Article A new diagnostic accuracy measure and cut-point selection criterion Tuochuan Dong, 1 Kristopher Attwood, 2 Alan Hutson, 1 Song Liu 2 and Lili Tian 1 Abstract Most diagnostic accuracy measures and criteria for selecting optimal cut-points are only applicable to diseases with binary or three stages. Currently, there exist two diagnostic measures for diseases with general k stages: the hypervolume under the manifold and the generalized Youden index. While hypervolume under the manifold cannot be used for cut-points selection, generalized Youden index is only defined upon correct classification rates. This paper proposes a new measure named maximum absolute determinant for diseases with k stages (k  2). This comprehensive new measure utilizes all the available classification information and serves as a cut-points selection criterion as well. Both the geometric and probabilistic interpretations for the new measure are examined. Power and simulation studies are carried out to investigate its performance as a measure of diagnostic accuracy as well as cut-points selection criterion. A real data set from Alzheimer’s Disease Neuroimaging Initiative is analyzed using the proposed maximum absolute determinant. Keywords Maximum absolute determinant, optimal cut-points, volume for the parallelotope, Alzheimer’s Disease 1 Introduction In diagnostic studies, the most straightforward classification rule is binary, i.e. non-diseased or diseased. The probabilities that a diagnostic biomarker correctly classifies a non-diseased subject or a diseased subject are defined as specificity or sensitivity, respectively. Plotting sensitivity against 1-specificity for all the possible cut-points or decision thresholds from a continuous biomarker leads to what is termed a receiver operating characteristic (ROC) curve. There exist many detailed reviews pertaining to inference in the framework of ROC curve. 1–4 For diseases with binary classification, the most popular diagnostic measure of accuracy is the area under the ROC curve (AUC), which has been extensively studied. 5–13 Another popular diagnostic measure, the Youden index, 14 is defined as 1 Department of Biostatistics, University at Buffalo, Buffalo, NY, USA 2 Department of Biostatistics and Bioinformatics, Roswell Park Cancer Institute, Buffalo, NY, USA Corresponding author: Lili Tian, Department of Biostatistics, 717 Kimball Tower, 3435 Main St. Bldg. 26 Buffalo, NY 14214, USA. Email: ltian@buffalo.edu Statistical Methods in Medical Research 0(0) 1–25 ! The Author(s) 2015 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav DOI: 10.1177/0962280215611631 smm.sagepub.com at UCSF LIBRARY & CKM on January 5, 2016 smm.sagepub.com Downloaded from