Most tests you carry out on anyone else will be negative, so even if you think there’s an 80-90% chance the patient is COVID-19 positive, you still get more information from running those tests than the lower symptomatic people.
Also, it does change all sorts of decisions. It probably changes what precautions the healthcare workers need to take, and it lets you tell the person’s family to self-isolate. Otherwise the husband is in critical condition, and the wife might be a week behind, so she’s in the waiting room making everyone sick.
Hm, can you say more about information? I believe you should get the most direct information (in the information-theoretic sense) out of running tests where the outcome is most in doubt (i.e. where your prior is approximately 50%, although I think this might budge a bit depending on the FP/FN rates of the test if they are different.) You also get information about their contacts—if their contacts have a lower-than-50% base rate of exposure, then it seems like you get more of that “secondary information” from a positive than from a negative. (I’m not too confident about that, but certainly at worst it’s equal, right?)
Most tests you carry out on anyone else will be negative, so even if you think there’s an 80-90% chance the patient is COVID-19 positive, you still get more information from running those tests than the lower symptomatic people.
Also, it does change all sorts of decisions. It probably changes what precautions the healthcare workers need to take, and it lets you tell the person’s family to self-isolate. Otherwise the husband is in critical condition, and the wife might be a week behind, so she’s in the waiting room making everyone sick.
Hm, can you say more about information? I believe you should get the most direct information (in the information-theoretic sense) out of running tests where the outcome is most in doubt (i.e. where your prior is approximately 50%, although I think this might budge a bit depending on the FP/FN rates of the test if they are different.) You also get information about their contacts—if their contacts have a lower-than-50% base rate of exposure, then it seems like you get more of that “secondary information” from a positive than from a negative. (I’m not too confident about that, but certainly at worst it’s equal, right?)