Just curious about something, and I’m terrible with conditional probabilities.
Given all that we know about the virus tests and the antibody tests, what’s the probability that someone has the virus and tests negative and then gets the antibody test and tests negative again?
This would seem to be pretty low, but statistics are funny.
I ask because I know someone who really had the symptoms (102 degree fever, difficulty breathing, no congestion) but tested negative when symptomatic and has now tested negative for the antibodies. She probably never had it (what other diseases even have that particular set of symptoms?), but I’m just curious about the probability that she had it and got unlucky with both tests.
I’m afraid I don’t have any hard data, but I did have a discussion with ICU RN daughter yesterday, where she said the COVID-19 infection test has a very high incidence of false-negatives, but seems pretty reliable on positives. I’m sure there are a lot of variances in play (quality of swabbing, perhaps different brands of tests, etc).
Right. My understanding is that there’s a 15-30% chance of a false negative on the virus test, and something pretty high (maybe also 15%?) for the antibody test.
Let’s say it’s 20% for the virus test and 15% for the antibody test – what are the chances that someone who actually has/had it to test negative for both? Do we have to take into account the percentage of the population that has it?
No, what you need to know is whether the test results are statistically independent, or if they are not you need the conditional probabilities.
At one extreme: if false negatives are a function of the biology, the way the infection manifests in a particular person, then a false negative for virus could almost always be accompanied by a false negative for antibody. Then the probability for two negatives might not be much lower than the probability for one negative, ~15%.
At the other extreme: if it’s nothing to do with the biology, but entirely due to technical issues with sampling and testing, and the two tests are conducted entirely separately, then the results could be completely independent. In that case, the probability of two negatives is the product of the two probabilites, 3%.
So the bounds are 3%-15%, we’d need more data to narrow it down.
If the two numbers (virus load and antibody titer) are completely independent, or the two test errors are completely independent (mixed up swabs and mixed up blood tests), then 15% of 20% is 3%. If they actually measure the same thing (very low antibody titer following a very low viral load), then it’s the smaller of the two errors: 15%
Nobody really understands the errors of the virus tests (Should we be doing blood tests? Do nose and throat swabs measure the same thing?), or the errors of the antibody tests (How long do antibodies persist? How long does it take to develop antibodies? Does everybody even get antibodies?),
… and the inter-dependence of the two unknowns is known unknown
