Table 1.

Comparisons of standard linear regression models, Mixed effects models and marginal models using generalized estimating equations (GEE)

	One-eye analysis	Two-eyes analysis
Characteristics of models	Standard linear regression models	Standard linear regression models	Mixed effects models	Marginal models using GEE
Assumption	Measure from an eye of a subject is independent of measure from other subjects	Measures from both eyes of a subject are independent, and also independent of measures from other subjects	Measures from both eyes of a subject are correlated, but independent of measures from other subjects	Measures from both eyes of a subject are correlated, but independent of measures from other subjects
Approach for accounting for inter-eye correlation	Not needed, as inter-eye correlation does not exist	None	By using random effects	By using “working correlation” for residuals of standard linear model
Estimation method	Least squares	Least squares	Maximum Likelihood	GEE
Estimate for mean response	Least squares means	Least squares means	Conditional on the random effects, the eye-specific outcomes are independent	Marginal, conditional only on covariates and not on other responses or random effects
Estimate of within-subject correlation	Not needed	None	Estimated together with the fixed effects	Separate from the estimate of marginal mean response
Regression coefficient estimate	Estimates change in mean value of an outcome corresponding to change in the covariate while holding constant other covariates	Estimates change in mean value of an outcome corresponding to change in the covariate while holding constant other covariates	Estimates change in expected mean value of outcome for an individual eye corresponding to change in the eye-specific covariates while holding constant other eye-specific covariates	Estimates change in mean value of all individuals corresponding to change in the covariate while holding constant other covariates
Interpretation of regression coefficient	Change in mean ocular outcome for a unit change of a covariate across all subjects	Change in mean ocular outcome for a unit change of a covariate across all subjects	Change in expected mean ocular outcome for a unit change in a covariate of a subject while keeping random effect fixed	Change in mean ocular outcome for a unit change in a covariate across all subjects
Missing data	Can handle data missing completely at random	Can handle unbalanced data and data missing completely at random	Can handle unbalanced data and missing at random	Can handle unbalanced data and missing completely at random
Advantage	Simplicity	Simplicity	Flexibility	Robustness to the mis-specification of covariance structure
Disadvantage	Loss of statistical power	Invalid inference	Easy to mis-specify the model (either random effect or fixed effect or covariance structure), lead to biased inference	May lose efficiency if covariance structure mis-specified or sample size too small
SAS procedure	PROC REG PROC GLM	PROC REG PROC GLM	RANDOM statement of PROC MIXED	PROC GENMOD
Stata procedure	REGRESS	REGRESS	XTMIXED	XTGEE