Test equality between two binary screening tests with a confirmatory procedure restricted on screen positives

In studies of screening accuracy, we may commonly encounter the data in which a confirmatory procedure is administered to only those subjects with screen positives for ethical concerns. We focus our discussion on simultaneously testing equality of sensitivity and specificity between two binary screening tests when only subjects with screen positives receive the confirmatory procedure. We develop four asymptotic test procedures and one exact test procedure. We derive sample size calculation formula for a desired power of detecting a difference at a given nominal [Formula: see text]-level. We employ Monte Carlo simulation to evaluate the performance of these test procedures and the accuracy of the sample size calculation formula developed here in a variety of situations. Finally, we use the data obtained from a study of the prostate-specific-antigen test and digital rectal examination test on 949 Black men to illustrate the practical use of these test procedures and the sample size calculation formula.