EPIDEMIOLOGY 375
was given as x to the mid-year population aged x : for each of
these quantities the age given as x would range from exact
age x (the x th birthday) to the day before the ( x 1)th birth-
day, and would thus average x 1/2. This mortality rate is
designated m x , such that m x d x / p x , where p x midyear
population aged x.
If we go back 6 months to the beginning of the calendar
year, the average age of those encumbered in the middle of
the year at x 1/2 would become x , but they should also be
augmented by half of the deaths (also of average age), on the
plausible assumption that they were divided approximately
equally between the two halves of the year. This is of course
because none would have died by the beginning of the year,
and furthermore their average age would then be x rather
than x 1/2. Now we can obtain the mortality rate at exact
age x sinceq x d x /( p x 1/2 d x )Dividing through by p x , this becomesq x m x /(1 1/2 m x )thus relating the two mortality rates.SURVIVAL RATES ADJUSTED FOR AGEStrictly speaking, the life table is a fi ction, in the sense that
it represents an instantaneous picture or snapshot of the
numbers of living at each single year of age, on the assump-
tion that the mortality rates at the time of its construction
remain unchanged at each period of life. Mortality rates
have generally tended to fall, though they are rather more
stable, on a worldwide basis, than they have been earlier in
the century. However, there are modern-day exceptions, as
is seen in the old Soviet Union countries where life expec-
tancy is declining (Men et al., 2003). Even though life
expectancy was lower than that for Western Europe, a dra-
matic decline has been observed after the fall of the Soviet
Union around 1991. This decline in life expectancy, an
increase in premature deaths, has been attributed to social
factors and alcohol use, resulting in increased incidence of
ischemic heart disease, infectious diseases (e.g., tubercu-
losis), and accidental deaths (Men et al., 2003). Changes
in mortality in the old Soviet Union show the dynamics of
epidemiology. However, for the world overall, especially
Westernized nations, this means that as time goes on the life
table is more pessimistic in its predictions than is the real-
ity of life experience. Nevertheless the life table can be put
to a number of uses within the fi eld of epidemiology, quite
apart from its commercial use in the calculation of life-
insurance premiums for annuities. One of these uses is in
the computation of age-adjusted survival rates. Frequently
in comparing the experience of different centuries, whether
geographically separated or over periods of time, with
respect to survival from cancer, a 5-year period is taken
as a convenient measure. Cancer patients are not of courseimmune to other causes of death, and naturally their risk of
them will increase progressively with age. In consequence,
a comparison using 5-year survival rates of two groups of
cancer patients, one of which included a greater proportion
of elderly patients than the other, would be biased in favor
of the younger group. By using the life table it is possible to
obtain 5-year survival rates for each group separately, taking
full account of their makeup by sex and age, but considering
only their exposure to the general experience of all causes of
death. The ratio of the observed (crude) 5-year survival rate
of the cancer patients to their life-table 5-year survival rate
is known as the “age-adjusted” or “relative” survival rate.
Changes in survival, by age adjustment, resulting from a
dramatic health effect, as seen in Africa from AIDS (Figure
5), can greatly impact the regional or national survival table.
When this procedure is done for each group, they are prop-
erly comparable since allowance has been made for the bias
due to age structure. Clearly the same mode of adjustment
should be used for periods other than 5 years, in order to
obtain survival rates free of bias of specifi c age structures.
If the adjusted rate becomes 100% it implies that there is no
excess risk of death over the “natural” risk for age; a rate
above 100% seldom occurs, but may imply a slightly lower
risk than that natural for age.OTHER USES OF THE LIFE TABLEThe ratio of / 70 to / 50 from the life table for females will give
the likelihood that a women of 50 will live to be 70. If a man
marries a woman of 20, the likelihood that they will both
survive to celebrate their golden wedding (50 years) can be
obtained by multiplying the ratio / 75 // 25 (from the male life
table) by / 70 // 20 (from the female life table). These are not
precise probabilities, and furthermore they include a number
of implicit assumptions, some of which have already been
discussed. Similar computations are in fact used, however,
sometimes in legal cases to assess damages or compensation,
where their degree of precision has a better quantitative basis
than any other.INFANT MORTALITY RATESIn the construction of life tables, as has been noted, it is nec-
essary to use a mortality rate centered on an exact age rather
than the conventional rate, centered half a year later. Only
one of the mortality rates in common use is defi ned in the
life-table way, and that is the infant mortality rate (IMR),
which measures the number of children born alive who do
not survive to their fi rst birthday. The numerator is thus the
number of deaths under the age of 1 year, and the denomina-
tor is the total number of live births; usually both refer to the
same calendar year, although some of its deaths will have
been born in the previous year, and likewise some deaths in
the following year will have been among its births. The rate
is expressed as the number of infant deaths per thousand
live births, and it has changed from an average of 150 inC005_011_r03.indd 375C005_011_r03.indd 375 11/18/2005 10:25:41 AM11/18/2005 10:25:41 AM