False positives mean cases may never vanish
Britain may never hit zero Covid-19 cases, even if the virus is wiped out entirely, because of a statistical quirk in testing that throws up false positives. Testing is never 100 per cent accurate and scientists must factor in false positive and negative rates when determining infection prevalence. The Government’s Sage scientific advisory group estimates the false positive rate may be 2.3 per cent but a BMJ review puts the figure at closer to 5 per cent.
If you are starting to feel like the coronavirus pandemic will never end, then you may be correct. A statistical quirk in testing means that Britain may never hit zero cases, even if the virus is wiped out entirely. The reason lies in the large number of false positives almost certain to creep in once case numbers drop very low, yet testing remains very high.
Testing is never 100 per cent accurate, and scientists must factor in false positive and negative rates when determining infection prevalence.
The problem is, nobody knows what those rates are.
The best guess at present is that Covid-19 tests pick up around 80-85 per cent of positive cases, and around 99.9 per cent of negative cases.
It may be a lot worse than that. In June, the Government Office for Science submitted a paper to the Sage scientific advisory group estimating that the false positive rate may be 2.3 per cent, suggesting that only 97.7 negative cases would be spotted.
A recent BMJ review concluded that the false positive rate might even be as high as 5 per cent.
Why does it matter? Well, even at the most optimistic levels, false positives could be hugely skewing the testing figures.
Take current testing rates. Roughly 310,000 tests are being carried out each day and the Office for National Statistics (ONS) suggests a community infection rate of 0.05 per cent.
It means that if testing was perfect, it should pick up 155 positive cases a day and 309,854 negative cases.
Yet with the current false negative rates, we would miss 20 per cent of the positive cases – picking up just 124. And more alarmingly, we would pick up 310 false positives, giving a total of 434 reported cases, nearly three times the real positive figure.
It means the probability of a person with a positive test actually being infected would be about 28.5 per cent.
The anomaly also means that even if there was no virus in the community, we would never fall below 310 cases a day if we were testing at current levels.
Carl Henegehan, an Oxford University professor of evidencebased medicine, said: “It does matter when your prevalence is very low. At this point if you have a positive test you are more likely not to be infected than to actually have the virus. Your chance of being infected is less than 30 per cent. The ONS currently cannot estimate prevalence because it does not know what the false positive rate of PCR testing is. It looks like we’ll struggle to get out of this. We’re now in a spiral of bad data.”
Testing is currently picking up around 1,000 positive tests per day, perhaps because it is targeting hotspots, rather than the country as a whole. Yet analysis suggests hundreds of those could be false positives.
The problem is so bad, that the ONS admitted in a recent analysis of its statistics that all its positive cases could be false from April 26 to June 28.
“Even in a purely hypothetical situation that the virus is not circulating, a test specificity of 99.9 per cent would be associated with an expected number of positive tests that is approximately equal to what we observed over the entire study period,” the ONS said.
In a report to Sage on June 3, Dr Carl Mayer and Dr Kate Baker, from the Government Office for Science, warned that Britain was facing a looming false positive problem.
“When only a small proportion of people being tested have the virus, the operational false positive rate becomes very important,” they wrote. “Unless we understand the operational false positive rate of the UK’S RT-PCR testing system, we risk overestimating the Covid-19 incidence, the demand on track and trace, and the extent of asymptomatic infection.”
There are a growing number of reports of false positives from real world scenarios. On July 24, it emerged that only one of seven staff members who tested positive at St Mirren FC, Paisley, actually had the virus. A Motherwell player also was retested and found to not be infected.
‘At this point if you have a positive test you are more likely not to be infected than to actually have the virus’
Mark Woolhouse, a University of Edinburgh professor of infectious disease epidemiology, said: “This is the public health version of the Prosecutor’s Fallacy where just because a rare event has happened, such as testing positive, we think it can only have one cause. But at low prevalence we actually face a high probability that other factors can be involved, such as false positives and, given the volume of testing, we would expect some false positives to occur.
“The positive predictive value is much lower where there is not a lot of disease around and for any diagnostic test that is potentially a concern and can lead to misdiagnosis so clinicians are very concerned about false positives.”
The answer, experts say, is to carry out follow-up testing and to weigh up other factors, such as symptoms, when determining if a test is real or not.
Prof Sheila Bird, the former MRC Biostatistics Unit programme leader at Cambridge University, said: “The answer to false positives is to repeat swab-test for a sufficient random sample of positives to find out and/or to offer antibody test four weeks after the first positive swab-date.
“We learn far too little without biological samples and brief self questionnaires for random samples of those quarantined.”
Until then, Britain may never reach zero cases and be able to call an end to the first wave of this epidemic because the data will never allow us to.
It is said that the truth is a stubborn thing, while statistics are pliable. In the case of coronavirus, however, it seems the statistics are proving intractable and the truth increasingly elastic.