Cross-reactivity is an issue in the ELISA test (the actual antibody test).
But they validated their results with a second step, the "pseudotype neutralisation assay". This test is highly specific for SARS-CoV-2 - as I understand it, they essentially introduce the virus to the hypothetically immune blood samples and then test that it is indeed neutralised by antibodies.
So, I think this Scottish serology test is pretty robust and accounts for these issues with cross-reactivity and specificity of the testing. In addition - they used a control sample from December 2019 none of which tested positive.
0 out of 100 controls and 6 out of 500 gives a very wide confidence interval. You could easily get those numbers with 1% false positives and no true positives in either group. Is your prior for false positives low enough to rule that out?
They did two independent assays so I would think the false positives rate should be far below 1% - certainly the authors seem to think so.
Secondly if they were false positives, I would expect them to be randomly distributed. Not concentrated in the affluent capital city, and not solely in the second cohort with none in the early march cohort (as you would predict if exponential growth is occurring).
Why even test 100 controls if your conclusion relies on a prior that false-positives are much less than 1%? I think that shows the author's are worried about false-positives and have failed to rule them out sufficiently.
But they validated their results with a second step, the "pseudotype neutralisation assay". This test is highly specific for SARS-CoV-2 - as I understand it, they essentially introduce the virus to the hypothetically immune blood samples and then test that it is indeed neutralised by antibodies.
So, I think this Scottish serology test is pretty robust and accounts for these issues with cross-reactivity and specificity of the testing. In addition - they used a control sample from December 2019 none of which tested positive.