Suppose XD represents the gene expression profile for a typical cancer specimen (ie, g = 1), and XD is the corresponding profile for a randomly chosen benign specimen. Note that in our situation, the diagnostic test is the linear combination β0TX. One relevant quantity is the false positive rate based on a cutoff c, defined to be FP(c)=P(β0TX>c|g=0). Similarly, the true positive rate is TP(c)=P(β0TX>c|g=1). The true and false positive rates can be summarized by the receiver operating characteristic (ROC) curve, which is a graphical presentation of {FP(c), TP(c) : −∞ < c < ∞}. The ROC curve shows the tradeoff between increasing true and false positive rates. Tests that are have {FP(c),TP(c)} values close to (0,1) indicate perfect discriminators, while those with {FP(c),TP(c)} values close to the 45° line in the (0, 1) × (0, 1) plane are tests that are unable to discriminate between the diseased and healthy populations. Examples of ideal and noninformative ROC curves are given in Figures 1a and 1b.
