Assessment of the Fidelity of the SARS-Cov-2 Rapid Antigen Test Using Bayes’ Equation

Introduction: Several publications have expressed concerns regarding the fidelity of the results obtained from the SARS-Cov-2 rapid antigen (or ‘lateral flow’) test, most notably relating to the rather high missed detection rate — given as 20% or more. Objectives: Concentrating on such a headline failure rate of this test is misplaced. It is proposed to make use of Bayes’ equation in conjunction with the full set of relevant probabilities to obtain a more comprehensive and reassuring view — at least from the perspective of the user of the test. Method: Bayes’ equation in conditional probability has been combined with the background rate of SARS-Cov-2 (Covid) in the general population, plus two characteristic failure probabilities associated with the lateral flow test, to obtain a probability that a user of the test has Covid, given that he or she has tested positive. It is asserted that it is this quantity that is of most relevance from a user’s point of view. Results: The lateral flow test can be considered satisfactorily ‘reliable’ from a user’s perspective over background rates of SARS-Cov-2 in the general population between about 1% and 25%. Bayes’ equation can also be used to demonstrate the significant benefits obtainable, in probabilistic terms, from a second independent lateral flow test or from successive independent tests. Conclusions: Bayes’ equation enables a systematic and comprehensive analysis of the probabilities associated with the lateral flow test, thus enhancing the understanding of test results. This equation is not confined to assessing just this test — the same analytical approach is applicable to any situation in which one has a background rate and two or more test error modes.