Impact of Correlation on Predictive Ability of a Biomarker

• Activity Number: 643
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Olga Demler*+ and Michael Pencina and Ralph D'Agostino, Sr.
• Companies: BWH and Boston University and Boston University
• Keywords: risk prediction ; correlation ; biomarker selection ; discrimination ; logistic regression ; linear discriminant analysis

Abstract

It is often assumed that a good new predictor should be uncorrelated with variables already in the model. We prove the opposite. We focus on risk-prediction models with a binary outcome and continuous multivariate normal predictors. First, we show that if effect size is positive then negative correlation between new variable and the old risk score is always beneficial for discrimination, whereas zero correlation is detrimental. This result holds rigorously for linear discriminant analysis and asymptotically for logistic regression. Second, we show that new predictor that regresses well on old predictors (has high multiple R-squared) improves quality of discrimination. As a practical guide to new variable selection, we recommend to calculate correlation matrix of the old risk score with all possible new predictors and select those that have negative correlation. We also recommend regressing each new predictor with the ones already in the model. New predictors that have high multiple R-square can improve quality of discrimination. These results are illustrated using real-life Framingham data suggesting that the same conclusion holds outside normality assumption.