In the UK over the last few weeks, there have been a growing number of reports of people testing positive for COVID on a lateral flow test (LFT) but then negative on a polymerase chain reaction (PCR) test. This stands out because we’ve been led to believe that PCR tests are the “gold standard” and LFTs are crude mass-testing devices – that PCRs should pick up situations LFTs miss, not the other way around.
A number of explanations have been put forward. Some have suggested a faulty batch of LFTs could be causing people to test positive when they don’t have COVID. Others have hypothesised a new variant could be circulating that isn’t detected by the standard PCR test. There have also been well-publicised stories of children faking a positive LFT consequence using the acidic similarities of soft drinks. These spoofers would afterward test negative on a follow-up PCR test.
The increase in these events also coincides approximately with the return of schools and big rises in the number of situations in children. These positive-then-negative sequences of tests might be something to do with the way children are being tested. Alternatively, vaccination may have changed where exactly in the body virus grows best, meaning different swabbing techniques used for different tests types are capturing more or less of the virus.
But there’s also a possible mathematical explanation, given neither test is 100% reliable. It’s all down to how often these tests give false positives and negatives.
Specificity and sensitivity
Despite their reputation for inaccuracy, if you test positive on an LFT, the overwhelming likelihood is that you have COVID. As the diagram below shows, upwards of 96% (7,000/7,297) of people testing positive on LFTs at the moment will be true positives.
This is largely because LFTs are very “specific” – they don’t give many false positives. Public Health England (now the UK Health Security Agency) has estimated that for every 10,000 LFTs taken by genuinely COVID-negative people, there will be fewer than three false positives (a specificity of 99.97%).
These can add up though. In a population of 1 million people where 1% have COVID, 297 people will have LFTs tell them they have the virus when they don’t. And because PCR tests are (almost) 100% specific, when they follow their LFT with one of these, they’ll then definitely get a negative consequence. This could explain some of what’s been recently reported.
But this is only one half of the accuracy question. LFTs have a attained their bad reputation because of their low “sensitivity” – meaning they have a high rate of false negatives. Estimates vary, but perhaps around 30% of the time when someone has COVID, an LFT won’t pick this up. PCR tests are much better, with a false negative rate of only 5%.
But this 5% false negative rate can also rule to a positive-then-negative testing ordern. As the diagram above shows, with the current prevalence of COVID, 7,000 of our 1 million people will correctly be flagged as having COVID by an LFT. Of these, 5% – so 350 people – will then get an incorrect false negative from their “confirmatory” PCR test.
It’s important to remember that because of their high specificity, you can be pretty confident that a positive LFT consequence is genuine – in our form above, for every 7,000 that are right, only 297 are wrong. And already if your positive consequence is followed by a negative PCR test, it’s currently more likely that you have COVID than don’t (350 vs 297). And if you’re symptomatic, the chance of being infected if receiving a positive LFT followed by a negative PCR is already higher.
Unexpected results draw more attention
There are a few further things to observe here. The first is that the rate of infected people testing positive on an LFT and then negative on a PCR test is around 3.5% (350 out of 10,000). This is perhaps higher than we might expect, given the bad rep of the LFT and the “gold standard” position of PCR tests. This may explain why reports of this positive-negative testing ordern seem to be swelling in number.
When something that we believe to be very doubtful happens to us, then we tend to try to make sense of our experience by sharing it with others. Reports of positive LFTs followed by negative PCR tests have been flooding Twitter in recent days and making national news, which in turn has caused more people to come forward. It’s possible that part of the increase in reports of this perceived-to-be-uncommon event are truly the consequence of this positive feedback loop.
A second thing to observe is that how well (or poorly) LFTs and PCRs perform overall and relative to each other depends on how common COVID is in the community. In the calculations above, I’ve been conservative and assumed that 1% of people have COVID – the Office for National Statistics estimates that currently it’s truly nearly 1.5% of people.
But if this falls, everything changes. The percentage of people testing positive on LFTs who are true positives will drop and at the same time, the number of positive LFTs followed by negative PCRs will also drop. If the prevalence of COVID increases, the opposite would happen: we’ll see already more of these “surprising” testing sequences than currently.
It’s important to emphasise that there’s no strong evidence however for any of the hypotheses progressive in this article. But understanding whether there’s something truly wrong or whether this is just a mathematical artefact has meaningful ramifications – for testing, contact tracing and the monitoring of the UK’s current COVID situation.
The UK Health Security Agency’s (UKHSA) chief medical adviser, Susan Hopkins, has noted that the organisation is looking into the issue. The UKHSA acknowledges that it doesn’t have an explanation as however but is investigating because it has “not experienced this before to such a degree”.
The hope is that the UKHSA will be able to carryout a methodic investigation and put the mystery of the conflicting results to bed.
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