Asymptotic analysis of reliability measures for an imperfect dichotomous test

To access the reliability of a new dichotomous test and to capture the random variability of its results in the absence of a gold standard, two measures, the inconsistent acceptance probability (IAP) and inconsistent rejection probability (IRP), were introduced in the literature. In this paper, we first analyze the limiting behavior of both measures as the number of test repetitions increases and derive the corresponding accuracy estimates and rates of convergence. To overcome possible limitations of IRP and IAP, we then introduce a one-parameter family of refined reliability measures, [Formula: see text] . Such measures characterize the consistency of the results of a dichotomous test in the absence of a gold standard as the threshold for a positive aggregate test result varies. Similar to IRP and IAP, we also derive corresponding accuracy estimates and rates of convergence for [Formula: see text] as the number k of test repetitions increases. SUPPLEMENTARY INFORMATION: The online version supplementary material available at 10.1007/s00362-021-01266-9.