Statistical Methods in Medical Research 4ed

alone may explain a difference in crude rates (just as, in Table 15.6, the contrast
between the `crude' proportions with factor A was strongly affected by the
different sex distributions in the disease and control groups). An example is
given in Table 19.1 (on p. 664), which shows the numbers of individuals and
numbers of deaths separately in different age groups, for two countries: A,
typical of highly industrialized countries, with a rather high proportion of
individuals at the older ages; and B, a developing country with a small proportion
of old people. The death rates at each age (which are called age-specific
death rates) are substantially higher for B than for A, and yet the crude death
rate is higher for A than for B.
The situation here is precisely the same as that discussed at the beginning of
§15.6, in connection with Example 15.6. Sometimes, however, mortality has to be
compared for a large number of different populations, and some form of adjustment
for age differences is required. For example, the mortality in one country
may have to be compared over several different years; different regions of the
same country may be under study; or one may wish to compare the mortality for
a large number of different occupations. Two obvious generalizations are: (i) in
standardizing for factors other than, or in addition to, ageÐfor example, sex, as
in Table 15.6; and (ii) in morbidity studies where the criterion studied is the
occurrence of a certain illness rather than of death. We shall discuss the usual
situationÐthe standardization of mortality rates for age.
The basic idea in standardization is that we introduce a standard population
with a fixed age structure. The mortality for any special population is then
adjusted to allow for discrepancies in age structure between the standard and
special populations. There are two main approaches: direct and indirect methods
of standardization. The following brief account may be supplemented by reference
to Liddell (1960), Kalton (1968) or Hill and Hill (1991).
The following notation will be used.
Standard Special
(1) (2) (3) (4) (5) (6)
Age
group Population Deaths
Death rate
(2)=(1) Population Deaths
Death rate
(5)=(4)
1 N1 R1 P1 n1 r1 p1
.
i Ni Ri Pi ni ri pi
.
19.3 Rates and standardization 661
k Nk Rk Pk nk rk pk