I thought about this for a while, and I think the entailment you point out is correct and we can’t be sure the numbers turn out as in my example.
But also, I think I got myself confused when writing the originally cited passage. I was thinking about how there will be a smaller absolute number of false-positive deaths than the absolute number of false-positive symptomatic cases, because there are fewer death generally. That doesn’t require the false-positive rates to be different to be true.
Also thinking about it, the mechanisms by which the false-positive rate would be lower on severe outcomes that I’d been thinking of don’t obviously hold. It’s probably more like if someone had a false-positive test and then had pneumonia symptoms, it’d be mistaken for Covid, and the rate of that happening is only dependent on the regular Covid test false-positive rate.
I thought about this for a while, and I think the entailment you point out is correct and we can’t be sure the numbers turn out as in my example.
But also, I think I got myself confused when writing the originally cited passage. I was thinking about how there will be a smaller absolute number of false-positive deaths than the absolute number of false-positive symptomatic cases, because there are fewer death generally. That doesn’t require the false-positive rates to be different to be true.
Also thinking about it, the mechanisms by which the false-positive rate would be lower on severe outcomes that I’d been thinking of don’t obviously hold. It’s probably more like if someone had a false-positive test and then had pneumonia symptoms, it’d be mistaken for Covid, and the rate of that happening is only dependent on the regular Covid test false-positive rate.