I have fallen mildly ill, as have my wife and son. So far we don’t have a positive Covid-19 test, and everyone is maximally vaccinated, but given the timing the obvious conclusions do seem likely. Wish me well, and hopefully Christmas will not be cancelled and I can keep the posts mostly going. I do have winter break to help me out.
(This question is for everyone.)
Suppose you, the reader, get sick. And you get a fast, negative, covid test.
What are the odds you have covid?
How do you find out if you do?*
*If the rapid test had some probability of success, like 70%, then if you took two test you might figure 1-(1-.7)^2 = 1-.3^2 = 1-.09 = 01% you have covid. But are the rapid tests independent?**
**Even if they were, how does probability a test comes back positive vary over time if you have covid?
How much/what evidence do you need to figure you have covid even if a test comes back negative?
VOI, another test still makes sense (even if only to ease your nerves). However, suppose you knew in advance you wouldn’t be symptomatic. How often/when should you take a test for other’s sake when you have nothing at stake yourself?
Definitely not fully independent. This paper has some data on the correlation between false-negative % and viral load:
in all groups, CareStart sensitivity followed Ct value distribution, with 96.3% sensitivity observed in all participants with Ct ≤25 and 79.6% in those with Ct ≤30. Although false-negative CareStart results were largely confined to those perhaps least likely to transmit SARS-CoV-2, the sensitivity of the CareStart test by Ct threshold cutoff was lower than observed in our recent study of the Abbott BinaxNOW in the same testing site [6] (99.3% with Ct ≤25, 95.8% with ≤30, and 81.2% with ≤35).
*If the rapid test had some probability of success, like 70%, then if you took two test you might figure 1-(1-.7)^2 = 1-.3^2 = 1-.09 = 01% you have covid. But are the rapid tests independent?**
You need to start with a prior for this calculation. This paper also discusses independence of tests. And I think you meant to write 91%.
I believe your calculation was 70% chance of not having it given a negative test, so if you have two independent negative tests, that would be 91% chance of not having it (1 − 0.09), or 9% chance of having it. But in reality, false negatives are very common. And you need to start with a prior probability to update from. From the paper I referenced, if you have some symptoms and were exposed, the prior probability of having COVID might be 91%, but after one negative result, you are still at 77-80% probability of having COVID. However, if your symptoms don’t match the common ones for COVID or if you don’t know you were exposed, then the prior probability of having COVID is much lower to start with. Then a negative test result would update downward slightly from that prior.
(This question is for everyone.)
Suppose you, the reader, get sick. And you get a fast, negative, covid test.
What are the odds you have covid?
How do you find out if you do?*
*If the rapid test had some probability of success, like 70%, then if you took two test you might figure 1-(1-.7)^2 = 1-.3^2 = 1-.09 = 01% you have covid. But are the rapid tests independent?**
**Even if they were, how does probability a test comes back positive vary over time if you have covid?
How much/what evidence do you need to figure you have covid even if a test comes back negative?
VOI, another test still makes sense (even if only to ease your nerves). However, suppose you knew in advance you wouldn’t be symptomatic. How often/when should you take a test for other’s sake when you have nothing at stake yourself?
Definitely not fully independent. This paper has some data on the correlation between false-negative % and viral load:
(Higher Ct values indicate lower viral loads.)
You need to start with a prior for this calculation. This paper also discusses independence of tests. And I think you meant to write 91%.
Why would there be a 91% change you have covid if two (statistically) independent tests say you DON’T have it?
I believe your calculation was 70% chance of not having it given a negative test, so if you have two independent negative tests, that would be 91% chance of not having it (1 − 0.09), or 9% chance of having it. But in reality, false negatives are very common. And you need to start with a prior probability to update from. From the paper I referenced, if you have some symptoms and were exposed, the prior probability of having COVID might be 91%, but after one negative result, you are still at 77-80% probability of having COVID. However, if your symptoms don’t match the common ones for COVID or if you don’t know you were exposed, then the prior probability of having COVID is much lower to start with. Then a negative test result would update downward slightly from that prior.
I wonder if they’re more independent when you alternate brands