Bayesian estimation of auc of a constant shape bi- weibull failure time distribution

Abstract

A Receiver Operating Characteristic (ROC) curve provides quick access to the quality of classification in many medical diagnoses. The Weibull distribution has been observed as one of the most useful distributions, for modeling and analyzing lifetime data in Engineering, Biology, Survival and other fields. Studies have been done vigorously in the literature to determine the best method in estimating its parameters. In this paper, we examine the performance of Bayesian Estimator using Jeffreys‘ Prior Information and Extension of Jeffreys‘ Prior Information with three Loss functions, namely, the Linear Exponential Loss,General Entropy Loss, and Square Error Loss for estimating the AUC values for Constant Shape Bi-Weibull failure time distribution. Theoretical results are validated by simulation studies. Simulations indicated that estimate of AUC values were good even for relatively small sample sizes (n=25). 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.