Skip to main content

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

(see also: Case-Control Study; Odds Ratio; Risk Assessment, Risk Management )


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.

Cite this article
Pick a style below, and copy the text for your bibliography.

  • MLA
  • Chicago
  • APA

"Relative Risk." Encyclopedia of Public Health. . 17 Feb. 2019 <>.

"Relative Risk." Encyclopedia of Public Health. . (February 17, 2019).

"Relative Risk." Encyclopedia of Public Health. . Retrieved February 17, 2019 from

Learn more about citation styles

Citation styles gives you the ability to cite reference entries and articles according to common styles from the Modern Language Association (MLA), The Chicago Manual of Style, and the American Psychological Association (APA).

Within the “Cite this article” tool, pick a style to see how all available information looks when formatted according to that style. Then, copy and paste the text into your bibliography or works cited list.

Because each style has its own formatting nuances that evolve over time and not all information is available for every reference entry or article, cannot guarantee each citation it generates. Therefore, it’s best to use citations as a starting point before checking the style against your school or publication’s requirements and the most-recent information available at these sites:

Modern Language Association

The Chicago Manual of Style

American Psychological Association

  • Most online reference entries and articles do not have page numbers. Therefore, that information is unavailable for most content. However, the date of retrieval is often important. Refer to each style’s convention regarding the best way to format page numbers and retrieval dates.
  • In addition to the MLA, Chicago, and APA styles, your school, university, publication, or institution may have its own requirements for citations. Therefore, be sure to refer to those guidelines when editing your bibliography or works cited list.