person-years

The CDC's Principles of Epidemiology in Public Health Practice sets out why a rate often needs a denominator made of time rather than of people. An incidence rate, which the same text also calls a person-time rate, divides the number of new cases during a period by the time each person was observed, totalled across everyone. One person followed for five years without developing the disease contributes five person-years. The denominator therefore stands for the total time the population was at risk of the condition and being watched for it.

That is what lets a study count people who arrive and leave at different moments. Someone lost to follow-up in year three, and someone diagnosed in year three, each contribute 2.5 person-years, on the convention that a person who left or fell ill part way through a year was free of the disease for about half of it. The simpler measure, the proportion of an initially disease-free group who develop the condition, cannot do that. The CDC's own worked example gives 2.5 cases per 1,000 person-years where the proportion gives an average of 1.9 per 1,000 per year, and notes that the proportion underestimates the true rate because it ignores the people lost to follow-up and assumes they stayed well.

One assumption comes with it, and the CDC states it plainly. Person-time treats the chance of the event as constant through the study period, so that ten people followed for one year counts the same as one person followed for ten. Because the risk of many chronic diseases rises with age, that assumption is often not valid. The same text offers the plainest translation of the jargon: replace person-years with persons per year, so 2.5 per 1,000 person-years reads as 2.5 new cases per 1,000 persons per year.