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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

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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).

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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

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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

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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

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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

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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.