## Risk

Risks (synomyms: incidence proportion, attack rate) are expressed as a percentage.

In a population, the risk of a disease measures the proportion of people that develops this disease between two specified points in time (T_{0} and T_{1}). It is calculated as the number of persons developing the disease during the observation period divided by the number of persons present at the beginning of the observation period. The denominator represents the population at risk of developing the disease at the beginning of the period of observation.The time spent by each individual in the observation period is not taken into account.

A risk is a probability. It will range from 0 to 1, or 0% to 100% if expressed as a percentage. The risk of disease is therefore also called incidence proportion.

In an example in which 50 out of 200 residents of a nursing home developed gastroenteritis between 12 and 20 May 2005, the risk of gastroenteritis is 50/200 = 0.25 or 25 %.

In intervention epidemiology risk is used for short periods of follow up like outbreaks during which all individuals are assumed to be followed for the same period of time.

In outbreaks the term risk is frequently replaced by attack rate, which is also expressed as a percentage. Even though widely accepted in the epidemiological community, the term “attack rate” is technically incorrect, as an attack rate is not a rate but a risk. In outbreaks, an food specific attack rate measures how many people who ate a certain type of food (or had an other exposure) became ill (else, "were attacked by that food").

The measurement of risk shows the probability of developing illness during a specific period of time. Without knowledge of the time period it is however impossible to interpret a risk [1]. A risk of death of 2% will imply different meanings if it expresses the risk of death during one month, one year or a 30 year follow up.

## Rates

Rates are a measure of occurrence of a phenomenon [2]. A rate is calculated as the number of events that have occurred, divided by the total time experienced by the population under observation, usually expressed in person years. Rates are usually multiplied by a power of 10, to converts the rate into a decimal or whole number which is easy to interpret.

In a study, it is possible that each person is experience the same event more than one time.

Incidence rates are a subset of rates, in which we are interested at quantifying *new* events ("new cases" of disease)

The term rate is sometimes used incorrectly in epidemiology. For example to replace the term risk (as in attack rates and case fatality rates).

[1] Rothman KJ; Epidemiology: an introduction. Oxford University Press 2002, p.24-28.

[2] Porta, M. A dictonary of Epidemiology, Fifth edition. Oxford University press, 2008.