The accuracy of a medical diagnostic test is often summarized in a receiver operating characteristic (ROC) curve. This paper puts forth an interpretation for each point on the ROC curve as being a conditional probability of a test result from a random diseased subject exceeding that from a random nondiseased subject. This interpretation gives rise to new methods for making inference about ROC curves. It is shown that inference can be achieved with binary regression techniques applied to indicator variables constructed from pairs of test results, one component of the pair being from a diseased subject and the other from a nondiseased subject. Within the generalized linear model (GLM) binary regression framework, ROC curves can be estimated, and we highlight a new semiparametric estimator. Covariate effects can also be evaluated with the GLM models. The methodology is applied to a pancreatic cancer dataset where we use the regression framework to compare two different serum biomarkers. Asymptotic distribution theory is developed to facilitate inference and to provide insight into factors influencing variability of estimated model parameters.