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Assessments of mortality at oldest-old ages by province in China's 2000 and 2010 censuses

2
females (R =0.93). The results of linear regression models based only on Sweden and Japan were
very similar to these four equations and thus not presented.
Based on the lower boundaries of the 95% confidence ellipses (Scenario A) and the four linear
ˆ
regression equations (Scenario B), we estimated 25 70 15 80
ˆ q and q for individual provinces in China.
We then estimated the average possible rates of underestimation for each five-year age group at ag-
es 70–95 and at ages 80–95, respectively (see Tables 1 and 2). For the probabilities of dying at ag-
es 70–95 (Table 1), under Scenario A (lenient criterion), we found almost no underestimation for
China as a whole for males and females in both censuses (because these four data points fell within
the 95% confidence ellipse). About 10–15 provinces were below of the lower boundary of the
95% confidence ellipses in the two censuses for males and females — assuming the probability of
dying at ages 60–70 was accurate. Under Scenario B, however, the underestimation rate of 25 70
q
for China as a whole was 11.5% for males and 22.2% for females in the 2000 census; and 16.5% for
males and 24.3% for females in the 2010 census, respectively, if the linear associations between
q and q was valid and if q was accurate in both censuses. For individual provinces,
25 70 10 60 10 60
most provinces had 10% or higher rates of underestimations. In some cases, the rates of underesti-
mation were more than 40%. For both scenarios, provinces in western China had greater rates of
underestimation than in eastern-coastal provinces; females had greater rates of underestimation than
males; and the 2010 census had larger rates of underestimation than the 2000 census. The patterns of
underestimation for probabilities of dying at ages 80–95 (Table 2) were similar to probabilities of
dying at ages 70–95.
To account for possible underestimations in mortality at ages 60 to 70 (or ages 70–80) in Chi-
nese censuses, we applied 1.15 to death rates at these two age groups, respectively (see Appendix A:
Note 3). The results were reported in Appendixes B1 and B2 and showed that these rates of underes-
timation were larger than those reported in Table 1. Appendix C re-plotted scattered distributions of
two pairs of probabilities of dying with these adjustments, and with few exceptions, the vast majority
of provinces were located below the lower boundary of the confidence ellipses.
3.2 Death Rates after Age 90 in Many Provinces are not Reliable

Figures 2 and 3 compare sex-age-specific death rates for ages 80–84 to ages 95–99 between the un-
adjusted observations and the fitted Kannisto-model estimates. Results are presented for all of China
and selected provinces in the 2000 and 2010 censuses, together with observed and fitted death rates
for Japanese males and females in the 2000s. For illustrative purposes, death rates from ages 60-64
to ages 75-79 were also presented.
For China as a whole, the age trajectory of mortality from the Kannisto model fit the data
well before age 90 for males and females if death rates at ages 60-70 were accurate. On average, age
trajectories of mortality in some eastern-coastal provinces fit the Kannisto curves better than other
provinces; whereas the age trajectories in some western provinces — such as Ningxia and Gansu —
fit poorly. It is also clear from the figures that the observed age-trajectories of mortality in the
2010 census fit the Kannisto curve slightly better than in the 2000 census. Figures 2 and 3 further
demonstrate that some provinces in China — such as Hainan, Tibet, and Xinjiang — exhibited
a crossover with the age-trajectory of mortality for Japanese females in the 2000s. Considering the
fact that Japanese females have the lowest mortality in the contemporary world and that Japan has
among the highest quality of data on death rates, the crossover of these provinces with Japan sug-
gests a substantial underestimation of death rates at oldest-old ages.
Table 3 presents the relative root-mean-square error (RMSE) between the fitted and observed
death rates for ages 80 to 99 by province in the 2010 census. With few exceptions, provinces with
majority populations of ethnic minorities generally had greater values of RMSE than other provinces
where Han Chinese dominate. The RMSE was much higher after age 90 than ages below 90, indi-
cating a deviation from the expected line for the age trajectory of mortality after age 90. On average,

8 International Journal of Population Studies | 2016, Volume 2, Issue 2