In the UK, there have been an increasing number of reports in the past few weeks of people who tested positive for COVID on a lateral flow test (LFT) but then negative on a polymerase chain reaction (PCR) test. What makes this stand out is that we believe that PCR testing is the “gold standard” and LFTs are crude mass testing equipment – that PCRs should pick up cases that LFTs miss, not the other way around.
A number of explanations have been made. Some have suggested that a faulty batch of LFTs could result in people testing positive if they don’t have COVID. Others have hypothesized that a new variant might be floating around the is not recognized by the standard PCR test. There were also well known Stories of children who use the acidic properties of soft drinks to simulate a positive LFT result. These spoofers would then turn out negative in a follow-up PCR test.
The rise in these events roughly coincides with the return of schools and the sharp rise in the number of cases among children. These positive-then-negative test sequences could have something to do with the way children are tested. Alternatively, vaccination may have changed where exactly in the body the virus grows best, meaning that different swab techniques used for different types of tests will capture more or less of the virus.
But there is also a possible mathematical explanation as none of the tests are 100% reliable. It all depends on how often these tests give false positives and negatives.
Specificity and sensitivity
Despite their reputation for inaccuracy, the overwhelming chance you have COVID if you test positive on an LFT. As the chart below shows, currently more than 96% (7,000 / 7,297) of people who test positive for LFTs will really be positive.
This is mainly because LFTs are very “Specific” – they don’t give a lot of false positives. Public Health England (now UK Health Security Agency) has estimated that for every 10,000 LFTs taken by people who are really COVID negative, fewer than three false positive results (a specificity of 99.97%) occur.
However, these can add up. In a population of 1 million people, 1% of whom have COVID, 297 people will be told by LFTs that they have the virus when they don’t. And because PCR tests are (almost) 100% specific, if you follow your LFT with one of these tests you will definitely get a negative result. This could explain some of what was recently reported.
But that’s only half the accuracy issue. LFTs get their bad reputation because of their low rating “Sensitivity” – which means that they have a high rate of false negative results. Estimates vary, but maybe about 30% of the time someone has COVID, an LFT won’t pick it up. PCR tests are much better with a false negative rate of only 5%.
But that 5% false-negative rate can also lead to a positive-then-negative test sequence. As the graph above shows, given the current prevalence of COVID, 7,000 of our 1 million people are correctly flagged as having COVID by an LFT. Of these, 5% – i.e. 350 people – receive a false false negative result in their “confirmatory” PCR test.
It’s important to remember that because of their high specificity, you can be fairly certain that a positive LFT result is real – in our model above, out of 7,000 correct ones, only 297 are false. And even if your positive result is followed by a negative PCR test, it is currently more likely that you have COVID than not (350 vs. 297). And if you’re symptomatic, the chance of infection is even higher if you get a positive LFT followed by a negative PCR.
Unexpected results attract more attention
There are a few more things to consider here. The first is that the rate of infected people who test 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 LFT’s bad reputation and the “gold standard” status of PCR testing. This could explain why the number of reports of this positive-negative test sequence seems to be increasing.
When something happens to us that we think is very unlikely, we tend to understand our experience by sharing it with others. Reports of positive LFTs followed by negative PCR tests have been made
in the last few days and make national newswhich in turn has led to more people getting in touch. It is possible that some of the increase in reports of this perceived unusual event was actually due to this positive feedback loop.
A second thing to keep in mind is that the performance of LFTs and PCRs overall and in relation to each other depends on how widespread COVID is in the community. In the above calculations, I was conservative and assumed 1% of people have COVID – the Office of National Statistics Estimates that currently it is actually almost 1.5% of people.
But when this falls, everything changes. The percentage of people who test positive for LFTs and who are really positive will decrease, and at the same time the number of positive LFTs followed by negative PCRs will decrease as well. If the prevalence of COVID increases, the opposite would happen: We will see even more of these “surprising” test sequences than we are currently seeing.
It is important to emphasize that none of the hypotheses presented in this article is backed by solid evidence. But understanding if something is really wrong or if it’s just a math artifact has a huge impact – for testing, contact tracing and monitoring the current COVID situation in the UK.
UKHSA’s Senior Medical Advisor Susan Hopkins has noticed that the organization investigates the problem. UKHSA admits that it has no explanation yet but is investigating because it “has not seen it to this extent”.
It is hoped that the UKHSA can conduct a systematic investigation and unravel the mystery of the conflicting results.