Many people are reporting testing positive on LFD tests, but then negative on PCR.

Here’s a quick thread to explain why this might be happening and why this diagram (where I’ve considered possible test results for 1,000,000 people at 1% prevalence) might be helpful.
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First, if you get a positive lateral flow result, the overwhelming likelihood is that you have covid.
Compare the 7000 true positives identified by LDF to the 297 false positives.
7000/7297 ~ 96% chance of genuinely being positive.
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Second, even if you test negative on a follow up PCR you are still more likely than not to be positive.
Compare the 350 true positives with a +ve/-ve test sequence to the 297 false positives with a +ve/-ve sequence.
Still a 54% chance of being genuinely positive.
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Thirdly the +ve LFD/-ve PCR test sequence is not as unlikely as you might think.
Although we think of PCR as “gold standard” they may give (upwards of) 5% false negatives.
This means 3.5% of positive people (350/10,000) might get the +ve/-ve sequence.
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So the +ve/-ve sequence is not as unusual as we might think.
Perhaps some of the increase in reporting of this is down to a positive feedback loop: the more people come forwards/the more media coverage, the more people share their similar “unusual” stories and so on.
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That said, other explanations might include a faulty batch of LFTs, a new variant that isn’t detected by the standard PCR test, people faking a positive LFT result or changes in test accuracy due to vaccination or demographic infected.
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This is not a definitive list of possibilities.

It does seem that something odd is going on in the South West, which is more than just a mathematical anomaly though.

We need to find out what’s happening because false negative PCR results have knock on consequences.
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For the calculations above, I’ve used 1% prevalence, which is an underestimate (ONS suggest 1.4%). It’s also much higher in some age groups (7% in yr 7-11s) so the +ve/-ve sequence will be even more likely.
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Sources/justifications for the figures I’ve used (including tests sensitivities and specificities) and a bit more nuance can be found in this @ConversationUK article.

ENDS/
https://theconversation.com/covid-why-are-people-testing-positive-on-lateral-flow-tests-then-negative-on-pcr-169502