Ratio

A ratio is an expression of the magnitude of one quantity in relation to another. Ratios are typically expressed by two numbers separated by a colon, for instance, 4:3, read as ‘four to three’ and meaning that there are four units of the first items for every three units of the second item. Ratios do not require that the two numbers have common units and in fact are typically used to express the relationship between two quantities consisting of different units. For instance, the ratio of male to female patients in a hospital might be expressed as 2:1, meaning there were twice as many male patients as female patients or that there were two male patients for every one female patient.

The concept of ratio has to be clearly distinguished from the definitions of proportion and of rate. A ratio is a fraction in which the numerator is not necessarily a part of the denominator or, in other words, in a ratio the numerator is not necessarily included in the population defined by the denominator. In contrast, in a proportion the numerator by definition is included in the denominator. Taking the hospital example again, if the ratio of male to female patients is 2:1, in order to express this as a proportion we must introduce the unit of ‘patient’ (as opposed to male patient and female patient) to be able to make the statement that proportion of male patients among all patients is 66.7% or two thirds; in this case of the proportion, male patients are included in both the numerator and denominator of the fraction. Ratios are distinguished from rates because ratios do not include a measure of time in the denominator.

The main properties of ratios are that they are greater than zero, they may or may not be greater than 100, and may or may not have units. Ratios may also be expressed as percentages. Ratios are commonly used in epidemiology and public health: For instance, the risk ratio, also known as relative risk, is used to [Page 895]express the risk of a person developing a condition given a particular exposure, relative to those lacking the exposure. Odds ratios similarly express the odds of developing a condition given an exposure, compared with those who do not have the exposure. Both the risk ratio and odds ratio are dimensionless.

Ratiosarealsousedinepidemiologytoexpress availability of services or cases of disease for a particular population. For instance, a commonly reported measure of health care availability is the number of hospitals or hospital beds per 10,000 people, which is calculated by dividing the number of hospitals or beds by the population size and multiplying by 10,000. Obviously, the numerator in these cases are hospitals or hospital beds, and the denominator in both cases are people, so they do not have a common unit. Similar examples include the per capita income: that is, the total income earned during a year by a group of people divided by the number of people (units = dollars per capita); and the mortality (or death) rate: that is, the number of deaths during a specified period divided by the number of persons at risk of dying during this period (units = deaths per 100 people; larger units such as per 10,000 people can be used for rare diseases or when mortality is rare). Note that the terms ratio and rate are sometimes used interchangeably, particularly when speaking of statistics such as the number of hospitals per 10,000 people. However, many epidemiologists prefer to reserve the term rate to refer to numbers expressed per unit time, such as infections per year.

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