Incidence is a measure of the risk of developing some new condition within a specified period of time. Although sometimes loosely expressed simply as the number of new cases during some time period, it is better expressed as a proportion or a rate^{[1]} with a denominator.
Incidence proportion (also known as cumulative incidence) is the number of new cases within a specified time period divided by the size of the population initially at risk. For example, if a population initially contains 1,000 nondiseased persons and 28 develop a condition over two years of observation, the incidence proportion is 28 cases per 1,000 persons, i.e. 2.8%.
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The incidence rate is the number of new cases per population in a given time period.^{[2]} When the denominator is the sum of the persontime of the at risk population, it is also known as the incidence density rate or persontime incidence rate.^{[3]} In the same example as above, the incidence rate is 14 cases per 1000 personyears, because the incidence proportion (28 per 1,000) is divided by the number of years (two). Using persontime rather than just time handles situations where the amount of observation time differs between people, or when the population at risk varies with time.^{[4]} Use of this measure implicitly implies the assumption that the incidence rate is constant over different periods of time, such that for an incidence rate of 14 per 1000 personsyears, 14 cases would be expected for 1000 persons observed for 1 year or 50 persons observed for 20 years.
When this assumption is substantially violated, such as in describing survival after diagnosis of metastatic cancer, it may be more useful to present incidence data in a plot of cumulative incidence over time, taking into account loss to followup, using a KaplanMeier Plot.
Consider the following example. Say you are looking at a sample population of 225 people, and want to determine the incidence rate of developing HIV over a 10 year period. At the beginning of the study (t=0) you find 25 cases of existing HIV. You followup at 5 years (t=5 yrs) and find 20 new cases of HIV. You again followup at the end of the study (t=10 yrs)and find 30 new cases. If you were to measure prevalence you would simply take the total number of cases (25 + 20 + 30 = 75) and divide by your sample population (225). So prevalence would be 75/225 = 0.33 or 33%. This tells you how widespread HIV is in your sample population, but little about the actual risk of developing HIV. To measure incidence you must take into account how many years each person contributed to the study, and when they developed HIV. When it is not known exactly when a person develops the disease in question, epidemiologists frequently use the actuarial method, and assume it was developed at a halfway point between followups. For example, at 5 yrs you found 20 new cases, so you assume they developed HIV at 2.5 years, thus contributing (20 * 2.5) 50 personyears. At 10 years you found 30 new cases. These people did not have HIV at 5 years, but did at 10, so you assume they were infected at 7.5 years, thus contributing (30 * 7.5) 225 years. That is a total of (225 + 50) 275 person years so far. You also want to account for the 150 people who never had or developed HIV over the 10 year period, (150 * 10) contributing 1500 personyears. That is a total of (1500 + 275) 1775 personyears. Now take the 50 new cases of HIV, and divide by 1775 to get 0.028, or 28 cases of HIV per 1000 population, per year. In other words, if you were to follow 1000 people for one year, you would see 28 new cases of HIV. This is a much more accurate measure of risk than prevalence.
Incidence should not be confused with prevalence, which is a measure of the total number of cases of disease in a population, rather than the rate of occurrence of new cases. Thus, incidence conveys information about the risk of contracting the disease, whereas prevalence indicates how widespread the disease is. Prevalence is the ratio of the total number of cases to total population. Prevalence can also be measured with respect to a relevant subgroup of a population (see: denominator data).
For example, consider a disease that takes a long time to cure, and that was spread widely in 2002, but whose spread was arrested in 2003. This disease will have a high prevalence and a high incidence in 2002; but in 2003 it will have a low incidence, although it will continue to have a high prevalence because it takes a long time to cure so the fraction of affected individuals remains high. In contrast, a disease that has a short duration may have a low prevalence and a high incidence. Prevalence is approximately the multiple of disease incidence and average disease duration , so Prevalence = Incidence x Duration but you cannot say that incidence = prevalence / Duration , because those measurement are of different matrix . The importance of this equation is the relation between prevalence and incidence , for example when the incidence go up then then the prevalence must go up also ^{[5]}
When studying etiology of a disease, it is better to analyse incidence rather than prevalence, since prevalence mixes in the duration of a condition, rather than providing a pure measure of risk.

