Aasthaa Bansal
When an existing marker does not have sufficient diagnostic accuracy on its own, new markers are sought with the goal of yielding a combination with better performance. Understanding the properties that a new marker should have in order to improve performance would help biomarker development. Assuming the joint distribution of baseline and new markers is bivariate normal in cases and controls, we quantify the improvement in the ROC curve as a function of the correlations and the relative performance of the new marker. The ROC is typically improved substantially only when the new marker performs well on its own and is weakly correlated with the existing marker. Surprisingly, in some realistic settings a very highly correlated marker can yield substantial improvement. We also show that combining markers incorrectly can lead to decrements in performance.