It is well known that test accuracy depends on many factors, including differences in readers and differences in various patient characteristics. For example, the age of the patient, their gender, the stage of the disease, and the therapy received, all have a bearing on the measured test accuracy. This chapter describes Bayesian regression procedures for estimating the effect of patient and reader covariates on test accuracy, as measured by classification probabilities, predictive probabilities, and diagnostic likelihood ratios. In the case of quantitative diagnostic scores, regression techniques will be used to allow for these patient and reader characteristics when estimating the receiver operating characteristic (ROC) area. For additional information on this, refer to Chapters 3 and 6 of Pepe [1] and Chapter 8 of Zhou et al. [2].