I don't think anyone disagrees that the sample has bias. On the other hand, since the majority of people have no choice but to grocery shop in person, I do not think the sample is as tilted as you imply.
And even if it were--- it's notable that it's this easy to find a subgroup with cleared infections this far above what was anticipated to be found across NY/NYC.
> “ since the majority of people have no choice but to grocery shop in person”
This is deeply flawed.
I live in NYC and have been making donations to have food delivered to elderly people since this started.
Just the other day, de Blasio announced that taxi and rideshare drivers would be paid by the city to deliver food - and city agencies would be serving as overflow dispatchers and tech support for it.
Many, many people do not have to go to the grocery store, or they have their healthy younger family member go in their place, etc.
To boot, as Gelman has written on his blog, these studies do not agree with a wide range of other studies, and in most cases the test specificity is on par with the incidence rate itself, making incidence rate estimates from _all_ of the studies very unreliable for correlated reasons, so that pooling the studies does nothing to overcome the huge uncertainty they suffer in incidence rates.
> and in most cases the test specificity is on par with the incidence rate itself,
????? We can't exclude that specificity may be 97% (it's unlikely, based on our data, but it's at the edge of the confidence interval), which is unfortunately on par with the studies returning 2-4% positives... but can't exactly explain a return of 21%. Subtract off 4% worst-case false positives from 21%, and where are you?
Since you want to appeal to authority with Gelman, this is what he said about this on his blog: "– Those California studies estimating 2% or 4% infection rate were hard to assess because of the false-positive problem: if a test has a false positive rate of 1% and you observe 1.5% positive tests, your estimate’s gonna be super noisy. But if 20% of the tests you observe are positive, then the false-positive rate is less of a big deal." ... "– In any case, the 20% number seems reasonable. It’s hard for me to imagine it’s a lot higher, and, given the number of deaths we’ve seen already, I guess it can’t be much lower either."
> so that pooling the studies does nothing to overcome the huge uncertainty they suffer in incidence rates.
The case count multiple from the serological study for New York state (and indeed, the California counties) is right in line with what's expected with a variety of statistical measures that were made without relying upon the serological data. So if you even peeked at my source you'd not be making this argument.
https://www.medrxiv.org/content/10.1101/2020.04.18.20070821v...
> First off, 3% does not sound implausible. If they said 30%, I’d be skeptical, given how everyone’s been hiding out for awhile, but 3%, sure, maybe so.
And even if it were--- it's notable that it's this easy to find a subgroup with cleared infections this far above what was anticipated to be found across NY/NYC.
And-- it's remarkably consistent with statistical estimates made through a variety of other means, e.g. https://www.medrxiv.org/content/10.1101/2020.04.18.20070821v...