The Impact of Repeating COVID-19 Rapid Antigen Tests on Prevalence Boundary Performance and Missed Diagnoses

A prevalence boundary (PB) marks the point in prevalence in which the false omission rate, R(FO) = FN/(TN + FN), exceeds the tolerance limit for missed diagnoses. The objectives were to mathematically analyze rapid antigen test (RAgT) performance, determine why PBs are breeched, and evaluate the merits of testing three times over five days, now required by the US Food and Drug Administration for asymptomatic persons. Equations were derived to compare test performance patterns, calculate PBs, and perform recursive computations. An independent July 2023 FDA–NIH–university–commercial evaluation of RAgTs provided performance data used in theoretical calculations. Tiered sensitivity/specificity comprise the following: tier (1) 90%, 95%; tier (2) 95%, 97.5%; and tier (3) 100%, ≥99%. Repeating a T2 test improves the PB from 44.6% to 95.2% (R(FO) 5%). In the FDA–NIH-university–commercial evaluation, RAgTs generated a sensitivity of 34.4%, which improved to 55.3% when repeated, and then improved to 68.5% with the third test. With R(FO) = 5%, PBs are 7.37/10.46/14.22%, respectively. PB analysis suggests that RAgTs should achieve a clinically proven sensitivity of 91.0–91.4%. When prevalence exceeds PBs, missed diagnoses can perpetuate virus transmission. Repeating low-sensitivity RAgTs delays diagnosis. In homes, high-risk settings, and hotspots, PB breaches may prolong contagion, defeat mitigation, facilitate new variants, and transform outbreaks into endemic disease. Molecular diagnostics can help avoid these potential vicious cycles.