Standardization Methods
Standardization methods are used to adjust for the
effects of age and sex, and possibly other factors, in
the comparison of disease rates between two or more
populations. In what follows, adjustment for age will
be described, but all the methods can be extended to
adjust for other factors, such as sex.
Standardization methods have a long history, and
rank among the earliest statistical tools developed.
Keiding [21] has traced their origins to eighteenth
century actuarial mathematicians (see Actuarial
Methods), though they were reinvented a century
later by Neison and Farr. Neison was a famous
statistician of his day, writing regularly in the
Journal of the Statistical Society on a wide variety
of subjects. Farr was a government official who
worked as the “compiler of abstracts” in the
Office of the Registrar General for England and
Wales from 1839 to 1880. These two eminent
men recognized that the comparisons of crude
death rates (see Vital Statistics, Overview) were
not sufficient for examining mortality patterns over
time (see Morbidity and Mortality, Changing
Patterns in the Twentieth Century), or between
geographic areas (see Geographic Patterns of
Disease; Mortality, International Comparisons).
They also showed that the average age at death was
not an appropriate index for assessing differences in
mortality [25].
In 1841, Farr published age-specific death rates
and compared them to rates for the previous three
years to show how the pattern of mortality had
changed (Registrar General 1841; see [37]). Exam-
ination of age-specific rates (usually stratified by sex
as well) is widely considered to be the most com-
prehensive way of comparing disease rates across
populations. However, when many populations and
types of disease are to be studied, the number of
individual rates requiring scrutiny, rapidly becomes
awkwardly large. A further summarization of the data
is therefore required.
Farr introduced the idea of an external standard
population, against which other populations could
be compared (Registrar General, 1853; see [37]).
His standard was the so-called “healthy counties” in
England and Wales. He calculated a set of standard
death rates for these counties against which those for
other counties could be compared. He then took each
of the age-specific rates in the “healthy counties”
and multiplied them by the numbers of people of
comparable age in the county of interest. In this way
he derived an expected number of deaths in each
age group.
This was not an entirely new method, as Neison
had performed similar calculations on rates from two
areas of London to prove that the method of com-
paring average ages at death was flawed [25]. Farr,
however, went on to sum the age-specific expected
deaths to give the total number of deaths in each
county that would be expected if the mortality was the
same as in the “healthy counties”. The expected num-
ber could be compared with the observed number to
assess how each county’s mortality differed from that
in the standard (see Excess Mortality). Multiplying
the ratio of observed to expected deaths by the crude
rate in the standard population provided a standard-
ized rate for each county (Registrar General 1857;
see [37]). This method is now known as indirect stan-
dardization and it has remained in widespread use to
this day. Since then, other methods have been sug-
gested, but indirect standardization is possibly still
the most popular.
Rates and Ratios
Standardized rates, such as those produced by Farr,
are expressed as the number of deaths (or cases of
disease) per head of population. These can be com-
pared with crude rates in the standard population and
are expressed in the same units as normally used for
the presentation of rates (e.g. number of deaths per
100 000 population). Possibly more often, however,
standardized ratios are quoted. These compare the
disease burden (see Burden of Disease) in the popu-
lation of interest with that in the standard population.
A ratio of 1 therefore indicates that the populations
are similar in terms of the disease in question. Often,
ratios are presented as percentages by multiplying
them by 100, although this convention will not be
used here. Some of the methods that will be described
do not provide standardized rates per se, but mul-
tiplying the ratio by the crude rate in the standard
population is a way of obtaining an adjusted rate.
Choice of Standard Population
Most methods of standardization require a standard
population against which the population of interest

2 Standardization Methods
Table 1 Notation
Index Standard
Description population population
Population in age group i ni Ni
Total population n =
∑
ni N =
∑
Ni
Deaths/events in age group ia di Di
Total number of deaths/events d =
∑
di D =
∑
Di
Death/event rate in age group i ri = di/ni Ri = Di/Ni
Crude death/event rate r = d/n R = D/N
Number of deaths from all causes in age group i ai Ai
Proportion of all deaths due to cause of interest in pi = di/ai Pi = Di/Ai
age group i
Number of deaths from all causes other than the si = ai − di Si = Ai − Di
specific cause of interest in age group i
Odds of death from specific cause compared to mi = di/si Mi = Di/Si
other causes
Number of years in age group i yi
Mid-point of ith age group hi
aFor proportional analyses, this is the numbers of deaths from a specific cause in age group
i. For all other indices, this can refer to deaths from all causes or specific causes, or to other
disease rates.
(index population) is to be compared. Usually, the
choice of standard is fairly obvious. Thus, for exam-
ple, in trying to summarize age-specific rates for
geographic regions within a country, the national
population could be used as a standard. When exam-
ining rates for a variety of countries, a world popu-
lation or the population of the appropriate continent
would be suitable standards. Frequently, however, the
sum of the set of index populations to be examined
is used as the standard.
A variety of standard populations have been used
in the successive volumes of Cancer Incidence in
Five Continents [31]. These have included estimated
African and European and world populations, and
a truncated world population that only includes the
ages 35–64 in five year age bands. The reason
behind the choice of this unusual population was to
avoid the examination of rates being dominated by
cancers occurring at older ages; cancers at younger
ages may give more clues to etiology than those
occurring later in life. The most recent volume on
cancer incidence [35] has, however, used only the
approximate world population.
The important point to note is that different
choices of standard population can give rise to differ-
ent results. Thus identifying a suitable standard is a
prerequisite for applying standardization methods. All
standardized measures represent a comparison with a
chosen standard population.
Notation
The notation used for the formulas for standardized
rates and ratios varies widely. The notation used here
is given in Table 1.
Indirect and Direct Standardization
Indirect and direct standardization are the two most
widely used methods for standardizing rates. Other
methods have been proposed, but have not achieved
the same popularity.
Indirect Standardization
The information required for use of the indirect
method is as follows:
1. age-specific rates in a standard population;
2. the size of the index population in each age
group; and
3. the total number of deaths (or cases of disease)
in the index population.
The formula for the indirectly standardized ratio is
d
∑
niRi
.