International Journal of Statistics in Medical Research, 2012, 1, 79-81 79 E-ISSN: 1929-6029/12 © 2012 Lifescience Global Performance Measures in Binary Classification Matthias Kohl* Department of Mechanical and Process Engineering, Furtwangen University, Jakob-Kienzle-Str. 17, D-78054 VS-Schwenningen, Germany Abstract: We give a brief overview over common performance measures for binary classification. We cover sensitivity, specificity, positive and negative predictive value, positive and negative likelihood ratio as well as ROC curve and AUC. Keywords: Sensitivity, specificity, positive predictive value, negative predictive value, positive likelihood ratio, negative likelihood ratio, prevalence, ROC curve, AUC, informative diagnostic test. PERFORMANCE MEASURES In many cases diagnostic tests are performed to distinguish between two groups reflecting presence or absence of a relevant medical condition. In this setup let us assume a group of N patients with true status y 1 , ..., y N where y i = 1 represents presence and y i = 0 absence of the medical condition. A diagnostic test T yields results t 1 , ..., t N where t i = 1 represents a positive and t i = 0 a negative test. The simplest approach to measure the performance of test T is to use the probability of misclassification (PMC) PMC = cardinality of {i = 1,…, Ny i  t i } N respectively, the accuracy (ACC) = 1 - PMC However, such a single performance measure may be misleading, as there are two possibilities for a correct respectively, wrong decision of the diagnostic test that are the correct respectively, wrong prediction of the presence or absence of the medical condition [1]. Thus, a pair of criteria should be used to obtain an exact description of the performance. In general, the results of a test can be summarized by the so called confusion matrix. The confusion matrix whose structure is presented in Table 1 includes the information on the prevalence (Pr) for the considered group. Pr = TP + FN TP + FN + TN + FP *Address corresponding to this author at the Department of Mechanical and Process Engineering, Furtwangen University, Jakob-Kienzle-Str. 17, D-78054 VS-Schwenningen, Germany; Tel: +49 (0) 7720 307-4746; Fax: +49 (0) 7720 307-4727; E-mail: Matthias.Kohl@hs-furtwangen.de Table 1: Confusion Matrix for Binary Classification Test result 0 1 0 True negative (TN) False positive (FP) True situation 1 False negative (FN) True positive (TP) In addition, it is the basis for the definition of various performance measures. The percentage of correct positive tests for patients having the medical condition is called sensitivity (Se), whereas the percentage of correct negative tests for patients not having the medical condition is called specificity (Sp). Se = TP TP + FN SP = TN TN + FP The accuracy can also be expressed as a weighted sum of sensitivity and specificity ACC = Pr * Se + (1  Pr) * SP The positive predictive value (PPV) is the probability that a patient with a positive test has the medical condition and the negative predictive value (NPV) is the probability that a patient with a negative test does not have the medical condition. PPV = TP TP + FP NPV = TN TN + FN The positive likelihood ratio (PLR) tells how likely patients with the medical condition are to have a positive test compared to patients without the medical condition. The negative likelihood ratio (NLR) tells how likely patients with the medical condition are to have a negative result compared to patients without the medical condition.