Comparison of correlated correlations

We consider a problem where k highly correlated variables are available, each being a candidate for predicting a dependent variable. Only one of the k variables can be chosen as a predictor and the question is whether there are significant differences in the quality of the predictors. We review several tests derived previously and propose a method based on the bootstrap. The motivating medical problem was to predict 24 hour proteinuria by protein—creatinine ratio measured at either 08:00,12:00 or 16:00. The tests which we discuss are illustrated by this example and compared using a small Monte Carlo study.