Using data from both eyes of participants: Evaluating the power and Type-I error rates of common approaches to ocular...

The aim of this study is to evaluate and quantify model performance for commonly used statistical approaches when using data from both eyes of participants. These models highlight different methods of accounting for interocular correlation.

We simulated a continuous outcome variable, a predictor variable measured per-eye (two correlated values per subject - termed bivariate), and a predictor measured once per subject (termed univariate). Both the outcome and the bivariate predictor shared the same correlation level in all simulations. Correlations were varied 0-0.9 in 0.1 steps, with sample sizes of 50, 100, and 150. Two thousand datasets were simulated under each correlation-sample size combination. The datasets were modeled using single-eye, averaged-eye, and assumed-independent two-eye approaches within linear regression, along with a mixed effects model and a generalized estimating equation (GEE).

Mixed effects models, modeling one eye per subject, and averaging eyes within subjects all controlled Type-I error at 0.05 across simulated conditions. GEEs slightly inflated Type-I error, especially with smaller sample sizes. Modeling both eyes independently inflated Type-I error as high as 0.194 in high correlation scenarios. This inflation increased with increasing correlation. For univariate predictors, GEEs, mixed effects modeling and averaging eyes within subjects attained similar power across scenarios. Single-eye modeling resulted in lower power, particularly in low correlation scenarios. For bivariate predictors, mixed effects modeling and GEEs yielded greater power than single-eye or averaged-eye modeling across scenarios.

Mixed effects models and GEEs out-perform other approaches when the predictor of interest is bivariate and correlated, assuming correlations are similar for the predictor and outcome. For univariate predictors, averaging the outcome across eyes within each subject performs similarly to mixed effects modeling. Treating correlated measurements as independent (such as when using data from both eyes without averaging or factored into a model) inflates Type-I error rates and yields inappropriately high power, especially as correlation increases; this modeling approach leads to inference errors and should be avoided.