Chances of False Positive on PCR test (Covid 19)

[neilparker62]

TL;DR Summary

what are the chances of a false positive

I recently had an incident in which a person visited my office and a few days later informed me he had tested positive for Covid. He had been healthy but took the test as required for any passenger boarding an airline. He later went for another test (the next day in fact) and that was negative. All the same I decided I should get myself tested and tested positive. Being similarly asymptomatic I also decided to go for a second test and once again it came back negative.

This is extremely concerning because it begs the question which of the two tests is one to believe. I remain completely healthy so presume the second result was correct but could I perhaps be an asymptomatic Covid carrier ?

In principle what is the probability of a false positive on a PCR test ?

 

[Vanadium 50]

This is why you never take an even number of tests.

Your question is actually underspecified, even if answered. Here's why: suppose the test is 90% accurate (in both directions, for simplicity). Now suppose 10% of the population actually has Covid. If you test positive, what's the probability you have Covid? Not 90%. It's about 50-50.

 

[pinball1970]

This is why you never take an even number of tests.

Your question is actually underspecified, even if answered. Here's why: suppose the test is 90% accurate (in both directions, for simplicity). Now suppose 10% of the population actually has Covid. If you test positive, what's the probability you have Covid? Not 90%. It's about 50-50.

Ive tried working this and can't get to 50%. what did you do?

Start with the probability of having Covid = 10%?

Then 90% probability of something to give you 40% - the something is 44 to add to the 10?

How did you get 44?

what am I missing? @Vanadium 50

 

[atyy]

In a PCR test, the viral fragments undergo successive cycles of multiplication until there are enough fragments to reach some detection threshold (roughly speaking). So the fewer cycles to reach the detection threshold (cycle threshold), the higher the level of viral fragments.

It could be that the first positive test had a high cycle threshold, meaning there was less viral fragments. And in the next test that was negative, the cycle threshold was much higher, consistent with even less viral fragments.

So the first test could be a "true positive" and the second test might be a "true negative" (obviously this is not an all or nothing thing), as would be if you got infected 10 days ago, and the viral load was decreasing from the first test on the 9th day to the second test on the 10th day. You can think of reasonable variations on this scenario.

Another possibility is that the first test was a "false negative" and the second one might be a "true negative" if you were infected months ago, and these are viral fragments that don't correspond to having any infectious virus at all.

https://www.thelancet.com/journals/lanres/article/PIIS2213-2600(20)30453-7/fulltext
"RT-PCR assays in the UK have analytical sensitivity and specificity of greater than 95%, but no single gold standard assay exists."

Sensitivity is the true positive rate.
Specificity is the true negative rate.
So the false positive rate is (1 - specificity).

More discussion in https://assets.publishing.service.g...9_Impact_of_false_positives_and_negatives.pdf
"It is possible that a proportion of infections that we currently view as asymptomatic may in fact be due to these false positives."

 

[Vanadium 50]

Ive tried working this and can't get to 50%. what did you do?

	Have Covid	Do not Have Covid
Test Positive	9%	9%	18%
Test Negative	1%	81%	82%
	10%	90%

If you test positive, you are in the 18%. Of that 18%, half, or 9%, have Covid.

 

[neilparker62]

This is why you never take an even number of tests.

Your question is actually underspecified, even if answered. Here's why: suppose the test is 90% accurate (in both directions, for simplicity). Now suppose 10% of the population actually has Covid. If you test positive, what's the probability you have Covid? Not 90%. It's about 50-50.

Thanks for this and your explanation in a later post. Does it mean that if you start out asymptomatic (pre-disposed towards 'do not have Covid' group) and get a + result, you can still consider yourself 50/50 in which case the next day you could easily test - as appears to have happened in the 2 cases I describe above. Would it make sense that if you are already ill and get tested + , the chances of a reversal , the next day are considerably less since you are pre-disposed towards the 'have Covid' group.

 

[Vanadium 50]

Does it mean

What it means is that a 90% accurate test doesn't mean that if it is positive you have a 90% chance of having the disease. That's all. The probability of A given B is not the same as the probability of B given A.