Does Faire actually have COVID after testing positive with mild cold-like symptoms?
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resolved Aug 23
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She woke up with a slight sore throat and took two rapid tests in a row, both positive. Later she developed a slightly runny nose and very occasional cough.
Twist: See this market:
https://manifold.markets/dreev/do-i-have-covid-despite-testing-neg
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Auxiliary market for the preceding question: https://manifold.markets/dreev/does-a-vaccinated-person-with-mild
If we ignore the fact that Faire and I probably have the same virus and just naively apply Bayes' rule for each of us, starting with some prior of having Covid given our symptoms and using the sensitivity/specificity in the pamphlet, we get this for posterior probability as a function of prior probability (blue line is positive test, orange line is negative):
https://user-images.githubusercontent.com/9928/168338624-1df49a71-a594-44ff-abbe-d00b2290af96.png
So, like, if you got a scratchy throat and slight cough and runny nose and were like "this seems like a 20% chance I have covid" and then you took a rapid test...
* if it says positive (like for Faire) then you go from a 20% chance to a 92% chance
* if it says negative (like for me) then you go from a 20% chance to a 1.4% chance
I just took another test as well (about 24 hours later) and still negative!
My symptoms today: sore throat gone, cough worse (but still not bad), ever so slightly headachy I guess but mostly pretty normal. Runny nose pretty much better, but was only ever very minor. I'm day 2 or 3. (Tuesday I had an inkling I was getting sick, Wednesday was the first day of actual symptoms, though still very mild.)
@dreev These numbers aren't enough to derive anything solid about your position, but having reviewed https://www.lesswrong.com/posts/cEohkb9mqbc3JwSLW/how-much-should-you-update-on-a-covid-test-result, I think I invested *much* too aggressively.
@brp Ah, thanks for that link! We're using the "iHealth COVID-19 Antigen Rapid Test" which isn't mentioned there. And of course the other confusing monkey wrench in our calculation is Faire testing positive but me testing negative with the same symptoms.
@dreev I'd probably use the average stats for all rapid tests, I suspect that most rapid tests are in the same rough ballpark. I also commented on the other market about this https://manifold.markets/dreev/does-a-vaccinated-person-with-mild - you should ignore the pamphlet stats, apparently they are completely bogus because the sample for them is highly infectious individuals (chosen to make the statistics pass arbitrary regulatory standards) - that's why it comes out with such a high sensitivity rate compared to the meta-review.
@brp There were no other tests or other evidence other than a bunch of math in the linked market so I resolved it to the market probability which I think is a pretty reasonable estimate based on everything we know!