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Yes, higher dose/severity probably means more likelihood of detectable antibodies:


> These data show that systemic IgA and IgG production against SARS-CoV-2 develops mainly in severe COVID-19, with very high IgA levels seen in patients with severe ARDS, whereas mild disease may be associated with transient serum titers of SARS-CoV-2-specific antibodies but stimulate mucosal SARS-CoV-2-specific IgA secretion. The findings suggest four grades of antibody responses dependent on COVID-19 severity.

But this does not eliminate the possibility raised by the GP, that some people could be clearing even a severe infection with antibodies that are not specific to SARS-CoV-2, and would never get a positive result on a highly-specific test.

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