Comparison of predictive values with paired samples

Positive predictive value and negative predictive value are two widely used parameters to assess the clinical usefulness of a medical diagnostic test. When there are two diagnostic tests, it is recommendable to make a comparative assessment of the values of these two parameters after applying the two tests to the same subjects (paired samples). The objective is then to make individual or global inferences about the difference or the ratio of the predictive value of the two diagnostic tests. These inferences are usually based on complex and not very intuitive expressions, some of which have subsequently been reformulated. We define the two properties of symmetry which any inference method must verify - symmetry in diagnoses and symmetry in the tests -, we propose new inference methods, and we define them with simple expressions. All of the methods are compared with each other, selecting the optimal method: (a) to obtain a confidence interval for the difference or ratio; (b) to perform an individual homogeneity test of the two predictive values; and (c) to carry out a global homogeneity test of the two predictive values.