such as age, gender, and race.Specific ratesconsider these di¤erences among
subgroups or categories of diseases.Adjustedorstandardized ratesare used to
make valid summary comparisons between two or more groups possessing dif-
ferent age distributions.
The annualcrude death rateis defined as the number of deaths in a calendar
year divided by the population on July 1 of that year (which is usually an esti-
mate); the quotient is often multiplied by 1000 or other suitable power of 10,
resulting in a number between 1 and 100 or between 1 and 1000. For example,
the 1980 population of California was 23,000,000 (as estimated by July 1) and
there were 190,237 deaths during 1980, leading to
crude death rate¼190 ; 247
23 ; 000 ; 000
1000
¼ 8 :3 deaths per 1000 persons per yearThe age- and cause-specific death rates are defined similarly.
As for morbidity, the disease prevalence, as defined in Section 1.1, is a pro-
portion used to describe the population at a certain point in time, whereas
incidenceis a rate used in connection with new cases:
incidence rate¼number of persons who developed the disease
over a defined period of timeða year;sayÞ
number of persons initially without the disease
who were followed for the defined period of timeIn other words, the prevalence presents a snapshot of the population’s morbid-
ity experience at a certain time point, whereas the incidence is aimed to inves-
tigate possible time trends. For example, the 35,238 new AIDS cases in Exam-
ple 1.11 and the national population without AIDS at the start of 1989 could
be combined according to the formula above to yield an incidence of AIDS for
the year.
Another interesting use of rates is in connection withcohort studies, epi-
demiological designs in which one enrolls a group of persons and follows them
over certain periods of time; examples include occupational mortality studies,
among others. The cohort study design focuses on a particular exposure rather
than a particular disease as in case–control studies. Advantages of a longitudi-
nal approach include the opportunity for more accurate measurement of expo-
sure history and a careful examination of the time relationships between expo-
sure and any disease under investigation. Each member of a cohort belongs to
one of three types of termination:
- Subjects still alive on the analysis date
- Subjects who died on a known date within the study period
- Subjects who are lost to follow-up after a certain date (these cases are a
14 DESCRIPTIVE METHODS FOR CATEGORICAL DATA