When all at risk people are not observed for the entire time period
This situation results when individuals migrate, die (due to other causes), are lost to follow-up, etc. Since the time under observation is not uniform, we calculate how much time each person was at risk and observed. This is called person-time, and may be expressed as person-months or person-years (py) of observation. The incidence rate thus calculated is also called incidence density, and the denominator is the sum of all person-times.
Let us consider person-years (py) in some detail:
If one person at risk is observed for one year, the person-time is equal to 1 person-year.
By extension, two persons at risk observed for one year yield 2 person-years of observation. One person observed for two years is also = 2 person-years. Four persons observed for 6 months each is also = 2 person-years.
Four persons were observed for four years, and the duration of observation for each is shown below:
Person-years are calculated for each year:
Year 1: All four persons were under observation. Therefore, we have 4 person-years of observation.
Year 2: Person 2 and 3 only were under observation. Therefore, we have 2 person-years of observation.
Year 3: Person 2 and 3 alone were under observation. Therefore, we have 2 person-years of observation.
Year 4: Only person 3 was under observation. Therefore, we have 1 person-year of observation.
The total person-time is the sum of person-years for each year: 4+2+2+1= 9 person-years.
If person 1 and 4 became cases after 1 year, then the incidence rate per 1,000 is calculated as:
(No. of new cases during specified time period/ Total person-time) *1,000 =2/9 *1,000 person-years