Estimating Receiver Operating Characteristic Curve (ROC) Using Birnbaum-Saunders Kernel

Many researchers use the receiver operating characteristic curve (ROC) as a popular way of displaying, evaluating and comparing the discriminatory accuracy of diagnostic tests. The most commonapproach for estimating the ROC curve is using nonparametric kernel estimates in two parts, sensitivity and specificity. Kernel estimators, however, at the beginning and end points of the data domain, known as boundary points, have a slower convergence rate than other points in the domain and are not convergent to the actual value of the probability distribution. This problem is known as the boundary problem. One way to solve the boundary problem in kernel estimators is to use asymmetric kernels. This paper proposes a new kernel estimator for the ROC curve based on the asymmetric Birnbaum-Saunders (B-S) kernel and the asymptotic convergence of the proposed estimator is shown. In addition, the analytical superiority of the proposed estimator over the corresponding symmetric kernel-type estimator is shown. The performanceof the proposed estimator is illustrated via a numerical study. The results show that the proposed estimator outperforms the other commonly-used methods. The application of the proposed method to a set of medical data is also presented.