Measuring association between two categorical variables: revisiting risk ratio and odds ratio

Khan, Shahjahan ORCID: and Memon, Muhammad Ashraf (2020) Measuring association between two categorical variables: revisiting risk ratio and odds ratio. International Journal of Statistical Sciences, 20 (2). pp. 153-170. ISSN 1683-5603


In many statistical analyses the relative risk or risk ratio (RR) and odds ratio (OR) are two commonly used measures of association between two categorical variables. The risk, and hence the RR, are defined in terms of probability. However, neither odds nor OR is defined in probabilistic term. Although the two ratios share similar mathematical structure, they are not the same. In reality, they are very different and hence should not be used as synonymous or interchangeably. Many epidemiological literatures inappropriately interpret OR as risk (cf. Chen (2010)). The main reasons for this confusion may be due to the fact that both represent `likelihood’ of events and that OR and RR share the same numerator, ignoring the other fact that they are measured in different scales (denominators). This paper identifies the differences between the two measures by exploiting their basic definitions, methods of computations, and interpretations of results.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: © 2020 Dept. of Statistics, Univ. of Rajshahi, Bangladesh.
Faculty/School / Institute/Centre: Current - Faculty of Health, Engineering and Sciences - School of Sciences (6 Sep 2019 -)
Faculty/School / Institute/Centre: Current - Institute for Resilient Regions - Centre for Health Research (1 Apr 2020 -)
Date Deposited: 13 Jan 2021 00:00
Last Modified: 19 Jan 2021 05:17
Uncontrolled Keywords: categorical outcomes; risk and odds; risk ratio; odds ratio; logistic regression
Fields of Research (2008): 11 Medical and Health Sciences > 1199 Other Medical and Health Sciences > 119999 Medical and Health Sciences not elsewhere classified
01 Mathematical Sciences > 0104 Statistics > 010404 Probability Theory
Fields of Research (2020): 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490506 Probability theory
Socio-Economic Objectives (2008): E Expanding Knowledge > 97 Expanding Knowledge > 970111 Expanding Knowledge in the Medical and Health Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Socio-Economic Objectives (2020): 20 HEALTH > 2004 Public health (excl. specific population health) > 200499 Public health (excl. specific population health) not elsewhere classified

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