A combined superiority and non-inferiority procedure for comparing predictive values of two diagnostic tests

Positive and negative predictive values are useful to quantify the performance of medical tests, and both are often used simultaneously. Although there are several methods to test the equality of these predictive values between two medical tests, these approaches separately compare positive and negative predictive values. Therefore, we propose a testing procedure that combines the approximate likelihood ratio test defined by Tang et al. with the non-inferiority test for predictive values. The procedure can confirm that compared to an existing test, a new medical test is non-inferior in terms of both positive and negative predictive values, as well as superior regarding at least one of these values. It can make a comprehensive judgment of the performance of the new test based on both measures. A simulation study showed that the performance of the proposed testing procedure is appropriate, and the procedure is considered useful for evaluating the performance of predictive values of medical tests.