Emergency (****); * (*): *-* This open-access article distributed under the terms of the Creative Commons Attribution NonCommercial 3.0 License (CC BY-NC 3.0). Copyright © 2015 Shahid Beheshti University of Medical Sciences. All rights reserved. Downloaded from: www.jemerg.com 48 Emergency (2015); 3 (2): 48-49 EDUCATIONAL Part 1: Simple Definition and Calculation of Accuracy, Sensitivity and Specificity Alireza Baratloo1, Mostafa Hosseini2, Ahmed Negida3*, Gehad El Ashal4 1. Department of Emergency Medicine, Shohadaye Tajrish Hospital, Shahid Beheshti University of Medical Sciences, Tehran, Iran. 2. Department of Epidemiology and Biostatistics, School of Public Health, Tehran University of Medical Sciences, Tehran, Iran. 3. Faculty of Medicine, Zagazig University, Zagazig, Egypt. 4. Faculty of Medicine, Cairo University, Cairo, Egypt. *Corresponding Author: Ahmed Negida; Faculty of Medicine, Zagazig University,El-Kanayat, El-Sharkia, Zagazig, Egypt. Tel: +201125549087; Email: ahmed01251@medicine.zu.edu.eg Received: December 2014; Accepted: February 2015 Introduction: mergency physicians, like other specialists, are faced with different patients and various situa- tions every day. They have to use ancillary diag- nostic tools like laboratory tests and imaging studies to be able to manage them (1-8). In most cases, numerous tests are available. Tests with the least error and the most accuracy are more desirable. The power of a test to separate patients from healthy people determines its ac- curacy and diagnostic value (9). Therefore, a test with 100% accuracy should be the first choice. This does not happen in reality as the accuracy of a test varies for dif- ferent diseases and in different situations. For example, the value of D-dimer for diagnosing pulmonary embo- lism varies based on pre-test probability. It shows high accuracy in low risk patient and low accuracy in high risk ones. The characteristics of a test that reflects the afore- mentioned abilities are accuracy, sensitivity, specificity, positive and negative predictive values and positive and negative likelihood ratios (9-11). In this educational re- view, we will simply define and calculate the accuracy, sensitivity, and specificity of a hypothetical test. Definitions: Patient: positive for disease Healthy: negative for disease True positive (TP) = the number of cases correctly identified as patient False positive (FP) = the number of cases incorrectly identified as patient True negative (TN) = the number of cases correctly identified as healthy False negative (FN) = the number of cases incorrectly identified as healthy Accuracy: The accuracy of a test is its ability to differen- tiate the patient and healthy cases correctly. To estimate the accuracy of a test, we should calculate the proportion of true positive and true negative in all evaluated cases. Mathematically, this can be stated as: Accuracy = TP + TN TP + TN + FP + FN Sensitivity: The sensitivity of a test is its ability to deter- mine the patient cases correctly. To estimate it, we should calculate the proportion of true positive in pa- tient cases. Mathematically, this can be stated as: Sensitivity = TP TP + FN Specificity: The specificity of a test is its ability to deter- mine the healthy cases correctly. To estimate it, we should calculate the proportion of true negative in healthy cases. Mathematically, this can be stated as: Specificity = TN TN + FP Examples: Scenario 1 Imagine we have a sample of 100 cases, 50 healthy and the others patient. If a test can be positive for all patients and be negative for all the healthy ones, it is 100% accu- rate. In figure 1, arrow shows the test and it has been able to differentiate the healthy and patient exactly. In this example, the sensitivity of the test is 50 divided by 50 or 100% and its specificity in determining the healthy people is 50 divided by 50 or 100%. Taking into account the mentioned statistical character- istics, this test is appropriate for both screening and final verification of a disease. Figure 1: A schematic presentation of an example test with 100% accuracy, sensitivity, and specificity. E This open-access article distributed under the terms of the Creative Commons Attribution NonCommercial 3.0 License (CC BY-NC 3.0). Copyright © 2015 Shahid Beheshti University of Medical Sciences. All rights reserved. Downloaded from: www.jemerg.com 49 Baratloo et al Figure 2: A schematic presentation of an example test with 75% accuracy, 50% sensitivity, and 100% specificity. Scenario 2 If the test can only diagnose 25 out of the 50 patients and has reported the others as healthy (Figure 2); accuracy, sensitivity, and specificity will be as follows: Accuracy: Of the 100 cases that have been tested, the test could determine 25 patients and 50 healthy cases correctly. Therefore, the accuracy of the test is equal to 75 divided by 100 or 75%. Sensitivity: From the 50 patients, the test has only diag- nosed 25. Therefore, its sensitivity is 25 divided by 50 or 50%. Specificity: From the 50 healthy people, the test has cor- rectly pointed out all 50. Therefore, its specificity is 50 divided by 50 or 100%. According to these statistical characteristics, this test is not suitable for screening purposes; but it is suited for the final confirmation of a disease. Scenario 3 This time we will assume that the test has been able to identify 25 of the 50 healthy cases and has reported the others as patients (Figure 3). In this scenario accuracy, sensitivity and specificity will be as follows: Accuracy: Of the 100 cases that have been tested, the test could identify 25 healthy cases and 50 patients cor- rectly. Therefore, the accuracy of the test is equal to 75 divided by 100 or 75%. Sensitivity: From the 50 patients, the test has diagnosed all 50. Therefore, its sensitivity is 50 divided by 50 or 100%. Specificity: From the 50 healthy cases, the test has cor- rectly pointed out only 25. Therefore, its specificity is 25 divided by 50 or 50%. According to these statistical characteristics, this test is suited for screening purposes but it is not suitable for the final confirmation of a disease. Acknowledgments: We would like to thank Dr. Saeed Safari and Dr. Mahmoud Yousefifard for their invaluable helps. Conflict of interest: None Figure 3: A schematic presentation of an example test with 75% accuracy, 100% sensitivity, and 50% specificity. 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