Computation and Measurement of Risk - Mathematics and Statistics for the Environment - page 189

The denominator of the person-time rate is the sum of all of the person-years for each study par-
ticipant. So, someone lost to follow-up in year 3 and someone diagnosed with the disease in year 3
each contributes 2.5 years of disease-free follow-up to the denominator.
8.3.2.1 Properties and Uses of Incidence Rates
An incidence rate describes how quickly disease occurs in a population. It is based on person-time,
so it has some advantages over an incidence proportion. Because person-time is calculated for each
subject, it can accommodate persons coming into and leaving the study. As noted in the previous
example, the denominator accounts for study participants who are lost to follow-up or who die dur-
ing the study period. In addition, it allows enrollees to enter the study at different times. 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, environ-
mental health practitioners 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 inci-
dent 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 1000 per-
son-years, environmental scientists might understand, but most others will not. Person-time is
environmental health 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 1000 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 are occurring in the
population.
Two example fractions commonly used in determining incidence rate are
Number of womeninFraminghamStudy who
dieddthrough last year fromheartdisease
Number of person-yearscontributed through lasttyear
by womeninitally enrolled in FraminghamStudy
Number of womeninState Anewlyydiagnosed with heartdiseasein 2011
Estimated numberofwomen living in StateAon July1, 2011
■ EXAMPLE 8.8
Problem: Investigators enrolled 2100 women in a study and followed them annually for 4 years to
determine the incidence rate of heart disease. After 1 year, none had a new diagnosis of heart dis-
ease, but 100 had been lost to follow-up. After 2 years, one had a new diagnosis of heart disease and
another 99 had been lost to follow-up. After 3 years, another 7 had new diagnoses of heart disease
and 793 had been lost to follow-up. After 4 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: 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. One hundred women were lost to follow-up by the first year, another 99 were lost to follow-up
after 2 years, another 793 were lost to follow-up after 3 years, and another 392 women were lost to
follow-up after 4 years, leaving 700 women who were followed for 4 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 1/2 year to the denominator.