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My question is fairly simple: There is a COVID-19 antibody test with a worst-case specificity of 98%, meaning that it yields potentially up to 2% false positives.

While that number is not bad it is problematic when the expected true positive rate is in the same range as the possible false positives: We end up with huge uncertainties.

My question is simply whether this false positive rate is random or a systematic error, i.e. whether false positive samples would be false positives again if tested a second time. Alternatively: Are there other tests which have different false positives? In both cases one could simply re-test original positives and achieve a very good combined specificity.

The background of the question is this critique by Andrew Gelman from Columbia University of the much-quoted Stanford antibody study pre-release.

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    I'm betting we don't know yet whether the error rates are random or patient-dependent. May 15 '20 at 14:29
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The short answer is: No.

Your question is a good question, but I think, in this case, that you should focus on the nature of testing in general, rather than on the specifics of this test.

Sensitivity and specificity of a test are an empiric result, with the test being held to some gold standard. Whether or not the false positives are false because of systematic error or random error doesn't matter when using the test in the sense you are using it here (generally and practically speaking).

If you were trying to improve the test itself, then it would (e.g. you were an engineer designing a better test, or a researcher designing a better trial looking at the se/sp of the test). But at the point of care, think of it as a black box: your pre test probability "multiplied by" your test (usually the likelihood ratio) is your post test probability.

To retest using the same test is nonsensical (though the explanation is beyond the scope of this question).

Of note, in some settings (HIV: elisa/western blot) you run tests in series, but you don't retest twice (elisa/elisa).

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    I don't understand your verdict "to retest using the same test is nonsensical". The reason for it is not beyond the scope of this question but at the core of it. If false positives occur because some reaction happens randomly in 2% of the cases then I can reduce false positives by testing the assumed positives again; the specificity would increase from 1-2/100 to 1-4/10000. What's wrong with this reasoning? Jan 31 at 15:16
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    This answer would be greatly improved by adding supporting references to its assertions of fact.
    – Carey Gregory
    Jan 31 at 17:23
  • I don't have an answer but it sounds to me the question refers to the precision of antibody tests, a piece of information that, at least intuitively, sounds like it can be determined.
    – Dan Burzo
    Mar 3 at 13:20

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