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Actual question

What would typically cause antigen tests to give a false positive or false negative and would these causes be typically independent (if we run the test twice it won't automatically fail twice) or would such tests typically fail in the same manner and thus consistently give the same result for the same person? Or is this completely different from antigen test to antigen test and nothing can be said in general?

I hope this question is narrow enough, and I totally accept an answer of 'nothing can be said in general'.

Background

Abbott’s BinaxNOW was recently approved by the FDA. These are the false positives and false negatives rates given by Abbott:

Abbott says that the test correctly diagnoses a coronavirus infection 97.1 percent of the time, and correctly returns a negative result 98.5 percent of the time.

Therefore, the probability that one has the disease given that they test positive is - if I didn't make a naive mistake in my application of Bayes theorem and assuming 1% of the population currently has it - only 39%. This obviously is... pretty bad.

The useful thing about Bayes theorem though is that we can also calculate the chance of actually having Covid19 if we take the test twice assuming that both trials are independent (97%).

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    $\begingroup$ Your interpretation with Bayes therom is likely on point, and this is a problem with broad testing of populations with low underlying rates. It's easy to find scenarios where are test is returning more false positives than true positives, even with what seems like a good specificity values around 99%. My intuition tells me that this might not be independent, and that retesting a false positive would yield similar result, since a false positive is likely the result of non-specific binding to similar antibody. But they say that immunology is the place where intuition goes to die. $\endgroup$ – MikeyC Aug 27 at 14:25
  • $\begingroup$ I don't know enough immunology to answer the question properly, but here's a cool article that goes through the numbers and talks about when it's useful vs. when it's harmful (blogs.sciencemag.org/pipeline/archives/2020/08/27/…) $\endgroup$ – Sol Aug 29 at 6:18

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