Statistical analysis of correlated binary data in ophthalmology: a weighted logistic regression approach

Ophthalmological studies often deal with correlated binary outcome variables. We propose a weighted logistic regression method to account for the intraclass correlations between eyes. Using simulation studies, we compared this method with two standard logistic regression approaches: a) based on eyes as the unit of analysis and b) treating individuals classified as cases if at least one eye is affected. The considered approaches were evaluated in terms of type I error, power and estimation properties. The simulation results reveal that the subject-based approach can lead to substantial bias in regression coefficient estimates when the correlation between eyes is heterogeneous across groups or when it is low, and that power is directly affected by this bias. Furthermore, the standard eye-based approach, which ignores intrasubject correlations, leads to inflated type I error rates. The proposed weighted approach performed well in all of the situations considered. This is a simple method which can be implemented using any current statistical or epidemiological package that includes logistic regression analysis.