Informational analysis to assess diagnostic accuracy of a medical test

Suppose one has a new diagnostic system (a computed tomography or ultrasound scanner, ...), or a new diagnostic test for detecting a disease (diabetes, prostate cancer, ...). Obviously we need to compare the performance of the new diagnostic system/test with the performance of the old one. How to proceed? It is customary to execute two series of “experiments” (for example 1000 mammography examinations for detecting breast cancer), one with the old method and one with the new one. To compare the quality of the two systems, we need the involvement of the so called “standard of reference” (SR); it is a sort of perfect test, that always gives the correct answer, but that cannot be used in daily practice since it is (for example) too invasive (a painful feeding tube), or destructive (a biopsy), or very expansive, or delayed in time (a follow-up mammogram obtained at last 10 months after). The outcomes of the two tests will be compared to the reports of the SR.