Positive and negative predictive values by the TOC curve

Abstract

Sensitivity and specificity are popular measures described by the receiver operating characteristic (ROC) curve. There are also two other measures such as the positive predictive value (PPV) and negative predictive value (NPV); however, the PPV and NPV cannot be represented by the ROC curve. Based on the total operating characteristic (TOC) curve suggested by Pontius and Si (International Journal of Geographical Information Science, 97, 570-583, 2014), explanatory methods are proposed to geometrically describe the PPV and NPV by the TOC curve. It is found that the PPV can be regarded as the slope of the right-angled triangle connecting the origin to a certain point on the TOC curve, while 1-NPV can be represented as the slope of the right-angled triangle connecting a certain point to the top right corner of the TOC curve. When the neutral zone exists, the PPV and 1-NPV can be described as the slopes of two other right-angled triangles of the TOC curve. Therefore, both the PPV and NPV can be estimated using the TOC curve, whether or not the neutral zone is present. © 2020 The Korean Statistical Society, and Korean International Statistical Society.