Case Fatality: Rate, Ratio, or Risk? : Epidemiology

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Case Fatality

Rate, Ratio, or Risk?

Kelly, Heath; Cowling, Benjamin J.

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Epidemiology 24(4):p 622-623, July 2013. | DOI: 10.1097/EDE.0b013e318296c2b6
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To the Editor:

“When I use a word,” Humpty Dumpty said, in a rather scornful tone, “it means just what I choose it to mean – neither more nor less.”

Lewis Carroll, Alice Through the Looking Glass

The acronym CFR in the epidemiologic literature can denote case fatality rate, case fatality ratio, or case fatality risk. “Rate,” “ratio,” and “risk” have distinct technical meanings when used in an epidemiologic context. Furthermore, their accepted meaning is not static in either usage. This can lead to linguistic disagreements, which may be settled by reference to an authoritative dictionary. For epidemiologic usage, we consult the Dictionary of Epidemiology.1

The Dictionary provides a long discussion of the epidemiologic use of the term “rate.” p. 207 Included are the following statements: “All rates are ratios” and “Some rates are proportions.” “Risk” is defined as “the probability that an event will occur.” p. 217 Given that a probability is a proportion, these definitions do not help with the distinctions among rate, ratio, and proportion (risk) if a rate could also be a proportion. Furthermore, in defining a ratio, the Dictionary explains that both a rate and a proportion are “types of ratios.” p. 208

Nonetheless, a possible consensus is emerging on the technical use of rate, ratio, and risk. Following the work of Elandt-Johnson2 and Vandenbroucke,3 many modern epidemiology or biostatistics texts4,5 define a rate as varying with time, having a dimension of time−1. Although agreement on this is not universal,6 rate defined as varying with time appears to be the most common usage. A ratio is a comparison of two like quantities. It has no dimensions and can take any value, where a ratio of 1 indicates equality between the two quantities being compared. Risk is a probability, usually associated in both normal and technical usage with an adverse outcome. Like a ratio, risk has no dimensions, but unlike a ratio, risk is confined to values between 0 and 1.

The probability of death among cases diagnosed with a disease is often used as a measure of disease severity. This quantity is usually estimated within a specified period of time by direct follow-up of cases and ascertainment of their death or recovery. Alternatively, the quantity could be estimated in a population within a specified time period by dividing the number of deaths associated with the disease by the number of cases of that disease. In principle, the persons included in the numerator should be a subset of the persons in the denominator. This conditional probability of mortality among classified cases can be termed the “case fatality risk.” Such a risk is not a rate because time is not part of the denominator. Recognizing this, many authors have preferred the term “case fatality ratio.” However, neither is this quantity strictly a ratio because it is not the comparison of like quantities. Case fatality estimates a conditional probability, and should thus be considered a risk.

Consistent with a living language, there is an evolution in usage. On 22 February 2013, searches of text strings in titles/abstracts in PubMed resulted in the following numbers of hits: “case fatality rate” = 3030; “case fatality ratio” = 332; and “case fatality risk” = 20. Although case fatality rate has been used traditionally, case fatality ratio started to appear only in the 1970s and the articles reporting case fatality risk were all published since 1990.

Although different usages of CFR are unlikely to result in any misunderstanding, it would be preferable if the technical usage of terms also used in nontechnical language were standardized. Although it seems only a linguistic distinction among rate, ratio, and risk for the CFR, it is important for other epidemiological measures because one does not analyze risk and rate by the same methods.


We thank Jessica Wong for technical assistance.

Heath Kelly

Victorian Infectious Diseases

Reference Laboratory

North Melbourne, Victoria, Australia

National Centre for Epidemiology and

Population Health

Australian National University

Canberra, Australian Capital Territory,


Benjamin J. Cowling

School of Public Health

Li Ka Shing Faculty of Medicine

The University of Hong Kong

Hong Kong Special Administrative Region


[email protected]


1. Porta M A Dictionary of Epidemiology. 20085th ed Oxford, England Oxford University Press
2. Elandt-Johnson RC. Definition of rates: some remarks on their use and misuse. Am J Epidemiol. 1975;102:267–271
3. Vandenbroucke JP. On the rediscovery of a distinction. Am J Epidemiol. 1985;121:627–628
4. Rothman K, Greenland S, Lash TL Modern Epidemiology. 20033rd ed Philadelphia, PA Lippincott Williams and Wilkins
5. Kirkwood BR, Sterne AC Essential Medical Statistics. 20032nd ed Malden, MA Blackwell Science
6. Miettinen OS. Estimability and estimation in case-referent studies. Am J Epidemiol. 1976;103:226–235
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