> That is a problem readily solved by serial testing. False positive rate is reduced exponentially by the number of tests.
This depends. There are two ways a test might deliver the wrong result:
(A) It should have delivered the right result, but somewhere along the line something happened the wrong way.
(B) The test correctly assessed the instrumental variable, but -- in this subject -- the instrumental variable did not reflect the variable of interest in the manner that it usually does.
That is, many medical tests are not actually testing for the outcome we care about. They're testing for something that is usually related to the outcome we care about, because we don't know how to test for the real thing, or we do know how but the reliable test is far more invasive, or some such. There is a very accessible example of this kind of thing right now - you can take a sample from someone and test for the presence of covid. Or you can test for the presence of covid antibodies. Those variables are related, but different, and we care about the presence of the virus a lot more than we care about the presence of antibodies.
If the test is failing in way (B), retests will not reduce the false positive rate, because it's actually a true positive that is being misinterpreted. Retesting will only solve failures of type (A). For type (B), you'd have to apply a different kind of test, and that might not be worth it if the first test is unreliable enough. Imagine an unreliable test where the reliable followup requires a bone marrow sample.
This depends. There are two ways a test might deliver the wrong result:
(A) It should have delivered the right result, but somewhere along the line something happened the wrong way.
(B) The test correctly assessed the instrumental variable, but -- in this subject -- the instrumental variable did not reflect the variable of interest in the manner that it usually does.
That is, many medical tests are not actually testing for the outcome we care about. They're testing for something that is usually related to the outcome we care about, because we don't know how to test for the real thing, or we do know how but the reliable test is far more invasive, or some such. There is a very accessible example of this kind of thing right now - you can take a sample from someone and test for the presence of covid. Or you can test for the presence of covid antibodies. Those variables are related, but different, and we care about the presence of the virus a lot more than we care about the presence of antibodies.
If the test is failing in way (B), retests will not reduce the false positive rate, because it's actually a true positive that is being misinterpreted. Retesting will only solve failures of type (A). For type (B), you'd have to apply a different kind of test, and that might not be worth it if the first test is unreliable enough. Imagine an unreliable test where the reliable followup requires a bone marrow sample.