Bi-power Lindley ROC curve analysis: Application to Malignant Tumors Diagnosis

Abstract This paper conducts Receiver Operating Characteristic (ROC) curve analysis for measurementsthat follow the recently proposed power Lindley distribution. A new index isintroduced to determine a cut-off point, providing an alternative to the well-known YoudenJ index. Firstly, several point estimators are examined for the cut-off points and the AreaUnder the Curve (AUC) measure in the bi-power Lindley (bi-PL) ROC model. Secondly,confidence intervals for these measures are discussed. The point and interval estimates arecompared by using a simulation study. Two numerical examples are presented, one involvingreal data and the other utilizing simulated data, for illustrative purposes. An R library calledPLindleyROC is being developed to enable practitioners to utilize the methodology proposedin this paper.