Ratio, rate, or risk?
Authors: Srinivas Mantha
Journal: The Lancet Infectious Diseases (2020)

In epidemiology, the terms ratio, rate, and risk have clear definitions.1Kelly H Cowling BJ Case fatality: rate, ratio, or risk?.Epidemiology. 2013; 24: 622-623Crossref PubMed Scopus (36) Google Scholar In the emerging publications related to coronavirus disease 2019 (COVID-19), the phrase case fatality rate is being used instead of case fatality ratio.2Guan WJ Ni ZY Hu Y et al.Clinical characteristics of coronavirus disease 2019 in China.N Engl J Med. 2020; (published online Feb 28.)DOI:10.1056/NEJMoa2002032Crossref Google Scholar, 3Rajgor DD Lee MH Archuleta S Bagdasarian N Quek SC The many estimates of the COVID-19 case fatality rate.Lancet Infect Dis. 2020; (published online March 27.)https://doi.org/10.1016/S1473-3099(20)30244-9Summary Full Text Full Text PDF PubMed Scopus (321) Google Scholar A ratio is a comparison of two similar quantities. Ratios have no dimensions and can take any value; a ratio of 1 means the two quantities being compared are equal to each other. The case fatality ratio is the ratio of deaths (numerator) to identified cases (denominator), and is usually expressed as percentage.2Guan WJ Ni ZY Hu Y et al.Clinical characteristics of coronavirus disease 2019 in China.N Engl J Med. 2020; (published online Feb 28.)DOI:10.1056/NEJMoa2002032Crossref Google Scholar, 3Rajgor DD Lee MH Archuleta S Bagdasarian N Quek SC The many estimates of the COVID-19 case fatality rate.Lancet Infect Dis. 2020; (published online March 27.)https://doi.org/10.1016/S1473-3099(20)30244-9Summary Full Text Full Text PDF PubMed Scopus (321) Google Scholar As clearly described by Kelly and Cowling,1Kelly H Cowling BJ Case fatality: rate, ratio, or risk?.Epidemiology. 2013; 24: 622-623Crossref PubMed Scopus (36) Google Scholar a rate has a time dimension (ie, time−1); it expresses changes in one quantity over a time period. Risk, however, is the probability associated with an adverse outcome that is likely to occur in the future during follow-up. Like ratios, risk has no dimensions but, unlike ratios, risk is confined to values between 0 and 1. From a scientific standpoint, these terms acquire different meanings depending on the variables being measured in the relevant study designs. In the context of the COVID-19 pandemic, case fatality ratios are obtained from cross-sectional studies, whereas risk estimates are obtained from prospective cohort studies. The infection rate is calculated by counting new infections in equally spaced time intervals (eg, daily or weekly). This growth rate reflects the speed and scale of new cases and can be used to monitor the effects of preventive interventions. Thus, in scientific research, these terms do not always align with their usual English language semantics and should not be used interchangeably. Ratio, rate, and risk have different meanings that are based on the variable being measured in the relevant study designs. It is hoped that future publications will use the terms appropriately, in line with the context. I declare no competing interests The many estimates of the COVID-19 case fatality rateSince the outbreak of coronavirus disease 2019 (COVID-19) began in December, a question at the forefront of many people's minds has been its mortality rate. Is the mortality rate of COVID-19 higher than that of influenza, but lower than that of severe acute respiratory syndrome (SARS)? Full-Text PDF Biostatistics to better detect fishy findingsWe commend Srinivas Mantha1 for the much needed clarification of the differences between risks, ratios, and rates, and of the latter's underlying notion of time. There is, however, an additional and important difference. Full-Text PDF