The number of events divided by the amount of person-time observed (E/NT) = incidence rate or density (not a proportion)
OR
E(vent)/N(umber)T(ime) = incidence rate or density
NT = person-time or product of persons times time
If the measure is a number of events divided by some number of persons at risk during some period, it is not a proportion (not a probability) because the denominator multiplies persons by time (100 persons followed for 2 years gives the same denominator as 200 persons followed for 1 year). The value of the fraction will change with the denominator and the units of the denominator are arbitrary.
If an incidence is presented as events per person-years, those person-years could be converted to person-months, or person-days, or even person-minutes with corresponding changes in the incidence rate (even though they all mean the same thing). And none of those fractions is constrained to be between 0 and 1. They can exceed 1. The concept of an incidence rate is not intuitive to everyone at first glance.
Incidence rates are useful in a variety of situations where you are comparing two or more populations where at least one population does not have individual-level data or where exposures are changing within subjects over time.
The denominator is the sum of the follow-up times for each individual. There are two methods for calculating the denominator.
The resulting ratio of E/NT is not a proportion (It may be greater than 1)
Value depends on unit of time used
An example: If the incidence rate of the event was 35 per 100 person-years, you can have anyone of the following combinations
In this example the time units are years but years could be replaced by days, months, decades, or any time unit and the rate would change accordingly. So the absolute value of the rate is determined by the units used in the denominator.
Incidence Rate Depends on the Time Units Used:
NOTE: time period during which rate is measured can differ from the units used (use data from 2 years of follow-up but report a rate per person-months)
Person-time concept may seem unfamiliar because often described as annual rate per 100,000 persons
A time units of follow-up on B persons is the same as B time units on A persons
Rates calculated over long time periods may be less meaningful
The assumption that the denominator of person-time units for a rate does not depend on the proportion of persons and amount of time in the calculation may result in a rate that is hard to interpret if it is based on a long period of follow-up.
There is no simple rule about how much time is too long for a period in which to calculate a rate since it depends on how rapidly the outcome being measured may change over time. For something that changes very little year to year, such as the overall mortality rate in the U.S., a period of time of several years might be reasonable.
Waiting time to a event is reciprocal of the incidence rate (1/rate)
If there are 3 events per year and the events are occurring at a constant rate, then a new event must occur on average, depending on how exactly the constant rate assumption is met, every 4 months.
So waiting time = 1/ person-time rate, a property to keep in mind.