These are incidence rates. They basically report the number of occurrences over a specific period "at risk" using the following formula.
Number of new cases of disease during specified time interval divided by Summed person-years of observation or average population during time interval.
This CDC page points out a few things to note regarding person-years
- Person-time has one important drawback. Person-time assumes that the probability of disease during the study period is constant, so that 10 persons followed for one year equals one person followed for 10 years. Because the risk of many chronic diseases increases with age, this assumption is often not valid.
- Long-term cohort studies of the type described here are not very common. However, epidemiologists far more commonly calculate incidence rates based on a numerator of cases observed or reported, and a denominator based on the mid-year population. This type of incident rate turns out to be comparable to a person-time rate.
- Finally, if you report the incidence rate of, say, the heart disease study as 2.5 per 1,000 person-years, epidemiologists might understand, but most others will not. Person-time is epidemiologic jargon. To convert this jargon to something understandable, simply replace “person-years” with “persons per year.” Reporting the results as 2.5 new cases of heart disease per 1,000 persons per year sounds like English rather than jargon. It also conveys the sense of the incidence rate as a dynamic process, the speed at which new cases of disease occur in the population.
So, where you asked
Does 35 per 100 person-years mean the recurrence is 35% or something else?
35 per 100 person-years means among the cohort studied, there were 35 cases per 100 people per year. If there were 1000 people in the cohort, you would expect, on average, 350 cases per year among those 1000 people.
You could take another 1000 people and get a different average because as previously highlighted in the CDC page
the risk of many chronic diseases increases with age,
Example provided at this CDC page with additional pointers added
Investigators enrolled 2,100 women in a study and followed them annually for four years to determine the incidence rate of heart disease. After one year, none had a new diagnosis of heart disease, but 100 had been lost to follow-up. After two years, one had a new diagnosis of heart disease, and another 99 had been lost to follow-up. After three years, another seven had new diagnoses of heart disease, and 793 had been lost to follow-up. After four years, another 8 had new diagnoses with heart disease, and 392 more had been lost to follow-up.
The study results could also be described as follows:
Number of new cases of the disease
No heart disease was diagnosed at the first year. Heart disease was diagnosed in one woman at the second year, in seven women at the third year, and in eight women at the fourth year of follow-up.
Person-years of observation
One hundred women were lost to follow-up by the first year, another 99 were lost to follow-up after two years, another 793 were lost to follow-up after three years, and another 392 women were lost to follow-up after 4 years, leaving 700 women who were followed for four years and remained disease free.
Calculate the incidence rate of heart disease among this cohort. Assume that persons with new diagnoses of heart disease and those lost to follow-up were disease-free for half the year,
and thus contribute ½ year to the denominator.
Numerator = number of new cases of heart disease
= 0 + 1 + 7 + 8 = 16
Denominator = person-years of observation
= (2,000 + ½ × 100) + (1,900 + ½ × 1 + ½ × 99) + (1,100 + ½ × 7 + ½ × 793) +
(700 + ½ × 8 + ½ × 392)
= 6,400 person-years of follow-up
or
Denominator = person-years of observation
= (0 × 0.5) + (1 × 1.5) + (7 × 2.5) + (8 × 3.5) + (100 × 0.5) + (99 × 1.5) + (793 × 2.5) +
(392 × 3.5) + (700 × 4)
= 6,400 person-years of follow-up
Person-time rate = Number of new cases of disease or injury during specified period Time each person was observed, totalled for all persons
= 16 ⁄ 6,400
= .0025 cases per person-year
= 2.5 cases per 1,000 person-years
