Is the Second Independent Diagnostic Test in Medical Diagnosis Useful

We consider usefulness of the second diagnostic test in medical diagnosis from the point of view of positive predictive value (PPV) and negative predictive value (NPV). We assume in this paper that medical diagnosis is given by the result of a single diagnostic test or group discussions of experts. We call the process the diagnostic test and consider the situation where an individual has chance to undergo two diagnostic tests. When the second diagnostic test is undertaken, two decision rules, Rule 1 and Rule 2, may be considered. Rule 1 is judge positive if the both tests are positive and negative otherwise. Rule 2 is judge negative if both tests are negative and positive otherwise. The test is called reasonable if, and only if it selects diseased person with higher probability than it does non-diseased persons. It is shown that when the first and second tests are reasonable, usefulness of the second test depends on one’s priority on PPV or NPV and whether one takes Rule 1 or Rule 2.