There are a lot of well-intended and well-written critiques of the Santa Clara Co. serology study but at some point it's not that complicated. A test that *could* have a false positive rate of up to ~2-3% isn't saying very much if it detects 2-3% positives in some population.
On the flip side, this is much less of a concern in areas with a greater underlying incidence in the population. If an area has been 15% infected, then a potential false positive rate of 1% or 2% or 3% isn't going to matter as much. So I'd look at those studies instead.
As a related thought: I think people underestimate how much more prevalent COVID-19 is in some areas than others. NYC has around *30 times* more deaths per capita than Santa Clara Co., Calif.
Deaths are not necessarily a perfect way to estimate infections (the IFR may vary from place to place for many reasons) but they're at least decently good. So it could *easily* be the case that say 30% of the population had COVID-19 in NYC but only 1.2% did in Santa Clara.
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