Constructing an ROC Curve to Assess a Treatment-Predictive Continuous Biomarker

This paper presents the idea of an ROC curve, which quantifies the discriminatory potential of a continuous biomarker for treatment selection when the outcome is continuous. The analysis assumes data from a randomized parallel group design. We use non-parametric density estimators to construct an ROC curve based on the probabilities that a (non-)responder, defined by better (worse) response to treatment as opposed to control, in the treatment group has a biomarker value above a value c. Our non-parametric approach comes close to the true AUC in a simulation study based on a normal distribution. Application to a real data set shows that despite a significant interaction term in a proportional hazards model, a biomarker may not be helpful for treatment decisions. Our proof-of-principle study opens the door to further developments and generalizations.