In addition to the other answers, there can also be issues of similar chemicals reacting. If you’re doing a urine test on an athlete for a performance in hanging drug, and you’re using a test that will turn red if the drug is present, it’s possible the athlete is on a rare medication that just so happens to react with the test in the same way. (I don’t know if that situation specifically has ever happened, but that’s the sort of thing that I’m talking about)
Even without things going wrong, no test is perfect. There is a chance of getting a false positive or false negative. This is because diagnostic tests use inferential statistics. The basic idea is that you must decide how much doubt you want to have when you make a choice based on limited information. You may have heard something like “95%” certainty or “alpha of 5%.” This literally is a choice to set false positive rate at 5%, and is the most common.
Then, the nature of the test then determines in concert with this arbitrary choice the chance of a false negative. Typically, medical tests are optimized to get false negative chances nearly 0, at the cost of having a high false positive rate. This is okay. We would rather a test catch everyone who is sick so we can treat them. Unfortunately, that means we have tests popping off scaring us. But we know that no test alone should be considered as proof, because of false positives.
Never had this discussion been so relevant as in the COVID era. Everyone treats the Covid tests as an absolute, which is frankly just not true. Symptoms at least should be considered. Yet cause of death has been determined strictly by a single test result, and on top of that — federal funding allocated on those results.
This is not a terrible system — but we should be aware of the limits of testing. No system is perfect. This is a crisis. Something is better than nothing. But it’s also not gospel.
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