Right, at least for sensitivity because generally more antibodies are available at certain time after exposure. As for specificity, a blood sample that is guaranteed to be free of the specific antibodies is needed, and the actual time/year (way before the pandemic) when the sample was collected would matter here; in this case, makes more sense that a specific number for specificity should be used. At least that's how I see it.
Everything I've said is my opinion. Nobody should trade based on what I've said.
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