How many are false positives?

[epythymy]

In terms of the recent second spike, I wonder what percentage of these are false positives. If the PCR test has a specificity of 99.9% (that is the chance of correctly identifying a negative result in a negative patient) then that would mean per 10,000 tests done there will be 10 false positive cases.

I don't know what the specificity of the test is as there is no data. I would imagine if it was 100% (highly unlikely) then the government would be bragging to us about the impossibility of false positives. I have seen estimates that range from as little as 97%

As the government is performing hundreds of thousands of tests per week at this point with no corresponding rise in deaths, could many of these be false positives?

I've just looked on the gov website and they are no longer making the number of tests carried out available.

So how many tests are being done and how many of those tests are positive?

So if 1 in 2000, say, have the virus, there would be 5 true positives and 10 false positives in the 10,000 tests? Do positive results lead to a 2nd, confirmation, test?

False negatives are far more likely though.

@HaveYouSeenMyFriendKimberley

False negatives are far more likely though.

Not if the rates of the virus are low. We know that the PCR tests sensitivity is about 80%

So if you have ten people that have the virus in a sample of 10,000 you'll get 8 true positives, 10 false positives and you'll have two people that actually have the virus but who have tested negative out there spreading it about...

"False negatives are far more likely though."

That depends on how many tests are carried out and how many cases there are out there, as well as the percentage of false negatives and false positives. Neither of which we know exactly.

Say, for the sake of easy arithmatic that the false negative and false positive rate are both 1%. If you take 2000 tests and 100 people have Covid, you would expect to have 99 true positives, 1 false negative and 20 false positives. If 200 people have Covid, you would expect 198 true positives 2 false negatives and still 20 false positives.

If you take 200,000 tests and 1000 people have Covid you would expect 990 true positives, 10 false negatives but now 2000 false positives. If 100 people have Covid you would expect to have 99 true positives, 1 false negative and still 2000 false positives.

You can play about yourself with different numbers and percentages, mine's just an example.

Thanks to pps.

I was working on the numbers I'd heard at the peak of the epidemic.

@amicissimma

"False negatives are far more likely though."

That depends on how many tests are carried out and how many cases there are out there, as well as the percentage of false negatives and false positives. Neither of which we know exactly.

Say, for the sake of easy arithmatic that the false negative and false positive rate are both 1%. If you take 2000 tests and 100 people have Covid, you would expect to have 99 true positives, 1 false negative and 20 false positives. If 200 people have Covid, you would expect 198 true positives 2 false negatives and still 20 false positives.

If you take 200,000 tests and 1000 people have Covid you would expect 990 true positives, 10 false negatives but now 2000 false positives. If 100 people have Covid you would expect to have 99 true positives, 1 false negative and still 2000 false positives.

You can play about yourself with different numbers and percentages, mine's just an example.

This is a very good example. Thanks.

@amicissimma

"False negatives are far more likely though."

That depends on how many tests are carried out and how many cases there are out there, as well as the percentage of false negatives and false positives. Neither of which we know exactly.

Say, for the sake of easy arithmatic that the false negative and false positive rate are both 1%. If you take 2000 tests and 100 people have Covid, you would expect to have 99 true positives, 1 false negative and 20 false positives. If 200 people have Covid, you would expect 198 true positives 2 false negatives and still 20 false positives.

If you take 200,000 tests and 1000 people have Covid you would expect 990 true positives, 10 false negatives but now 2000 false positives. If 100 people have Covid you would expect to have 99 true positives, 1 false negative and still 2000 false positives.

You can play about yourself with different numbers and percentages, mine's just an example.

Also, how does this fit with the 20 per 100,000 thing with regards to foreign travel and countries that are or are not added to the quarantine list, I wonder...

There was recently 6 cases of staff at St Mirren football club testing positive when they were actually negative. Don’t know if it was a duff batch of tests or whatever?

These types of tests are usually designed to give more false positives than negatives; same with pregnancy tests. False alarm is better than delayed/missed alarm.

Yes

10 false positive in 10,000 cases isn't a lot

But

If there only 10 people in 10,000 that actually have the virus it becomes far more problematic.

You do 10,000 tests
10 people have it but only 8 of these test positive. There are 2 false negatives - who can then spread the virus, if they feel well enough to go out

You also get 10 false positives. They haven't got it but they have to isolate because of the false positive