NPV i1 an1 1 a n2

In comparing these formulas to Table 5, these are the ö-diagonal terms divided by the sum of the corresponding column. Both will have the value 1

in a noise-free system. For more than two outcomes, these can be generalized to D-predictive values (DPV), where DPV = P[Si\Di] and n q.

This is the probability that the clinician would use if considering only one diagnosis against all others. More commonly, a clinician is considering a number of diagnoses simultaneously; this is called the differential diagnosis. A list of probabilities would be appropriate for this situation. Since only one D is chosen in the information framework, a probability for each potential signal given D can be created to arrange the differential diagnosis in order of decreasing probability. The D-differential value can be defined as DjDV = P[S;\Dj] and calculated as n q.

which is just proportion for each cell in the D j column for each S. These are the numbers that a clinician would use to order the differential diagnosis according to probability. Therefore, the context for the utility of a biomarker really depends on how it will be used.

The ROC (receiver operating characteristic) curve is a common way to evaluate biomarkers. It combines specificity and sensitivity. Figure 3 illustrates how the ROC curve is constructed. These represent the probability density p(y) for a continuous Gaussian biomarker y. S1 has mean 0 and standard deviation 1 in all cases. For cases A and D, S2 has mean 4 and variance 1; for cases B and C, the means are 0.01 and 2, respectively. The vertical black line represents the partition determined by some optimality rule: The y values to the left of the line represent R1 , and the values to the right, R2 , If the signal observed is on the left side (D1), the signal is called S1; if on the right side (D2), it is called S2. The total channel noise (N) is given by

These are the off-diagonal terms in Table 5. One optimization rule is to choose the cut point z so that N is minimized. This leads to the relationship n1 p1 (z) = 1 n p2 (z)

which can be rewritten in a simpler form 