Bayesian analysis with inaccurate rapid antigen testing for detecting someone is positive

Abstract

This paper examines how testing accuracy plays a key role in detecting someone is positive. Bayesian-theorem exploits how an inaccurate rapid antigen test with a high true-positive rate and a low false-positive rate affects the detection of the probability that someone is positive. The probability is calculated with three determinants in actual dental practices: Infection rate, true positive rate, and false positive rate. The result suggests that in a high infection rate, the false positive rate of rapid antigen tests plays a key role in detecting positive individuals. In 6.5% infection rate, 0.991 true positive rate, and 0.0005 false positive rate, the probability is 0.992 while it with 0.05 false positive rate is reduced to 0.579. The proposed Bayesian analysis can be used for future analysis with imprecise tests in other applications.