Comparison of alternative regression models for paired binary data

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Abstract
We used simulated data, derived from real ophthalmologic examples, to evaluate the performance of alternative logistic regression approaches for paired binary data. Approaches considered were: standard logistic regression (ignoring the correlation between fellow eyes, treating individuals classified on the basis of their more impaired eye as the unit of analysis, or considering only right eyes); marginal logistic regression models fitted by the maximum likelihood approach of Lipsitz, Laird and Harrington or the estimating equation approach of Liang and Zeger; and conditional logistic regression models fitted by the maximum likelihood approach of Rosner or the estimating equation approach of Connolly and Liang. Taylor series approximations were used to compare conditional and marginal parameter estimates. Consideration of type I and II error rates found application of standard logistic regression to be inferior to methods that treated the eye as the unit of analysis and accounted for the correlation between fellow eyes. Among these latter approaches, none was uniformly superior to the others across the range of conditions considered.