In diagnostic medicine, it is important to be able to accurately distinguish between a diseased and non-diseased population. The area under the curve (AUC) is a commonly used measure index to evaluate the accuracy of the diagnostic test. Sometimes in research, it is costly and time consuming to sample the variables of interest, ranked set samples (RSS) is a more effective sampling method than the simple random sampling which can be obtained by ranking, thereby providing samples which are representative of the population of interest, in balanced ranked set samples (BRSS), there is an equal number of cycles for each set. In this thesis, we propose the empirical likelihood and jackknife empirical likelihood methods using BRSS and multistage RSS for the AUC. The simulation results show that our proposed method improves on the estimation of AUC. We performed two real data analysis to illustrate the proposed methods.