1.3.5 Standardized Mortality Ratio
In a cohort study, the follow-up death rates are calculated and used to describe
the mortality experience of the cohort under investigation. However, the ob-
served mortality of the cohort is often compared with that expected from the
death rates of the national population (used asstandardorbaseline). The basis
of this method is the comparison of the observed number of deaths,d, from the
cohort with the mortality that would have been expected if the group had
experienced death rates similar to those of the national population of which the
cohort is a part. Letedenote the expected number of deaths; then the com-
parison is based on the following ratio, called thestandardized mortality ratio:
SMR¼
d
eThe expected number of deaths is calculated using published national life
tables, and the calculation can be approximated as follows:
eFlTwhereTis the total follow-up time (person-years) from the cohort andlthe
annual death rate (per person) from the referenced population. Of course, the
annual death rate of the referenced population changes with age. Therefore,
what we actually do in research is more complicated, although based on the
same idea. First, we subdivide the cohort into many age groups, then calculate
the productlTfor each age group using the correct age-specific rate for that
group, and add up the results.
Example 1.20 Some 7000 British workers exposed to vinyl chloride monomer
were followed for several years to determine whether their mortality experience
di¤ered from those of the general population. The data in Table 1.22 are for
deaths from cancers and are tabulated separately for four groups based on
years since entering the industry. This data display shows some interesting fea-
tures:
- For the group with 1–4 years since entering the industry, we have a
death rate that is substantially less than that of the general population
TABLE 1.22
Years Since Entering the Industry
Deaths
from Cancers 1–4 5–9 10–14 15 þ Total
Observed 9 15 23 68 115
Expected 20.3 21.3 24.5 60.8 126.8
SMR (%) 44.5 70.6 94.0 111.8 90.7
30 DESCRIPTIVE METHODS FOR CATEGORICAL DATA