Does my friend have covid? (mixed test results, close contact with covid-positive)
37%
chance
Jun 18
M\$393 bet
Jack is betting NO at 37%
I updated my spreadsheet with a bit more refined version of my previous analysis: https://docs.google.com/spreadsheets/d/1o95SAKOTFgIqrE-Y7nwZrBsqvJzyeJtMHS4QAJw0hus/edit#gid=0 I tried to adjust for correlation between tests a bit and figure out how much we can infer from one person's results about the other's - I think those are the biggest question marks in my stats at the moment. My current estimate is about 15%.
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Jack is betting NO at 37%
I will leave this open for a bit longer while I think more about the stats and see if anyone else has input, but planning to resolve within the next few days.
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Jack sold M\$5 of NO
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Jack is betting NO at 40%
Update: Bob's PCR test from Friday also came back negative. So Alice and Bob both got a positive PCR on Wednesday from one lab (bioiq), and a negative PCR on Friday from another lab (county testing site, not sure what lab it was). Trying to find out what proportion of people test positive vs negative on PCR tests after recovery was kind of difficult because most of the reporting on the topic just says that you _may_ continue testing positive for a month, not how likely it is. But eventually I found this meta-review https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7609379/ - see figure 4, which shows percentage of positive PCR tests vs days since symptoms start. Look at the upper respiratory tract curve (that includes nose and throat, so this should be most of the tests we're used to). The figure shows that it drops to 50% positive at about 15 days from symptoms start. (Most of the studies here did not look at asymptomatic infections.) Also, note that it's not the case that tests consistently go from negative to positive some time after infection to negative some time after recovery. Tests can give intermittent positive/negative results. Another study https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7956402/ that analyzed a population of 20k Covid patients in Wuhan who had a positive PCR test followed by 2 consecutive negatives at least 24 hours apart (which was the criteria for hospital discharge) found that 12% had a positive PCR test afterwards. So getting a negative and then staying negative is most common but re-positives are not rare.
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If Alice's viral load was initially very small, isn't it possible she just got over COVID very quickly? How are you planning to resolve this market if Alice continues testing negative and never has symptoms?
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Jack is betting NO at 38%
@fortenforge My impression was that PCRs generally kept returning positive for about a month. But I'm not sure if that's still true with very low viral loads - although my impression was also that they were tuned to be very sensitive. I plan to resolve to the best estimate I can come up with based on discussion here. We're also waiting for Bob's second PCR test which should be helpful.
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Jack is betting YES at 77%
Update: negative PCR test from yesterday. This is quite surprising and causes me to update down substantially. So that makes 1 positive PCR (on day 6 from the close contact), 1 negative PCR (day 8), 2 negative rapid NAATs, and 1 negative rapid antigen. If we just looked at those tests I think it would be very likely a false positive. If we also look at Bob's positive PCR test result, it seems less clear. I'm not familiar with the research on interpreting inconsistent test results, but I think PCR tests are estimated around 95% sensitivity and 99% specificity and I updated my rough estimates above assuming the test results are mostly independent to get to a overall estimate of 15% (see spreadsheet)
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Austin bought M\$10 of YES
Anecdotally, the rapid tests take a few days to show results. Not sure about Cue, they might be more accurate, but I had been symptomatic and testing daily for about 3 days before my first positive: https://manifold.markets/Austin/do-i-have-covid
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Jack is betting YES at 77%
@Austin Yeah I agree, the rough timeline I've seen is that PCR starts returning positive at ~5 days and rapid antigen at ~6 days. Here the positive PCR was at 6 days and the latest negative Cue was at 7 days. So I don't think the Cue negative is a matter of it being too early.
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Jack is betting YES at 77%
Oh and symptoms starting at ~2-3 days for vaxxed people. So that matches perfectly with your timeline.
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