14/n Serology tests are used to find antibodies, and they are (as all tests are) imperfect So, usually we correct for the imperfections to get a better estimate of the true number of people with antibodies
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15/n In this case, the study found that 1.8% of people in the mask group had antibodies, compared to 2.1% of people in the non-mask group But those are just the RAW figurespic.twitter.com/NtiZuV9Uml
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16/n If we use the Rogen-Gladen estimator, which is a pretty standard correction for test characteristics, we see instead that 1.59% and 1.95% of people in masks/no masks were probably infected, respectivelypic.twitter.com/d4rPZ5kJVw
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Replying to @GidMK
I may be getting it wrong but would you mind checking your calculations? I get 1.07% and 1.51% respectively using the formula above. I use 90.2% for sensitivity and 99.2% for specificity as provided in the paper. [I get 0.65% and 1.11% for the sensitivity analysis of the authors]
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Replying to @MikeDeeeeeee
So, I was slightly off in those numbers, it's actually 1.56% vs 2.09% using the main results and the sens/spec from the internal validation study rather than the manufacturer. You have to take into account that some infections were confirmed by PCRpic.twitter.com/5jpxWkUItP
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Replying to @GidMK @MikeDeeeeeee
So it's 1.8-0.2 = 1.6% for masks and 2.1-0.4 = 1.7% for non-masks, corrected that becomes 1.34% and 1.46%, add back in the PCR (for whom spec is ~100%) and you get 1.54% and 2.06%
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Replying to @GidMK @MikeDeeeeeee
Ugh, just realized it should be 2.1-0.6 for the non-masks, which changes the numbers again to 1.54% vs 1.82%. Same general problem, an estimated 1.68% infected in the study
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Replying to @GidMK
Sorry to be a pain, but can you check your Rogan-Gladen correction and/or the sensitivity/specificity numbers you use? When I use the formula, I get lower true prevalence. In the fully corrected version of yours, I get to 1.04% (masks) and 1.43% (control).
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Replying to @MikeDeeeeeee
I'm still not excluding the pre test people tho, this is just the numbers from the main analysis
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Replying to @GidMK
Me neither in the numbers above. Take mask group. AB confirmed 37 out of 2383 = 1.55%. Rogan-Gladen correction with specificity 99.2% and sensitivity 90.2%: (1.55%+99.2%-1)/(99.2%+90.2%-1) = 0.75%/89.4% = 0.84%
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Yep but I'm using the internal validation numbers for sens/spec rather than the manufacturer numbers, so 82.5% and 99.5%
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Replying to @GidMK @MikeDeeeeeee
I'm generally very mistrustful of manufacturer numbers because they are almost always higher than those found in validation studies by other people
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