Stuff like this[1] ought to have some impact on the "real world" results, right?
> false positives have a linear cost.
That's a strong assumption. Assuming constant testing happens in an environment of quarantining of the person who tested positive and their contacts and possibly their contacts (which is the goal of the whole trace & quarantine fever of 2020), it is hard to argue that the costs of false positives do is linear in the number of false positives. They are hard to observe and record because they are mostly in foregone productive activities and negative impacts on mental health, but that does not make them go away.
> Stuff like this[1] ought to have some impact on the "real world" results, right?
The real world results, as measured, showed a 0.3% false positive rate. If your [1] has a measurable effect, it's included in that 0.3%.
> > false positives have a linear cost.
> That's a strong assumption. Assuming constant testing happens in an environment of quarantining of the person who tested positive and their contacts and possibly their contacts (which is the goal of the whole trace & quarantine fever of 2020), it is hard to argue that the costs of false positives do is linear in the number of false positives.
It's not hard at all. It literally follows from the problem setup. If one person has 4 contacts, and each of those contacts has 4 more, and you quarantine all of them, then that's 17 people quarantined from a single positive test. That "17" is a linear constant. There's no feedback mechanism: one positive test leads to 17 quarantines only, and you're done. It's linear. It might have a higher constant factor than you personally think is justified, but that's a very different question.
> The real world results, as measured, showed a 0.3% false positive rate.
Try as I did, I can't find a source for this claim. The best I could find was[1] which seems to indicate a 1.1% false positive rate for people without symptoms (keep in mind my argument is against widespread, unconditional testing). PCR results in the real world seem to vary a lot, but a 3% false positive rate seems appropriate.
> 17 people quarantined from a single positive test. That "17" is a linear constant.
That is a faulty argument. You are assuming total costs of a trace/quarantine regime are linear in the number of people prevented from participating in society and productive activities.
The specificity of the test was recorded as 99.68% - the
overall false positive rate was 0.32%, although this was
lowered to 0.06% in a lab setting.
> PCR results in the real world seem to vary a lot, but a 3% false positive rate seems appropriate.
Not to me. Again, first page of google: https://www.ons.gov.uk/peoplepopulationandcommunity/healthan... puts an _upper_ bound on the PCR false positive rate of 0.08%, and that would require all the positives in that survey to have been false. And that's a real-world result across 208,730 samples.
But given the existence of LFTs and how cheap and immediate they are, I don't think anyone's talking about population-wide PCR testing anyway.
> You are assuming total costs of a trace/quarantine regime are linear in the number of people prevented from participating in society and productive activities.
For the proportion of the population removed at any given time? As close to linear as makes no difference, yes. Is your argument that there's a quadratic factor in network effects? You haven't explained what your cost model actually is. For your argument to work you need those costs to follow an exponential curve, and there's just no mechanism for that to happen.
> false positives have a linear cost.
That's a strong assumption. Assuming constant testing happens in an environment of quarantining of the person who tested positive and their contacts and possibly their contacts (which is the goal of the whole trace & quarantine fever of 2020), it is hard to argue that the costs of false positives do is linear in the number of false positives. They are hard to observe and record because they are mostly in foregone productive activities and negative impacts on mental health, but that does not make them go away.
[1]: https://www.theguardian.com/world/2021/jul/02/uk-pupils-oran...