The Receiver Operating Characteristic (ROC) curve is commonly used for evaluating the discriminatory ability of a biomarker. The conventional ways expressing the true accuracy of the test is by using its summary measure Area Under the ROC Curve (AUC) and intrinsic measures Sensitivity and Specificity. We propose a Bayesian approach for the estimation of the AUC under the Constant Shape Bi-Weibull Distribution using Extension of Jeffreys’ Prior Information with three Loss Functions. Theoretical results are validated by simulation studies.Simulations indicated that estimate of AUC values was good even for relatively small sample sizes (n=25). Bayes estimation with General Entropy loss function provides the highest AUC values when the loss parameter is -1.6, according to the extension of Jeffreys prior value is 0.4 or 1.4. When AUC≤0.6, which indicated a marked overlap between the outcomes in diseased and non-diseased populations. An illustrative example is also provided to explain the concepts
