# Does the false positive covid-19 PCR % referred to by Surkova & Nikolayevskyy in The Lancet mean % of all tests, or % of positive tests?

The current rate of operational false-positive swab tests in the UK is unknown; preliminary estimates show it could be somewhere between 0·8% and 4·0%

My questions:

1. Are there any more accurate estimates or research done on the real false positive rate than what Surkova & Nikolayevskyy are referring to?
2. Is Surkova & Nikolayevskyy referring to a percentage of total tests done, or a percentage of positive tests?

To clarify. Let us, for the sake of example, say that the false positive rate they are talking about is 1%, and one day we test 100.000 people, and that we get 5000 positive results. Will that mean that:

A: 1% of the 100.000 are false positives, therefore there are 1000 false positives?

or that

B: 1% of the 5000 that tested positive are false positives. Therefore, 50 are false positives?

• Check the references supplied for those numbers in the article - they explain how the numbers are derived.
– bob1
Apr 22 at 10:04
• I’m voting to close this question because it requires one to read a specific external source to assess and possibly answer. This site is for general problems in biology, not for interpreting particular papers. Apr 22 at 12:43

Since it's not possible for a patient with the disease to have a false positive, we get to ignore them in calculating a false positive rate. So a false positive rate would be the number of false positives out of the total number of possible false positives (or the percentage of patients without the disease who test positive). With an ideal data set in which you knew both the test result and true infection status of each patient, you could calculate it like this: $$FPR = \frac {False\ Positives}{False\ Positives + True\ Negatives}$$ The thing is, we don't usually use this in evaluating clinical diagnostics, but rather it's complementary value, which is called "specificity" (for some reason), and is essentially true negative rate.
$$Specificity = \frac {True\ Negatives}{False\ Positives + True\ Negatives}$$