In the field of medical diagnostic testing, the receiver operating characteristics(ROC) curve has long been used as a standard statistical tool to assess the accuracy of tests that yield continuous results. Although previous research in this area focused mostly on estimating the ROC curve, recently it has been recognized that the accuracy of a given test may fluctuate depending on certain ... [Show full abstract] factors, which motivates modelling covariate effects on the ROC curve. Comparing the corresponding ROC curves between two or more tests is a special case of covariate effect modelling. In this manuscript, we introduce a linear regression framework to model covariate effect on the ROC curve. We assumes the ROC curve takes a specific parametric form for each covariate level and the covariate effect reflects on the parameters of the curves. The new method provides an unified approach for the ROC curve analysis and it is intuitive and easy to apply. Two real data sets are used to illustrate the new approach.