demographic yearbook annuaire demographique 1951
demographic yearbook annuaire demographique 1951
demographic yearbook annuaire demographique 1951
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tions than do conventional central death rates such as<br />
those shown in table 17.<br />
Table 27 presents life table mortality rates. This rate<br />
represents the probability of dying during a given age<br />
interval, usually one year. It is the basic function of the<br />
life table and is commonly indicated by the symbol qx, the<br />
subscript referring to the age and values for specific ages<br />
being written q0 for "under 1", q1 for age 1 etc. The values<br />
shown in table 27 are expressed as 7,000 qx and represent the<br />
number dying per 1,000 persons reaching age x or the<br />
probability per 1,000 of dying within one year after reaching<br />
age x.<br />
The life table mortality rate differs from the central<br />
death rate in that it refers to persons reaching the given<br />
age during the course of a year rather than to persons of<br />
that age at the middle of the year. Thus the rates are<br />
similar in concept to the infant mortality rates shown in<br />
table 19. But the life table mortality rate for persons under<br />
1 year of age usually differs from the type of infant mortality<br />
rate shown in table 19 through being so adjusted<br />
that infant deaths are related to the cohort of births among<br />
which they occurred.<br />
The complete life table gives values for each single year<br />
of age. Most of the data presented in table 27 are of this<br />
type. An abridged life table gives values for grouped ages,<br />
usually 5-year age groups. Some of the data in table 27<br />
are of the latter type and are so noted. In these cases, the<br />
mortality rate is the probability of dying, not within one<br />
year after reaching the age indicated, but within 5 years<br />
of that age (or within the specified number of years).<br />
Details of procedure in life table construction vary somewhat,<br />
depending in large measure upon the availability<br />
and form of basic data. The values of qx are generally so<br />
derived as to correspond to the death rates of persons of<br />
that age in a particular period of time. The basic data<br />
ordinarily consist of (a) deaths in a given period classified<br />
by age and sex and (b) the mean population of each age<br />
and sex during that period. The most usual procedure is<br />
to utilize statistics of deaths in a three-year or five-year<br />
period centered at the census date so that the census figures<br />
can be taken as the mean population. Sometimes the period<br />
covered is that between two censuses and the population<br />
figures utilized are averages of the results of the two<br />
censuses. A correction for the effect of migration is occasionally<br />
made. In a few rare cases (for example, in India)<br />
approximate life tables have been computed without the<br />
use of data on deaths by deriving qx values from the comparison<br />
of the population in an age group as enumerated<br />
at one census with the survivors at the next census. It is<br />
common to make adjustments in order to correct for misstatements<br />
of age in the census and death registration data<br />
and in order to obtain successive values of qx which vary<br />
smoothly from one age to the next.<br />
Special problems arise in deriving qx values for the very<br />
young ages and for the end of life. For the young ages qx<br />
values are frequently obtained by using the statistics of<br />
births occurring in the last few years and estimating from<br />
them the number of persons at risk of dying in the period<br />
to which the life table relates. At the older ages data are<br />
frequently so scanty or unreliable that they have to be<br />
subjected to considerable manipulation if a reasonable<br />
series of qx values is to be derived from them. In many<br />
cases the life table qx values at the high ages do not depend<br />
in any wayan the registered deaths at those ages, but have<br />
been estimated on the basis of qx figures for younger ages.<br />
Table 28 gives Ix values from the same life tables as those<br />
shown in table 27. These figures were derived from the qx<br />
values and represent the number surviving to each age<br />
among 100,000 born alive and subjected thereafter to the<br />
mortality rates of the given life table. In other words, they<br />
are the probabilities, per 100,000, of surviving from birth<br />
to the exact age specified.<br />
Table 29 gives the "expectation of life" (ex) or the average<br />
number of years of life remaining for persons reaching<br />
the specified ages. These data are also based on the mortality<br />
rates of the life table and are to be interpreted strictly<br />
in terms of the underlying assumption that surviving cohorts<br />
are subjected to the age-specific mortality rates of the<br />
period to which the life table refers. Thus, in interpreting<br />
~:50 in the 1931-1941 life table for Switzerland, it may be<br />
said that, if males reaching age 50 were to experience for<br />
the rest of their lives the same age-specific mortality rates<br />
that obtained during the period 1931-1941, they would, on<br />
the average, live 21.3 years past the age of 50.<br />
The life table, though first developed for actuarial purposes,<br />
has many applications in the <strong>demographic</strong> field.<br />
Among these are: (1) the preparation of population projections<br />
by age and sex; (2) analysis of effects of mortality<br />
on the age and sex composition of a population; (3) comparisons<br />
of summarizing measures of mortality, as the life<br />
table death rate (the reciprocal of the expectation of life<br />
and birth), expectation of life at various ages etc.; (4) computation<br />
of net reproduction rates; and (5) the appraisal<br />
of the accuracy of census enumerations and vital registration<br />
data. In addition, life table techniques have been<br />
applied to the analysis of other types of <strong>demographic</strong> data,<br />
for example, in the computation of probabilities of marriage,<br />
specific for age and sex, on the basis of census data classified<br />
by marital status.<br />
The majority of life tables, and all those contained in<br />
this Yearbook, are based on qx values obtained from the<br />
deaths of persons of different ages occurring in the same<br />
period. Thus, they do not represent the actual mortality<br />
experience of anyone generation. Where the necessary<br />
statistics of population and deaths are available over long<br />
periods of time it is possible to calculate qx values representing<br />
the experience of a group or persons born in a<br />
specified period and traced throughout life. For example,<br />
a life table can be computed using for qo the infant mortality<br />
of 1880, for q1 a value derived from the deaths of<br />
infants aged one in 1881, for q2 a figure based on the deaths<br />
of children aged two in 1882 and so on. Such "generation"<br />
life tables may differ significantly from conventional tables<br />
in countries where mortality rates have been changing<br />
rapidly. However, not many such tables have been calculated<br />
and for most countries the required statistics are not<br />
available.<br />
The accuracy of life tables depends mainly upon the<br />
accuracy and completeness of the registration of deaths<br />
and of the enumeration of the population at the census.<br />
Deficiencies in death registration are likely to be greater<br />
than in census enumeration. Where this happens death<br />
rates are understated and the Ix and ex values are exaggerated.<br />
The mortality rates computed from population<br />
and death statistics at the very young ages are particularly<br />
likely to be understated, and such an error affects the Ix<br />
values throughout the table. As indicated earlier, infant<br />
mortality rates obtained by relating the number of infant<br />
deaths to the number of births in countries where registration<br />
is deficient may be either too low or too high, and the<br />
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