Assume a test is 90% specific and sensitive, and the disease it is testing has a 1% incidence.
You test 1000 people - 10 actually have the disease.
Of these 10 the test will correctly pick up 9 (true positives) and miss 1 (false negative). 1/5

But it will also say that 100 have the disease when they don’t (false positives).

So out of 109 positive results only 9 actually have it.

This is the problem with mass testing for low incidence disease with a low specificity test. 2/5

For @NHSEngland hospitals this is an issue. It doesn’t really matter that much that you’ve missed the 1 person who has it but tested negative. Assuming they are asymptomatic we didn’t know about them before so we’ve not really lost anything. 3/5

It does matter that you’ve now got 100 staff (and their families) that have to isolate because they have wrongly been told they have it.

The lower the specificity the worse the problem gets.

The problem is also psychological for staff 4/5

Repeated false positives (proven by repeat PCR testing) will destroy trust in the test and may alter the behaviour of those being tested.

Please correct my maths if I am wrong - I’ve tried hard to understand it but always hated sens/spec stuff! 5/5