In the UK over the last few weeks, there have been a growing number of reports of people who test positive for COVID in a lateral flow test (LFT) but then negative in a polymerase chain reaction (PCR) test. This stands because we believe that PCR tests are the “gold standard” and LFTs are mass test devices – that PCRs should pick up cases that LFTs don’t capture, not the other way around.
Delivered a number of explanations. Some have suggested a defective batch of LFTs that could cause people to test positive when they don’t have COVID. Others assume a new variation may be circulating there was not noticed by standard PCR testing. There is also publicized properly stories of children faking a positive LFT result using the acidic properties of softdrinks. These spoofers will subsequently test negative in a follow-up PCR test.
The increase in these incidents also coincided with the repatriation of schools and a large increase in the number of cases among children. The positive-after-negative sequences of these tests may be related to the method of testing in children. Alternatively, the vaccination may have changed where exactly the body virus grows, meaning different swab techniques used for different types of testing get more or less of the virus.
But there is also a potential mathematical explanation, given either test is 100% reliable. It’s all up to how often these tests give false positives and negatives.
Specific knowledge and sensitivity
Despite their reputation for inaccuracy, if you test positive with an LFT, the high probability that you have COVID. As shown in the diagram below, upwards of 96% (7,000 / 7,297) of people who are positive on LFTs today will be truly positive.
This is mainly because LFTs are very “Specific” – they don’t give a lot of false positives. Public Health England (now the UK Health Security Agency) already has estimated that for every 10,000 LFTs taken by true COVID-negative people, there will be fewer than three false positives (a specificity of 99.97%).
They can add even. In a population of 1 million people where 1% have COVID, 297 people have LFTs that tell them they have the virus when they don’t. And because PCR tests are (almost) 100% certain, when they observe their LFT on one of them, they will definitely get a negative result. This may explain some of what has been reported recently.
But this is only half the question of accuracy. LFTs got their bad reputation because of their low “sensitivity” – means they have a high rate of false negatives. Estimates vary, but probably around 30% of the time when someone has COVID, an LFT won’t pick it up. PCR tests were better, with a false negative rate of only 5%.
But this 5% false negative rate can also lead to a positive-then-negative test sequence. As shown in the diagram above, in the current prevalence of COVID, 7,000 out of our 1 million people will be properly flagged as having the COVID of an LFT. Of these, 5% – thus 350 people – will get a false false negative from their “confirmation” PCR test.
It’s important to note that because of their high specificity, you can be quite confident that a positive LFT result is real – in our model above, for every 7,000 corrects, only 297 are incorrect. And even if your positive result is followed by a negative PCR test, you are currently more likely to have COVID than none (350 vs. 297). And if you introduce yourself, the chance of becoming infected if receiving a positive LFT followed by a negative PCR is even higher.
Unexpected results are getting more attention
There are a few more things to keep in mind here. The first is that the rate of infected people who are positive on an LFT and then negative on a PCR test is at 3.5% (350 out of 10,000). Perhaps this is higher than we might expect, given the bad rep of LFT and the “gold standard” status of PCR tests. This may explain why reports of this positive negative test sequence seem to be bloated in number.
When something we believe is unlikely to happen to us, then we tend to try to make sense of our experience by sharing it with others. Reports of positive LFT followed by negative PCR tests were flooding Twitter in recent days and making national news, which in turn caused many people to move forward. Possibly part of the increase in reports of this perceived unusual event is the real result of this positive feedback loop.
The second thing to keep in mind is how well (or poorly) LFTs and PCRs perform in general and relative to each other depends on how prevalent COVID is in the community. In the above calculations, I became conservative and assumed that 1% of people have COVID – the Office for National Statistics estimate that at present it is almost 1.5% of the people.
But if it falls, everything changes. The percentage of people who test positive on LFTs that are truly positive will fall and at the same time, the number of LFT positives followed by negative PCRs will also decline. If the prevalence of COVID increases, the opposite will happen: we will see more of these “surprising” test sequences than at present.
It is important to emphasize that there is not yet strong evidence for any of the assumptions advanced in this article. But understanding whether something is really wrong or whether it is just a mathematical artefact has significant implications – for testing, contact tracking and monitoring the current UK COVID situation.
The UK Health Security Agency’s (UKHSA) chief medical adviser, Susan Hopkins, has mentioned that the organization is looking at the issue. The UKHSA acknowledges that it has no explanation yet but is investigating because “it has never been experienced before to such a degree”.
The hope is that the UKHSA will be able to conduct a systematic investigation and lay to bed the mystery of the conflicting results.