Notes on testing non-inferiority under the partial verification design with a confirmatory procedure limited to screen positives

When a new test with fewer invasions or less expenses to administer than the traditional test is developed, we may be interested in testing whether the former is non-inferior to the latter with respect to test accuracy. We define non-inferiority via both the odds ratio (OR) of correctly identifying a case and the OR of correctly identifying a non-case between two tests under comparison. We focus our discussion on testing the non-inferiority of a new screening test to a traditional screening test when a confirmatory procedure is performed only on patients with screen positives. On the basis of well-established methods for paired-sample data, we derive an asymptotic test procedure and an exact test procedure with respect to the two ORs defined here. Using Monte Carlo simulation, we evaluate the performance of these test procedures in a variety of situations. We note that the test procedures proposed here can also be applicable if we are interested in testing non-inferiority with respect to the ratio of sensitivities and the ratio of specificities. We discuss interval estimation of these ORs and sample size calculation based on the asymptotic test procedure considered here. We use the data taken from a study of the prostate-specific-antigen (PSA) test and the digital rectal examination (DRE) test to illustrate the practical use of these test procedures, interval estimators and sample size calculation formula.