Tutorial on Biostatistics: Statistical Analysis for Correlated Binary Eye Data.

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.