Biomarker discovery involves exploratory analysis to identify informative biomarkers of interest. The recent development of methods that identify a wider class of biomarkers that do not have a typical monotone relationship with a binary outcome has created a need for new methods that can classify biomarkers based on their relationship with a binary outcome of interest. We discuss three distinct informative biomarker types: traditional, nontraditional, and restricted traditional, and propose using a sequence of two hypothesis tests to classify biomarkers into their appropriate category. The first step uses the area-preserving ROC curve to identify nontraditional biomarkers. The second step tests for restricted traditional biomarkers. This test, proposed by Parodi and colleagues, is used to make the final distinction between traditional and restricted traditional for biomarkers not classified as nontraditional. We explore the performance of the hypothesis tests under simulation to explore the merits and limitations of each test. We apply the methods to three mineral and bone density biomarkers, calcium, phosphorus, and iPTH, using data from the Hemodialysis Study to ascertain biomarker type.