Assessing the accuracy of an imperfect dichotomous test in a multiple testing context

In this paper we address the situation where a well-established, but invasive, expensive or time-consuming diagnostic test may be replaced by multiple repetitions of a different diagnostic test which is known to be imperfect but less invasive or expensive. With an imperfect diagnostic test repeated several times on the same patient, we first introduce the sensitivity and specificity of that test for any given number of test repetitions. We also derive the corresponding asymptotic limits for sensitivity and specificity as the number n of test repetitions increases. Given those limits, we then derive sharp upper bounds for the differences between the sensitivity and specificity, obtained for a given number n of test repetitions, and the corresponding asymptotic limit. Specifically, we provide exact rates for the convergence of the empirical sensitivities and specificities. Our analysis is motivated, among other things, by the current discussion on rapid SARS-CoV-2 testing where the real-time polymerase chain reaction (RT-PCR) test may be replaced with a sequence of rapid lateral-flow antigen tests.