Relationships among three popular measures of differential risks: relative risk, risk difference, and odds ratio.
The relative risk, risk difference, and odds ratio are the three most commonly used measures for comparing the risk of disease between different groups. Although widely popular in biomedical and psychosocial research, the relationship among the three measures has not been clarified in the literature. Many researchers incorrectly assume a monotonic relationship, such that higher (or lower) values in one measure are associated with higher (or lower) values in the other measures. In this paper we discuss three theorems and provide examples demonstrating that this is not the case; there is no logical relationship between any of these measures. Researchers must be very cautious when implying a relationship between the different measures or when combining results of studies that use different measures of risk.
Department of Biostatistics & Computational Biology, University of Rochester, Rochester, NY, United States; ; Department of Anesthesiology, University of Rochester, Rochester, NY, United States ; Department of Anesthesiology, University of Rochester, Rochester, NY, United States.
Changyong
C
Feng
Department of Biostatistics & Computational Biology, University of Rochester, Rochester, NY, United States;
Hongyue
H
Wang
Department of Biostatistics & Computational Biology, University of Rochester, Rochester, NY, United States;
Bokai
B
Wang
Department of Biostatistics & Computational Biology, University of Rochester, Rochester, NY, United States;
Xiang
X
Lu
Department of Biostatistics & Computational Biology, University of Rochester, Rochester, NY, United States;
Hao
H
Sun
Department of Biostatistics & Computational Biology, University of Rochester, Rochester, NY, United States;
Xin M
XM
Tu
odds ratio; relative risk; risk difference
Int J Epidemiol. 1994 Feb;23(1):201-3
8194918
JAMA. 1998 Nov 18;280(19):1690-1
9832001
Nat Rev Genet. 2009 Apr;10 (4):264-9
19238176
Nat Rev Cancer. 2013 Apr;13(4):233-45
23467302
Br J Cancer. 2004 Feb 9;90(3):646-51
14760379
Epidemiol Rev. 1998;20(2):218-36
9919440
Ann Epidemiol. 2002 Oct;12(7):452-4
12377421