Classifiers that refrain from classification in certain cases can significantly reduce the misclassification cost. However, the parameters for such abstaining classifiers are often set in a rather ad-hoc manner. We propose a method to optimally build a specific type of abstaining binary classifiers using ROC analysis. These classifiers are built based on optimization criteria in the following three models: cost-based, bounded-abstention and bounded-improvement. We demonstrate the usage and applications of these models to effectively reduce misclassification cost in real classification systems. The method has been validated with a ROC building algorithm and cross-validation on 15 UCI KDD datasets.