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OCR for page 64
CHAPTER 5
MORTALITY IN CHINA
METHODS
The accuracy of age reporting and the apparent con-
sistency of coverage in the censuses of 1953, 1964, and
1982 makes it possible to construct life tables for each
intercensal period, life tables that express the average
mortality during the intervals of 1953-64 and 1964-82.
Calculation of life tables expressing survival rates and
death rates beginning at age zero is possible because the
accurate age-specific fertility rates reported from the
fertility survey provide the basis for accurate deter-
mination of the number of births for each intercensal
year.
The construction of life tables is facilitated by a
set of relations that are exactly fulfilled in any
population that does not gain or lose by migration. The
relation relevant to the construction of an intercensal
life table is
N(x) = N(0)e
J.o r(y)dy
(Qx/20) '
where N(x) is the total number of persons who attain
exact age x during a specified time period, r(y) is the
average rate of increase of persons at age y during the
period, and Qx/Qo is the proportion of persons
surviving from birth to age x in a hypothetical cohort
subject at each age to the mean death rate at that age in
the intercensal period. The mean death rate is defined
as the total number of deaths in a given age interval
during the time period divided by the total number of
person-years-lived in that age interval. This equation
can be solved for Qx/Qo' i.e.,
64
OCR for page 65
65
~ Q r(y)dY
Qx/Qo = (N(x)/N(O))e
.
Consequently, to construct a life table it is necessary
only to estimate the total number who attain each single
year of age x during the intercensal period and to
calculate the average growth rates (lrO, lrl, lr2' etc.)
of persons at age zero to 1, 1 to 2, etc. during the
period. To be precise, these rates are the increase in
the number of persons at a given age (say 10-11) divided
by the number of person-years-lived at that age. If N(x)
is the number attaining age x, the number of person-years-
lived from x to x + 1 is approximately (N(x) + N(x+l))/2.
In short, a highly precise life table can be formulated
for the period between two censuses if the number attain-
ing each age N(x) can be determined with precision. If
the census age distributions recorded in the two censuses
are exact and the annual number of births is accurately
recorded, N(x) can be accurately calculated. The tech-
nique for accurate determination of N(x) is cohort
interpolation. For example, it is possible to estimate
the number of people who attained exact age 10 of those
who were 6-7 in 1953 and 17-18 in 1964 by subtracting a
fraction of the total decrease in this cohort during
those 11 years. The overall decrease is the number of
deaths the cohort experienced between ages 6-7 and ages
17-18; the relevant fraction of the decrease is the
proportion of deaths from 6.5 to 17.5 that occur between
6.5 and 10.0. This fraction--an interpolation factor--
can be taken roughly as 3.5/11 (on the assumption of an
even distribution of deaths) or, more precisely, from a
model life table at an approximately appropriate level of
mortality.9
When the number of people attaining age x has been
determined for each cohort that passes through x between
the censuses, N(x) is found by taking the total for all
such cohorts. The number at age zero is the number of
births between the censuses, which is equal to the sum of
the number of births calculated for each intercensal year
from the number of women at each age from 15 to 49
multiplied by the age-specific fertility rates. Annual
births are divided into male and female on the assumption
of 106 male births for every 100 female births (51.5
percent male).
OCR for page 66
66
LIFE TABLES
The female life tables are more soundly based than the
male life tables, because it was necessary to correct the
number of males at young adult ages (see above). Abridged
life tables for each sex are given in Table 9.
Expectation of life at birth (the mean duration of
life or average age at death) according to the average
mortality in 1953-64 was 42.2 years for males and 45.6
years for females. In 1964-82 it rose to 61.6 years for
males and 63.2 for females. ~ ~ ~ ~~
An increase or nearly zu
years in life expectancy in about 15 years is a very
rapid increase indeed, even when allowance is made for
the high mortality in 1959-61.
Two other data sources from which life tables for
China can be calculated were noted earlier, the 1973-75
epidemiological survey and a large-scale survey in 1978.
Figure 17 shows female mortality rates at ages 0-1, 1-5,
5-10, 10-15, . . . 80-85 for the two intercensal life
The age pattern
tables and the two survey-based sources.
of mortality is quite similar, and the evolution of
mortality rates is in the expected direction. Since the
sample data from the 1978 survey were inflated to match
exactly the official year-end population and the official
figure for the number of deaths, it follows that the
death rates derived from the survey are, on average, a
little too low.
The 1982 census collected information about deaths in
1981, classified by age and sex, in each household. A
life table calculated on the basis of those reported
deaths and the 1981 age distribution derived from the
1982 census was presented in March 1984 at the inter-
national seminar on the 1982 census held in Beijing
(Jiang et al., 1984-). According to this life table,
there was a further increase in expectation of life at
birth to 66.4 years for males and 69.4 years for females.
CRUDE DEATH RATES
The crude death rate from less to 1982 based on the
officially recorded number of deaths is shown in Table 10
together with an estimated sequence in which the rates
are adjusted for underreporting.
year is based on a crude estimate of the annual proportion
underreported, an estimate based on the assumption of
rising completeness of recorded deaths until 1964 and
The adjustment for each
OCR for page 67
67
TABLE 9 Abridged Life Tables, Male and Female, 1953-64
and 1964-82: China
Male
Female
Age 1 (x) m (x) e (x) 1 (x) m (x) e (x)
1953-64
0 1.00000 0.13789 42.20 1.00000 0.14212 45.58
1 0.87101 0.02354 47.38 0.86731 0.02586 51.47
5 0.79368 0.00630 47.85 0.78315 0.00708 52.85
10 0.76909 0.00384 44.31 0.75592 0.00360 49.67
15 0.75443 0.00498 40.11 0.74243 0.00314 45.52
20 0.73S88 0.00680 36.05 0.73087 0.00433 41.20
25 0.71127 0.00849 32.21 0.71521 0.00618 37.04
30 0.68168 0.01010 28.50 0.69344 0.00728 33.12
35 0.64807 0.01415 24.84 0.66863 0.01024 29.26
40 0.60372 0.01880 21.48 0.63S21 0.01332 2S.66
4S 0.54948 0.02373 18.3S 0.59427 0.01S60 22.25
50 0.48786 0.03133 1S.34 O.S4964 0.01894 18.86
SS O.41688 0.04424 12.S2 0.49989 0.02660 1S.48
60 0.33366 0.06446 10.00 0.43737 0.04169 12.32
6S 0.24090 0.09186 7.88 0.3S446 0.064S0 9.S9
70 0.15125 0.13100 6.10 0.25580 0.09824 7.31
75 0.077S4 0.18663 4.63 O.1S518 0.14834 5.44
80 0.02968 0.26500 3.47 0.07246 0.22303 3.96
85 0.00747 0.37475 2.56 0.02271 0.33336 2.82
90+ 0.00103 O.S3677 1.86 0.00388 O.S0614 1.98
1964-82
0 1.00000 0.05042 61.64 1.00000 0.05467 63.22
1 0.95082 0.00616 63.81 0.94679 0.00700 6S.75
5 0.92778 0.00292 61.36 0.92078 0.00334 63.57
10 0.91437 0.00122 S7.24 O.90SSS 0.00120 59.61
15 0.90882 0.00190 52.57 0.90014 0.00167 54.95
20 0.90022 0.00308 48.04 0.89267 0.00229 50.39
25 0.88648 0.00338 43.75 0.88249 0.00267 45.94
30 0.87162 0.00357 39.45 0.87077 0.00315 41.52
35 0.85618 0.00381 35.12 0.8S718 0.00374 37.14
40 0.84002 0.00442 30.74 0.84131 0.0043S 32.80
45 0.82165 0.00618 26.37 0.82322 0.00572 28.46
50 0.79664 0.01025 22.12 0.79999 0.00864 24.21
55 0.7S676 0.01681 18.14 0.76611 0.01319 20.16
60 0.69556 0.02793 14.51 0.71711 0.02165 16.36
65 0.60441 O.04507 11.29 0.64322 0.03542 12.93
70 0.48150 O.07363 8.51 0.53813 0.05755 9.95
75 0.33133 0.11940 6.22 0.40223 0.09216 7.44
80 0.17967 0.19251 4.39 0.25155 0.14698 5.39
85 0.06596 0.30775 3.01 0.11799 0.23294 3.79
90+ 0.01279 0.49929 2.00 0.03480 0.38571 2.59
OCR for page 68
68
.5000
.2000
.1000
.0500
.
.0200
.0100
.0050
.0020
.00 1 0
.0005
.0002
N9~.~'
,,,,
`9131 - If.
L
1 1 1 1 1 1 1 1 1
0 10 20 30 40 50 60 70 80 90
AGE
FIGURE 17 Age-Specific Mortality Rates, Females,
1953-64, 1964-82, 1973-75, and 1978: China
constant thereafter. The officially recorded deaths show
a large reduction in the crude death rate, interrupted by
an increase during the crisis years of 1958-61, with a
peak rate of over 25 deaths per 1,000 population in
1960.
Because deaths were much less completely recorded in
1953-64 than in 1964-82, it is clear that the true
decline in the death rate was much greater than indicated
by the official rates. The crisis years of greatly
elevated mortality are within the first intercensal
period, when in 11 years an estimated 38 percent of
deaths were not recorded, but completeness of recording
probably improved and the crisis was near the end of the
intercensal interval. In the next interval from 1964 to
1982 only 16 percent of deaths were not recorded. The
adjusted deaths given in Table 10 are based on the
assumption that about 55 percent of deaths were recorded
from 1953 to 1956 and that completeness of recording then
rose to 84 percent in 1964, with an average completeness
of 62 percent. On this assumption, about 66 percent of
deaths were reported in 1960, implying a crude death rate
of nearly 39 per 1,000. The number of deaths calculated
from the officially listed death rate is 5.90 million in
OCR for page 69
69
TABLE 10 Crude Death Rates (per 1,000), 1953-81:
China
Year
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
From Official
Sources
14.0
13.18
12.28
11.40
10.80
11.98
14.59
25.43
14.24
10.02
10.04
11.50
9.50
8.83
8.43
8.21
8.03
7.60
7.32
7.61
7.04
7.34
7.32
7.25
6.87
6.25
6.21
6.20
6.19
Roughly Corrected
for Understatement
25.5
29.1
22.4
20.8
19.0
20.4
23.3
38.8
20.5
13.7
13.0
13.5
11.1
10.4
9.9
9.6
9.4
8.9
8.6
8.9
8.3
8.6
8.6
8.5
8.1
7.3
7.3
7.3
7.3
1957 and 8.02 million in 1964. Had deaths followed a
linear trend from 5.9 million to 8.0 million over these
years, the total number of deaths in 1958-63 would have
been 41.8 million. The number derived from officially
recorded death rates is 57.4 million; by this calculation
OCR for page 70
70
the crisis led to an excess of about 16 million deaths
The number of deaths in 1957 and 1964 adjusted for
underregistration are 10.4 and 9.4 million. With a
linear trend, the adjusted total number of deaths in
1958-63 would have been 59.4 million. The actual total
(adjusted for estimated underregis- tration) is 86.2
million, an excess above the linear trend of about 27
million deaths. Thus, excess deaths are 16 million with
no allowance for underreporting and 27 million with a
rough allowance.
VARIATION OVER TIME
A comparison of the number of persons enumerated at each
single year of age in 1982 (from 0-1 to 30-31) with the
constructed number of births in each year from 1952 to
1982 provides partial additional evidence of the time
variation of mortality in China. If the number of births
from July 1 to June 30 were known exactly and if the
census enumeration had been exact, the ratio of the
enumerated population at age x to x + 1 to the number of
births from July 1 x years before 1982 to June 30 x + 1
years before 1982 would be a cohort survival rate. (See
note 4 for a description of how fiscal year births were
estimated.) The sequence of cohort survival rates
indicates which cohorts suffered heavy mortality and
which suffered relatively light mortality. These
survival rates are shown in Table 3 (above), as are the
number of births estimated for each fiscal year and the
number in the corresponding cohort in 1982. The survival
rate is 0.9 or higher for cohorts born in 1968-69 or
later, is at its lowest for cohorts born in 1966-67 and
1963-64, and is below 0.8 for all cohorts born before
1961-62 except 1959-60.
These calculated cohort survival rates do not support
the natural hypothesis of especially high infant and
child mortality in the cohorts born during the crisis
years. The survival rate for the birth cohort of 1960-61
is lower than the survival rate of adjacent cohorts, but
not as low as the survival rate of the cohorts born in
1958-59 and earlier. The implied proportions surviving
to age 5 in these cohorts, given the proportion surviving
from 1964 to 1982, are no higher than 75 to 80 percent.
Representative terms from entire chapter:
death rate
