Impact of correlation on predictive ability of biomarkers

In this paper, we investigate how the correlation structure of independent variables affects the discrimination of risk prediction model. Using multivariate normal data and binary outcome, we prove that zero correlation among predictors is often detrimental for discrimination in a risk prediction model and negatively correlated predictors with positive effect sizes are beneficial. A very high multiple R-squared from regressing the new predictor on the old ones can also be beneficial. As a practical guide to new variable selection, we recommend to select predictors that have negative correlation with the risk score based on the existing variables. This step is easy to implement even when the number of new predictors is large. We illustrate our results by using real-life Framingham data suggesting that the conclusions hold outside of normality. The findings presented in this paper might be useful for preliminary selection of potentially important predictors, especially is situations where the number of predictors is large.