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Incidence is the number of new events arising within a specified time period. The word incidence usually denotes incidence rate.
Incidence rate is the rate at which new events occur in a population. The numerator is the number of new events arising in a specified time period; the denominator is the population at risk of an event during this time period, sometimes expressed as person-time.
Observed annual incidence of x is therefore the number of new cases of x diagnosed in a given population over a year divided by the number of the population at risk of x during that year.
The use of person-time as opposed to just "time" enables you to handle situations where there are drop-outs in a study or where you have not been able to follow an entire cohort at risk to watch for the event under investigation. Using person-time calculations, the follow up period does not have to be the same for all individuals studied. Person-time for a group is the sum of the times of follow up for each participant in that group. See person-time incidence rate comparisons and Poisson rate confidence interval for more information.
Prevalence is the number of events in a population at a designated time. The word prevalence usually denotes point prevalence ratio.
Point prevalence is the number of persons with a disease or attribute at a point in time. Point prevalence ratio is expressed as below.
Period prevalence is the number of persons who have had the disease or attribute at any time over a specified period. Period prevalence is often expressed as below but it is not strictly a ratio it is a rate.
Prevalence ratio is equal to the incidence rate multiplied by the duration of the event.