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Person time and person years are measures used in epidemiology and medical research to estimate the amount of time that individuals are at risk of experiencing an event, such as developing a disease or dying. Person time is the sum of the time periods that each individual in a study is followed, whereas person years is person time expressed in years.

The formula for calculating person time is:

Person time = Σ (follow-up time for each participant)
where Σ denotes the sum of the follow-up times for each individual in the study.

The formula for calculating person years is the same as the formula for person time, but the result is expressed in years instead of units of time. Therefore, the formula for person years is:

Person years = Σ (follow-up time for each participant) / 365.25
where 365.25 is the average number of days in a year, taking into account leap years.

For example, let's consider a hypothetical study investigating the incidence of lung cancer among smokers and non-smokers. The study includes 1000 participants, 500 of whom are smokers and 500 are non-smokers. The follow-up period is 10 years.

If all participants are followed for the full 10 years, the person time for the entire cohort is:

Person time = 1000 participants x 10 years = 10,000 person-years

If we want to calculate person time separately for smokers and non-smokers, we need to take into account the fact that not all participants are followed for the full 10 years. Let's say that 20 smokers drop out of the study after 5 years and 30 non-smokers drop out after 7 years.

The person time for smokers is:

Person time for smokers = (500 smokers - 20 dropouts) x 5 years + 20 dropouts x (5 years/2) = 2,460 person-years

The person time for non-smokers is:

Person time for non-smokers = (500 non-smokers - 30 dropouts) x 7 years + 30 dropouts x (7 years/2) = 3,465 person-years

In this example, the total person-years for the entire cohort is the sum of the person-years for smokers and non-smokers:

Total person-years = 2,460 person-years + 3,465 person-years = 5,925 person-years

Person time and person years are important measures for calculating incidence rates (the number of new cases of a disease in a given time period) and mortality rates (the number of deaths in a given time period), and for comparing these rates between different groups of individuals, such as smokers and non-smokers in our example.

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