Receiver operating characteristics (ROC) curve analysis has been a popular tool in diagnostic accuracy modeling to evaluate the prognostic capacity of a biomarker in predicting binary disease outcomes. However, for disease outcomes with more than two categories, this framework becomes ineffective and a more general framework of manifold becomes necessary. We propose a placement value-based ROC surface regression approach in the presence of an ordinal outcome with three categories. The use of placement value is to facilitate a direct assessment of covariate effect on the measure of diagnostic accuracy. Simulation studies are provided to assess the performance of the proposed model under various scenarios. To illustrate the model’s applicability, we analyze the NICHD Fetal Growth Study data to estimate the diagnostic ability of Estimated fetal weight (EFW), an ultrasound biomarker in predicting abnormal birth categories: small-for-gestational-age (SGA), appropriate-for-gestational-age (AGA), and large-for-gestational-age (LGA).