; and (3) AREDS (Age-Related Eye Disease Study) where treatment was systemic and outcome was eye-specific (both eyes in the same treatment group).

Results: In the CAPT (n = 80), treatment group (30% vision loss in treated vs. 44% in observed eyes) was not statistically significant (p = 0.07) when inter-eye correlation was ignored, but was significant (p = 0.01) with McNemar’s test and the marginal model. Using standard logistic regression for unfavorable vision in ETROP, standard errors and p-values were larger for person-level covariates and were smaller for ocular covariates than using models accounting for inter-eye correlation. For risk factors of geographic atrophy in AREDS, two-eye analyses accounting for inter-eye correlation yielded more power than one-eye analyses and provided larger standard errors and p-values than invalid two-eye analyses ignoring inter-eye correlation.

Conclusion: Ignoring inter-eye correlation can lead to larger p-values for paired designs and smaller p-values when both eyes are in the same group. Marginal models or mixed effects models using the eye as the unit of analysis provide valid inference.

KEYWORDS:

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

Declaration of interest

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

Funding

This study was 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

This study was 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.