Rate

A rate is a measure of change in one quantity with respect to change in another. As used in epidemiology, this typically refers to an incidence rate, where the numerator is the number of new events and the denominator is total person-time at risk. This is one of the key measures of occurrence of disease in populations and gives an estimate of how fast disease or death is happening in a given population.

An example calculation of an incidence rate can be done using data from Table 1. A total of three events occurred, and the total person-time at risk summed over all population members is 30 + 17 + 22 + 11 + 20 =100 person-years, giving a rate of 3/100 or 0.03 per year. In calculating a rate, events counted in the numerator should be those occurring among people contributing person-time to the denominator. Likewise, the denominator should include only person-time during which any events experienced by the subject would be counted in the numerator. Sometimes the denominator can be estimated as average population size times follow-up time for a relatively short period of time with stable population level. For example, this is often done for an annual mortality rate in a geographic area, such as a state.

Some properties of incidence rates include the following:

• They range from 0 to infinity.
• Units are (time) − 1, where any unit of time can be used.
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• The actual measure depends on the unit of time used in the denominator.

For example, the following are equivalent:

The same rate may arise through alternate scenarios involving different lengths of follow-up time and population sizes. For example, following 100 people for an average of 1 year each and observing three events would give an incidence rate of 0.03 per year. Thesamerateof0.03peryearwouldalsobecalculated if three events were observed among only five people followed for an average of 20 years, as shown in the example above.

Incidence rates are occasionally reported in terms of change in a unit other than person-time—for example, motorist fatality rates per person-mile or aviation events per pilot-flight hour. The rates given simply per unit time as opposed to per unit person-time may be referred to as absolute rates.

The term rate has sometimes been used in a more general sense to refer to proportions or ratios. The concept of rate as different from risk (a proportion) was elucidated in the 19th century by William Farr. Farr reported vital statistics for England and contrasted cholera with tuberculosis. The former had a higher rate of death among patients, because the disease could be quickly fatal; whereas the latter had ahigher risk of death, since a greater percentage of those falling ill would eventually succumb to the disease. Even so, use of terminology such as attack rate and prevalence rate for measures that are technically proportions still persists.

Incidence rate is also known as incidence density, person-time rate, and force of morbidity or mortality.