Statistical Methods for Best and Worst Eye Measurements

The focus is often on the best and worst eyes to detect early predictive and non-invasive biomarkers of diabetic retinopathy. Typically, such data have been dealt with in a case-control setting, which applies two-sample tests and ignores the correlation between the fellow eyes. Practitioners are mostly unaware that such measurements hide the labels of the fellow eyes, which rules out standard tools, such as paired t or signed-rank tests.

This report discusses the problems with such data on best and worst eye measurements, and illustrates alternative paired tests for equality of means or locations using a case-control dataset.

This report illustrates that methods which ignore the correlation between fellow eyes result in grossly conservative tests. A battery of Z-tests which consider this correlation can resolve this issue.

This finding emphasizes the importance of selecting an appropriate control group for the detection of possible markers. Further, it cites an example to show that using data from fellow eyes and adjusting for their correlation may not always be the best option, contrary to common perception.