Widely used in diagnostic medicine, Quantitative imaging biomarkers (QIB) are measurements derived from medical images using well-defined computer algorithms. For example, hepatic stiffness and relative fat fraction are quantified from magnetic resonance (MR) electrography of the liver for detection of nonalcoholic steato-hepatitis. Different QIBs may carry information on different aspects of the disease status. As a result, they may yield a more accurate diagnostic test when properly combined than used individually. To find the optimal rule of combination, we develop a nonparametric model under the sole assumption that the risk score is monotone with respect to each biomarker in question. The nonparametric, monotonicity-constrained risk score is estimated by an EM-type algorithm and is then used as an ordinal diagnostic test. Simulation studies show that our approach outperforms standard parametric models or machine learning techniques for classification based on the multiple QIBs. As an illustration, we apply the proposed methodology to a real study on nonalcoholic fatty liver disease patients undergoing MR electrography.