If a health worker gets tested weekly when swab test has like x% false positive chance, wouldn’t the person almost certainly gets falsely tested once?
In: Biology
Yeah, the chance of at least one false positive increases, and approaches 100% as you take more tests. That doesn’t mean that taking more tests is bad, because the ramifications of a false positive are that you miss 2 weeks of work, while the ramification of a missed case is guaranteed spread and potential death.
No, and it’s a probability problem not specific to virus testing.
Say the test has a 10% chance of giving a false positive. That does not mean that if you issue 10 tests you’ll certainly get 1 false positive (10%*10=100%). It means each test has a 10% chance of a false positive. You could have none, you could have 10.
It depends on the specificity of the test.
Tests like that don’t really have a “false positive rate” – there will be a certain number of false positives for every true negative (specificity), but the % of positives overall that are false also depends on the number of true positives, which depends on how prevalent the disease is in the population being tested.
If the “population” just consists of 1 person being tested over and over, but they’re never actually infected, the false positive rate will be either 0% or 100%, because there will never be any true positives. But if the specificity is really high (a low rate of false positives to true negatives), it may not really matter in a practical sense.
If the specificity is 95%, then 5/100 would be false positives, so if you get tested every week for a year (52 times), there’s a 93% chance of at least one false positive.
But if the specificity is 99%, the odds of a false positive after 52 tests drops to 41%. And if it’s 99.9% specific, then it’s only 5%.
The actual specificity of PCR tests is estimated to be about 98-99%.
Dependant on how many test they take and the value of x. If x=90% false positive over 10 tests, then it is highly likely they get a false. If x=.1% over 100 tests its easily possible that they never have one.
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