False positives do not explain the rise in confirmed cases. This article looks at what false positives are, and the recent rise of confirmed cases. In this article, testing is binary: producing positive or negative results. In reality, diagnostic analysis is not binary — retests and other checks inform clinical judgements.

There are strong claims of “no evidence” of rising prevalence of the SARS-CoV-2 virus in the UK. These claims often involve reference to false positives in imperfect tests.

This article looks at what false positives are, and the recent rise of confirmed cases.

Broadcaster Julia Hartley Brewer (Talk Radio) claimed:

Nine out of ten of positive cases of COVID-19 we’re finding in the community — when we do random testing, when anyone just puts themselves forward — will be wrong. They will not be people who’ve got coronavirus.

Sir Desmond Swayne MP (New Forest West, Conservative) made a similar point in a question:

To what extent is there a possibility that it is the exponential increase in testing itself, in identifying genuine new cases, and the very significant possibility of false positives, that is giving a distorted impression of the trajectory of the disease?

Testing is imperfect. A **false positive** is when someone who does not have the virus gets a positive test result. A **false negative** occurs when someone who has the virus receives a negative result. For example, a swab sample may not contain virus cultures — leading to a false negative result.

In this article, testing is binary: producing positive or negative results. In reality, diagnostic analysis is not binary — retests and other checks inform clinical judgements.

The **false positive rate** is the false positives as a proportion of tests on people without the virus. The **false negative rate** is false negative results as a percentage of tests on people with the virus.

In the statistical jargon, **specificity** is 100% minus the false positive rate. **Sensitivity** is 100% minus the false negative rate.

Suppose we had a population of 10,000 people. The viral prevalence was 0.1% — 10 people have the virus. Our test has a false positive rate of 1% and a false negative rate of 30%. We test everyone once. These illustrative examples use central expectations: there would be random variation too.

Among those 10 people with the virus, there are 7 true positive results and 3 false negative results. For the 9,990 uninfected people, there are 100 false positive results and 9,890 true negative results.

There are 107 positive results — of which only 7 are true positives. With a low false positive rate, very low prevalence meant most positives were false. The false positive paradox is important in the study of rare diseases.

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