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The gist of it

Though there are many types of Covid tests, I think none have 100% sensitivity or specificity. What I would like to know is if the event of getting, e.g., a false negative on two tests are independent events.

Details

Suppose I take two samples from the same person in rapid succession (not on consecutive days but 1 minute apart) and run the same type of test on each sample. Is it possible to have one test come back negative and the other positive, assuming the samples are not contaminated and the tests were run properly?

Basically I would like to know if the randomness occurs in the biology of the person, at sampling, or in the biochemical analysis phase of testing.

Perhaps the answer may vary depending on the type of test. (I am also curious about tests for other diseases, but I guess that would make the question too broad.)

Prior research

I read the CDC's Testing Overview, and several questions on this SE, e.g.,
Do having multiple COVID tests decrease the chance of a false negative?
How accurate are coronavirus tests?
What is the expected false positives/negatives for COVID-19 tests?
and also at Biology
What's happening in the “C” and “T” stripes of a covid test kit?

but found no answers. (There was a vague statement in a comment but no reference or explanation was given.)

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    Re: "I would like to know if the randomness occurs in the biology of the person, at sampling, or in the biochemical analysis phase of testing." The answers are yes, yes and yes, but what matters are the relative magnitudes, which I don't know, but will vary from test type to test type, variant to variant, and person to person. It's worth looking at how a given false positive/negative can happen molecularly. Also, don't exclude contamination on high-amplification tests like PCR.
    – Armand
    Aug 8, 2021 at 19:01
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    Very doubtful you'll be able to find a quantified answer to this. In fact, try finding a quantified answer for a broader question: what are the main sources of Covid testing errors... The best you can probably find are qualitative discussions.
    – Fizz
    Aug 9, 2021 at 2:38
  • The stuff/data that is somewhat easier to find is that e.g. in the UK up to a fifth of people with symptoms tested negative throughout. assets.publishing.service.gov.uk/government/uploads/system/…
    – Fizz
    Aug 9, 2021 at 2:49
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    @Fizz the "up to a fifth of people...tested negative throughout" was a modeled result given certain disease prevalence assumptions, not actual observed data (Kucirka et al 2020).
    – Armand
    Aug 9, 2021 at 11:42
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    "Are they independent" has an easy trivial answer: no, certainly not. How independent they are is another question altogether and is quite difficult to answer. Some types of errors are definitely correlated. Others less so.
    – Bryan Krause ♦
    Aug 9, 2021 at 17:12

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