Receiver operating characteristic (ROC) curve is widely used in biometric identification. It is a plot of the detection power virus false alarm rate. It is an objective measure of accuracy. Positive biometrics identification is one-to-many match. ROC curve has been served as a "golden" criterion in measuring the accuracy of biometrics system for positive biometric identification. However, in this paper, we will analyze the problems of using ROC curve as the sole criterion in positive biometrics identification. From the view of detection and estimation theory, ROC curve only took concerns of system variance, and would not be able to detect the system bias, which could give wrong conclusion in evaluating system accuracy across multiple databases. ROC curve does not reflect the cost function, the database size, the quality of the image, and many other factors that are important in system performance and accuracy. We will use iris recognition as an example to discuss these issues. At the end, we will discuss some possible solutions to solve these problems.