The problem of false positives from Covid-19 tests means UK is inflating its numbers – and taking wrong decisions

When seven staff at a Scottish football club tested positive for coronavirus, alarm bells went off. But really alarming was when six of those results turned out to be wrong. Such inaccurate tests are exaggerating the problem.

Last weekend, at very short notice, the UK reintroduced quarantine measures for people arriving from Spain. For those already in Spain, or for whom it was too late to postpone their trip, the decision is very inconvenient. For those who can't work at home when they return, it may mean missing out on wages for the two weeks they will have to spend in isolation when they get back. But what if the apparent rise in cases has been exaggerated by seemingly small flaws with testing?

The potential for problems was illustrated by Scottish football team St Mirren last week. The club, based in Paisley, a town just west of Glasgow, reported seven positive test results for Covid-19 among its staff. Alarm bells went off about what this might mean for the new Scottish football season. But this “cluster” was a mirage. When the seven people were re-tested using a more accurate method, just one of them was found to be Covid-positive.

In Spain, half of the reported cases have been in people who had no symptoms. We know that many people who test positive never suffer any symptoms. But what if many of these people don't have Covid-19 at all?

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If that sounds implausible, it's important to know that tests are not perfect. There are currently two kinds of tests to see if you have the disease. One kind, the molecular real-time polymerase chain reaction (RT-PCR) test, looks for genetic material from the virus. This kind seems to be very accurate, but it's expensive and time-consuming. The other kind, the antigen test, detects specific proteins on the surface of the virus. This is quicker, easier and cheaper, but it's much less accurate. In developed countries, RT-PCR testing is the norm, but poorer countries may have to make do with antigen testing.

The difficulty at the moment is that there are relatively few cases of Covid-19 in the community, but more and more testing is being done. So even if the RT-PCR test has a high “specificity” – that is, a tiny fraction of test results are false positives – the number could actually be quite significant. For example, let's say that 99.9 percent of the time, a test correctly identifies someone without the disease as negative. Just 0.1 percent of tests produce false positives.

Recently, in the UK, it was estimated that 0.04 percent of people had the virus outside of care homes and hospitals. So, if we tested 10,000 people, we should find four cases of Covid-19, on average. Of the 9,996 other people tested, in this hypothetical example, 0.1 percent who don't have the virus would also test positive – that's 9.996 – in other words, 10 people. So, even if the test is very accurate indeed, we could easily end up with four positive tests from people who really do have the virus and 10 false positives from people who don't.

For any particular individual, the chances of the test being a false positive is small. But when we look at the big picture, we could easily be fooled into thinking that there are many more cases than there really are. Indeed, with a test accuracy of 99.9 percent, if you tested a million people, none of whom actually had the disease, you would produce 1,000 positive results. And for tests with less accuracy – as with St Mirren FC – the situation could be even worse.

The UK government has now performed nearly 11 million tests. Could there be 11,000 “cases” that are simply a mistake? In turn, that means governments and other authorities might be introducing additional restrictions on people's lives that are actually unnecessary.

The problem of false positives is much less significant when the disease really is in wide circulation. It doesn't change the picture much for the period from mid-March through to the start of June. (In any event, in the UK at least, there was very little testing capacity thanks to the jaw-dropping incompetence of bodies like Public Health England.)

Let's look at the latest figures. On Sunday, July 26, for example, 142,954 tests were processed. Of these, 747 were found to be positive. If 0.1 percent of tests are false positives, we would expect 142 of those 747 positives to be false. If the test turns out to be slightly less accurate – perhaps 'only' 99.5 percent accurate (which still seems very good), then 710, almost all the reported positives, could be false.

We should also bear in mind, when trying to assess the overall situation, that there will be some false negatives. There will also be people who don't show symptoms who do have the virus and never get tested. But this understanding shows that we do need to be careful about reading too much into every small blip in the number of cases. We should be particularly sceptical about imposing new restrictions like mandatory quarantine. And if we rely solely on these tests, we could have the crazy situation where Covid-19 apparently never disappears, even when nobody has got it.

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