Ratio, rate, or risk?

In epidemiology, the terms ratio, rate, and risk have clear definitions.¹ In the emerging publications related to coronavirus disease 2019 (COVID-19), the phrase case fatality rate is being used instead of case fatality ratio.2, 3 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.2, 3 As clearly described by Kelly and Cowling,¹ 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.