Prevalence Threshold, Screening Curves and Screening Probability Square Plane S

In this chapter, we describe the properties of the main screening curves, notably the receiver-operating characteristic curve (ROC) and the PPV-prevalence curve, \(\rho (\phi )\) , both of which are depicted in the screening probability square plane S, a Cartesian plane of dimensions \(1\times 1\) . Using classical differential geometry, we derive the radius of maximum curvature R of \(\rho (\phi )\) , and determine the prevalence point of maximum curvature of the PPV-prevalence curve, which is henceforth referred to as the “prevalence threshold”. We introduce the fundamental theorem of screening as the unifying equation between the positive predictive value and the screening coefficient.