Claims that Covid-19 testing gives too many false positive results have led some to believe they shouldn’t be relied on to shape responses to the pandemic.
This view began on social media and blog sites and has gained traction in recent weeks.
It is not a sensible view to hold.
The argument stems from a genuine issue with medical tests about the risk of false positive results. It’s certainly true that some tests which show as positive may be false positives. It’s equally true that some of the negative results will be false negatives.
This Insight examines what can affect test results and explain why we can’t always apply general mathematic principles to specific situations (like Covid-19).
How to assess the accuracy of tests (in general)
For a test to pick up a high proportion of genuine cases, it depends on a combination of the sensitivity and specificity of the test and the population being tested. SAGE has suggested the current Covid-19 test has 99% specificity and sensitivity.
Sensitivity looks at how well a test can identify true positive cases.
A test that is very sensitive will flag up almost everyone who has a disease and won’t give you many false negative results.
For example, if a Covid-19 test has a sensitivity of 90% it will correctly identify 90 people in every hundred who genuinely have Covid-19 but will give a negative result (a false negative) for 10 people who do actually have the disease.
Specificity looks at a test’s ability to correctly give a negative result for people who really don’t have the disease.
So, a Covid-19 test with 90% specificity will correctly tell 90 people in every hundred that they don’t have Covid-19 but will tell 10 others that they have Covid-19 when they don’t.
The population being tested
Even with a highly sensitive and specific test, the likelihood of it returning some false results depends on the population being tested. This is known as the pre-test probability, meaning the likelihood that the person being tested does have the disease.
For Covid-19 tests, this likelihood depends on whether someone has symptoms of Covid-19, has been in contact with someone who has Covid-19, or if there are high levels of infection circulating in the community. If most of the people being tested have symptoms, then the pre-test probability will be high.
What’s a realistic rate of false positives?
Although we can’t give an exact figure for the number of false positives, there’s no evidence to suggest it’s high enough to make test results useless.
The main problem with claims about huge amounts of false positives is that they’re based on the assumption we know the prevalence of Covid-19 in the population being tested. It assumes that because Office for National Statistics surveillance shows that 0.1% of the population is infected with Covid-19, this can be used as pre-test probability for Covid-19 tests.
However, most testing is undertaken with symptomatic people or those who have been in contact with someone who has tested positive. Therefore, the pre-test probability is likely to be high as these are not people randomly selected from the population.
Even if we are very cautious and assume a relatively low pre-test probability of just 1% and apply this to the estimated 99% specificity and sensitivity of Covid-19 tests highlighted by SAGE, we would reach a stage where false positives and true positives are roughly even.
Anything above 1% would result in true positives outweighing the number of false positives. The table below illustrates this using an example of 10,000 tests. The final example shown uses a 10% pre-test probability rate and this results in the number of false positives being relatively small (90) in comparison with true positives (990).
You can use the interactive BMJ Covid Test Calculator to plug in a few figures and see how different scenarios affect the chance of getting meaningful results.
Positive results on the rise
Another important point to emphasise is that although more people are being tested now, in recent weeks the number of positive results has gone up faster than the number of tests performed. There’s no evidence that the testing process has radically changed, so the recent rise in positive results is likely to be because the number of real cases of Covid-19 has increased.
On balance, it seems the idea that test results can and should shape our response to the pandemic is a wise one.
About the author: Rachael Harker is a statistician in the House of Commons library specialising in health and social care.