AN OPTIMAL COMBINATION OF SEVERAL BINARY MARKERS BASED ON NEYMAN-PEARSON LEMMA: WITH AN APPLICATION TO IMMUNOHISTOCHEMICAL MARKERS FOR THE DIAGNOSIS OF CLASSICAL HODGKIN LYMPHOMA

Combining the results of different binary diagnostic markers to reach maximum area under the receiver operating characteristic (ROC) curve is the aim of the present study. To this end, the Neyman-Pearson lemma is utilized to combine the results of several binary diagnostic markers to obtain an optimum decision rule. The applied procedure has two advantages: (1) no distributional assumptions are considered for diagnostic markers, and (2) the derived rules are optimal in the sense that their ROC curves are maximized at each point. As an application, eleven different subsets of six diagnostic markers of classical Hodgkin lymphoma (CD15, CD20, CD30, CD3, Pax-5 and LCA) are applied. Four best subsets are then selected based on the area under the ROC curve (AUC) and their optimal decision rules are derived at 0.05 error rate.