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Treating these as gold standards can bias receiver operating characteristic (ROC) curve analysis. To address this issue, we propose a novel likelihood\u2010based method under a non\u2010parametric density ratio model. This approach enables the reliable estimation of the ROC curve, area under the curve (AUC), partial AUC, and Youden's index with favorable statistical properties. To implement the method, we develop an efficient expectation\u2010maximization (EM) algorithm. Extensive simulations evaluate its finite\u2010sample performance, showing smaller mean squared errors in estimating the ROC curve, partial AUC, and Youden's index compared to existing methods. 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