Question for medical science folks. I realize that having a messy cohort of participants is normal, but with the estimates that we’ve only positively identified

Question for medical science folks. I realize that having a messy cohort of participants is normal, but with the estimates that we’ve only positively identified 10-20% of COVID cases, and with antibody tests having a wide margin of error, what are the chances that a non-trivial portion of the “control” group were also post-infection?