Positive and negative predictive values of a diagnostic test are key clinically relevant measures of test accuracy. Surprisingly, statistical methods for comparing tests with regard to these parameters have not been available for the most common study design in which each test is applied to each study individual. In this paper, we propose a statistic for comparing the predictive values of two diagnostic tests using this paired study design. The proposed statistic is a score statistic derived from a marginal regression model and bears some relation to McNemar's statistic. As McNemar's statistic can be used to compare sensitivities and specificities of diagnostic tests, parameters that condition on disease status, our statistic can be considered as an analog of McNemar's test for the problem of comparing predictive values, parameters that condition on test outcome. We report on the results of a simulation study designed to examine the properties of this test under a variety of conditions. The method is illustrated with data from a study of methods for diagnosis of coronary artery disease.