# RELATIVE RISK

The epidemiological term "relative risk" can confuse the uninitiated. Risks are the same as chances, and are derived from rates. The risk of an event, such as the occurrence of a specified disease or a death from a specified cause, is calculated from the incidence or death rate of the specified disease. For example, if the infant mortality rate in a given population is ten per one thousand live births, this means that a newborn infant has a one in one hundred chance, or risk, of dying in its first year of life. About one in every five persons dies eventually of cancer; thus the lifetime risk of dying of cancer is about one in five, or 20 percent; about one in every four of us gets cancer at some time during life; so the lifetime risk of getting cancer is about 25 percent. The concept of relative risk is more complex, and it is not made easier by the fact that the term has more than one meaning although its different usages are similar. The three common meanings are:

1. The ratio of the risk of a disease or death among those exposed to a specified risk to those not exposed to this risk. This meaning of the term is commonly called the "risk ratio."
2. The ratio of the cumulative incidence rate in those exposed to a specified risk to the cumulative incidence rate in those not exposed to a specified risk. This is called the "cumulative incidence ratio."
3. Relative risk is probably most often equated with the "odds ratio" that is calculated from the results of analyzing the data obtained in a case-control study. Although the odds ratio is not a rate, if the condition being studied is relatively raresay occurring less often than one in one thousand members of a population it approximates to what the rate would be if the numbers studied were large enough. Thus, in published epidemiological papers (and media reports of them) relative risk is often used as a synonym for the odds ratio. Again, an example may help to clarify this: In a case control study of 50 cases and 50 controls, 20 cases and 12 controls were exposed to the risk factor; the odds ratio therefore is (20 × 38) ÷ (12 × 30) = 2.1:1 (usually expressed as 2.1).

Note that the correct technical name for this is the "odds ratio approximation of relative risk," though this is often abbreviated to "relative risk" and is cited as such in media reports. It is a valid approximation only if the numbers and the differences between exposed and unexposed groups are large enough to exceed the limits of chance variation, and if the case-control study abides by the assumption that the condition under study is relatively rare. Mathematically inclined epidemiologists have written voluminously and in abstruse detail about the arcane details involved in the "rare disease assumption" and in the proper and improper uses of the odds ratio approximation of relative risk.

John M. Last

## Bibliography

Breslow, N. E., and Day, N. E. (1980). Statistical Methods in Cancer Research, Vol 1: The Analysis of Case-Control Studies. Lyon: IARC Publications.

Schlesselman, J. J. (1982). Case-Control StudiesDesign, Conduct, Analysis. New York: Oxford University Press.

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