Emergency (****); * (*): *-* This open-access article distributed under the terms of the Creative Commons Attribution NonCommercial 3.0 License (CC BY-NC 3.0). Copyright ยฉ 2015 Shahid Beheshti University of Medical Sciences. All rights reserved. Downloaded from: www.jemerg.com 170 Emergency (2015); 3 (4): 170-171 EDUCATIONAL Evidence Based Emergency Medicine Part 3: Positive and Negative Likelihood Ratios of Diagnostic Tests Alireza Baratloo1, Saeed Safari1, Mohamed Elfil2, Ahmed Negida3* 1. Emergency Department, Shohadaye Tajrish Hospital, Shahid Beheshti University of Medical Sciences, Tehran, Iran. 2. Faculty of medicine, Alexandria University, Alexandria, Egypt. 3. Faculty of medicine, Zagazig University, Zagazig, 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: July 2015; Accepted: August 2015 Introduction: n the previous two parts of educational manuscript series in Emergency, we explained some screening characteristics of diagnostic tests including accuracy, sensitivity, specificity, and positive and negative predic- tive values (1, 2). In the 3rd part we aimed to explain positive and negative likelihood ratio (LR) as one of the most reliable performance measures of a diagnostic test (3). To better understand this characteristic of a test, it is first necessary to fully understand the concept of sen- sitivity and specificity. So we strongly advise you to re- view the 1st part of this series again (1, 2). In short, the likelihood ratios are about the percentage of people with and without a disease but having the same test result (4). The prevalence of a disease can directly influence screening characteristics of a diagnostic test, especially its sensitivity and specificity. Trying to eliminate this ef- fect, LR was developed. Pre-test probability of a disease multiplied by positive or negative LR can estimate post- test probability. Therefore, LR is the most important characteristic of a test to rule out or rule in a diagnosis. A positive likelihood ratio > 1 means higher probability of the disease to be present in a patient with a positive test. The further from 1, either higher or lower, the stronger the evidence to rule in or rule out the disease, respectively (5). It is obvious that tests with LR close to one are less practical. On the other hand, LR further from one will have more value for application in medicine. Usually tests with LR < 0.1 or > 10 are considered suita- ble for implication in routine practice. Calculation: Positive likelihood ratio (LR+): It is the ratio of probability of a patient with a disease and having positive test result divided by probability of a patient without a disease but having positive test result (5). It can be directly calculated from this equation: ๐‘ณ๐‘น+= ๐ฌ๐ž๐ง๐ฌ๐ข๐ญ๐ข๐ฏ๐ข๐ญ๐ฒ ๐Ÿ โˆ’ ๐ฌ๐ฉ๐ž๐œ๐ข๐Ÿ๐ข๐œ๐ข๐ญ๐ฒ Example 1: Imagine that there is a diagnostic test, which has sensitivity and specificity of 80% and 60%, respec- tively. In this scenario, the positive likelihood ratio of this test will be calculated as follows: LR+ = 0.80/ (1-0.60) = 0.80/ 0.40 = 2 Negative likelihood ratio (LR โˆ’): It is the ratio of probability of a patient with a disease but having negative test result divided by probability of a pa- tient without a disease and having negative test result (5). It can be directly calculated from this equation: ๐‘ณ๐‘นโˆ’= ๐Ÿ โˆ’ ๐ฌ๐ž๐ง๐ฌ๐ข๐ญ๐ข๐ฏ๐ข๐ญ๐ฒ ๐ฌ๐ฉ๐ž๐œ๐ข๐Ÿ๐ข๐œ๐ข๐ญ๐ฒ Example 2: Imagine that we have a diagnostic test with sensitivity and specificity of 90% and 70%, respectively. In this case, the negative likelihood ratio is calculated as follows: LR โˆ’ = (1-0.9)/ 0.7 = 0.1/0.7 = 0.14 Example 3: In the study by Aminiahidashti et al., the sen- sitivity and the specificity of the ascites fluid appearance as a diagnostic test for the detection of spontaneous bac- terial peritonitis were 46.9% and 87.5%, respectively (6). So, positive and negative likelihood ratios of this test can be calculated as follows: LR + = 46.9 % / (1 - 87.5%) = 0.469 / (1- 0.875) = 0.469 / 0.125 = 3.8 LR โˆ’ = (1- 0.469) / 0.857 = 0.531 / 0.875 = 0.6 Example 4: In Taghizadieh et al. study, chest X-Ray in di- agnosis of pleural effusion had sensitivity and specificity of 66.7% and 77.8%, respectively (7). Given this data, the LR + and LR โ€“ can be calculated as follows: LR + = 0.667/ (1-0.778) = 0.667/ 0. 222 = 3 LR โˆ’ = (1-0.667)/ 0.778 = 0.333/ 0.778 = 0.4 I This open-access article distributed under the terms of the Creative Commons Attribution NonCommercial 3.0 License (CC BY-NC 3.0). Copyright ยฉ 2015 Shahid Beheshti University of Medical Sciences. All rights reserved. Downloaded from: www.jemerg.com 171 Baratloo et al References: 1. Safari S, Baratloo A, Elfil M, Negida AS. Part 2: Positive and negative predictive values of diagnostic tests. Emergency. 2015;3(3):87-8. 2. Baratloo A, Hosseini M, Negida A, El Ashal G. Part 1: Simple Definition and Calculation of Accuracy, Sensitivity and Specificity. Emergency. 2015;3(2):48-9. 3. McGee S. Simplifying likelihood ratios. J Gen Intern Med. 2002;17(8):647-50. 4. Grimes DA, Schulz KF. Refining clinical diagnosis with likelihood ratios. Lancet. 2005;365(9469):1500-5. 5. Deeks JJ, Altman DG. Diagnostic tests 4: likelihood ratios. BMJ. 2004;329(7458):168-9. 6. Aminiahidashti H, Hosseininejad SM, Montazer H, Bozorgi F, Jahanian F, Raee B. Diagnostic Accuracy of Ascites Fluid Gross Appearance in Detection of Spontaneous Bacterial Peritonitis. Emergency. 2014;2(3):138-40. 7. Taghizadieh A, Ala A, Rahmani F, Nadi A. Diagnostic Accuracy of Chest x-Ray and Ultrasonography in Detection of Community Acquired Pneumonia; a Brief Report. Emergency. 2015;3(3):114-6. Introduction: Calculation: Positive likelihood ratio (LR+): It is the ratio of probability of a patient with a disease and having positive test result divided by probability of a patient without a disease but having positive test result (5). It can be directly calculated from this equation: Negative likelihood ratio (LR โˆ’): References: