But this is only one half of the accuracy question. LFTs have a gained 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 lead to a positive-then-negative testing sequence. As the diagram above shows, with the current prevalence of Covid-19, 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 result is genuine – in our model above, for every 7,000 that are right, only 297 are wrong. And even if your positive result 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 even higher.
Unexpected results draw more attention
There are a few further things to note 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” status of PCR tests. This may explain why reports of this positive-negative testing sequence seem to be swelling in number.
When something that we believe to be very unlikely 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-unusual event are actually the result of this positive feedback loop.
A second thing to note is that how well (or poorly) LFTs and PCRs perform overall and relative to each other depends on how prevalent 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 actually 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 plunge. If the prevalence of Covid increases, the opposite would happen: we’ll see even more of these “surprising” testing sequences than currently.
It’s important to emphasise that there’s no strong evidence yet for any of the hypotheses advanced in this article. But understanding whether there’s something truly wrong or whether this is just a mathematical artefact has significant 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 yet 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 systematic investigation and put the mystery of the conflicting results to bed.