Confidence Interval Estimation of an ROC Curve: An Application of Generalized Half Normal and Weibull Distributions

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Abstract
In the recent past, the work in the area of ROC analysis gained attention in explaining the accuracy of a test and identification of the optimal threshold. Such types of ROC models are referred to as bidistributional ROC models, for example Binormal, Bi-Exponential, Bi-Logistic and so forth. However, in practical situations, we come across data which are skewed in nature with extended tails. Then to address this issue, the accuracy of a test is to be explained by involving the scale and shape parameters. Hence, the present paper focuses on proposing an ROC model which takes into account two generalized distributions which helps in explaining the accuracy of a test. Further, confidence intervals are constructed for the proposed curve; that is, coordinates of the curve (FPR, TPR) and accuracy measure, Area Under the Curve (AUC), which helps in explaining the variability of the curve and provides the sensitivity at a particular value of specificity and vice versa. The proposed methodology is supported by a real data set and simulation studies.

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