[BostonCard]

...much higher than the 0.5% the Santa Clara paper indicates (2 positives out of 371, though this was by the manufacturer; they also validated with 30 samples at Stanford and had no false positives).

I will repeat what I said earlier... one of the failures of the that paper and  its "2 positives out of 371" is that they screwed that up too.  The paper is a little convoluted.  It appears they claim the manufacturer indicates 2 positives out of 371 for IgM and (unstated, other than "100%") 0 positives for IgG.  The manufacturer's site (dated 2/27/2020, and as archived on April 22) indicates 3 positives out of 371 for IgM and 2 positives out of 371 for IgG.  The study's definition of positive was that either antibody was found ("The total number of positive cases by either IgG or IgM in our unadjusted sample was 50"). The paper didn't take that into account (using 100% for IgM). 

Updating with CovidTestingProject.org numbers
IgM:   Mfgr: 3/371  Stanford 0/30   CTP.org 2/108    Total: 5/509   99.018%
IgG:   Mfgr: 2/371  Stanford 0/30   CTP.org 1/108     Total  3/509  99.411%
If you consider the two tests as independent, that suggests a FP rate of   1.57%.
On 3330 tests * 1.57% FP rate =  52 false positives.
Bingo!  Practically right on what they measured.

One of the problems of proving what you expected is that you likely will revisit any calculation that isn't what you expect but not necessarily all the ones that give the "right" answer.  Clearly they didn't review this calculation.  But why would they, since it gives the number they expect?

Just like their testing on only 30 samples on their own.  If they had expected a 0.5% FP rate, 30 seems too low to measure it as anything but 0.  (Indeed, I wonder if they had gotten 1 false positive in their 30, maybe that would have messed up their numbers enough that they would have tested more.)

You can't consider the two tests independent, though.

BC

[BostonCard]

...much higher than the 0.5% the Santa Clara paper indicates (2 positives out of 371, though this was by the manufacturer; they also validated with 30 samples at Stanford and had no false positives).

I will repeat what I said earlier... one of the failures of the that paper and  its "2 positives out of 371" is that they screwed that up too.  The paper is a little convoluted.  It appears they claim the manufacturer indicates 2 positives out of 371 for IgM and (unstated, other than "100%") 0 positives for IgG.  The manufacturer's site (dated 2/27/2020, and as archived on April 22) indicates 3 positives out of 371 for IgM and 2 positives out of 371 for IgG.  The study's definition of positive was that either antibody was found ("The total number of positive cases by either IgG or IgM in our unadjusted sample was 50"). The paper didn't take that into account (using 100% for IgM). 

Updating with CovidTestingProject.org numbers
IgM:   Mfgr: 3/371  Stanford 0/30   CTP.org 2/108    Total: 5/509   99.018%
IgG:   Mfgr: 2/371  Stanford 0/30   CTP.org 1/108     Total  3/509  99.411%
If you consider the two tests as independent, that suggests a FP rate of   1.57%.
On 3330 tests * 1.57% FP rate =  52 false positives.
Bingo!  Practically right on what they measured.

One of the problems of proving what you expected is that you likely will revisit any calculation that isn't what you expect but not necessarily all the ones that give the "right" answer.  Clearly they didn't review this calculation.  But why would they, since it gives the number they expect?

Just like their testing on only 30 samples on their own.  If they had expected a 0.5% FP rate, 30 seems too low to measure it as anything but 0.  (Indeed, I wonder if they had gotten 1 false positive in their 30, maybe that would have messed up their numbers enough that they would have tested more.)

You can't consider the two tests independent, though.

BC