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Danan Gu, Runlong Huang, Kirill Andreev, et al.

justments should be used before applying them.
Third, the accuracy of mortality beyond age 100 was not assessed in this study due to the limited
availability of data. However, we suspect that the underestimation of mortality among centenarians
is at the least same (or greater) than that for adults ages 80 to 99. Indeed, Zeng and Vaupel (2003)
showed that the age trajectory of mortality after age 100 was mildly below the Kannisto curve for
Han centenarians in the 1990 census.
A final limitation is that we assumed that migration had no effect on the relationships between
q and q and between q and q ; and had no effect on age-specific death rates.
10 60 25 70 10 70 15 80
However, it is likely that migration may increase or decrease population exposures and number of
deaths, thereby affecting mortality at these ages — especially before age 70. In provinces with rela-
tively large percentages of in- or out-migration, the effects of migration should be taken into account
to obtain more robust estimates.
Despite these limitations, our findings have important implications. To obtain reliable and mean-
ingful age-specific estimates of death at oldest-old ages in China, appropriate adjustments are needed
and the Kannisto model should be applied after adjustment. Additional research is needed to further
understand how to assess the underestimation and how to obtain factors for adjustment. In estimating
mortality at old and oldest-old ages, the Brass relational logit system (Brass, 1971), the modified
logit system for linking to a model or a standard life table (Murray, Ferguson, Lopez et al., 2003), or
flexible two-dimensional mortality model (Wilmoth, Zureick, Canudas-Romo et al., 2012) can be
used to estimate age-specific mortality if accuracy in the selected mortality indicators in the linking
function of the relational logit system can be ensured.
Age misreporting and death underreporting are challenging to demographic research and aging
studies (Zeng and Vaupel, 2003). Therefore, it is important to recognize and minimize data errors in
population estimates. Given the rapid growth of oldest-old populations, the accuracy of death counts
will not only impact demographic analysis, but will also have important implications for the distri-
bution and equity of social welfare systems. Currently, China has several systems to collect data on
deaths (see Liu, Li, Wei et al., 2016). Greater harmonization of these different collection systems
would help establish a more reliable system that would be more cost-effective than several unin-
tegrated systems. Fortunately, the China Center for Disease Control and Prevention has established
an internet-based nationwide cause-of-death reporting system since 2004 (Zhou, Wang, Zhu et al.,
2016). As of 2015, more than 93% of counties throughout China have been covered by this system
(Zhou and Yin, 2016). With further development of this system, we can expect that there will be fur-
ther improvements in the completeness of death registration and reductions in age misreporting and
the underestimation of deaths. It will also be possible for researchers to better assess the accuracy of
mortality at oldest-old ages in the census (or other surveys) and establish more robust age-trajecto-
ries of mortality at old and oldest-old ages.
5. Conclusions

Based on the 2000 and 2010 Chinese censuses, this study examined (i) the possible underestimation
of mortality at age 70 and older and (ii) age trajectories of mortality after age 80. We found sizeable
rates of underestimated mortality at old and oldest-old ages for most provinces and for both sexes.
We also found that the age-patterning of mortality after age 90 in most provinces was not reliable —
even when an overall adjustment for old ages or the oldest-old ages as a whole were applied. Overall,
provinces in eastern coastal areas (mainly with relatively high socioeconomic development)had
higher data quality; whereas provinces in western China had more problematic data. Age-sex-spe-
cific adjustments by province and/or the application of some classic models should be simultane-
ously used to obtain robust estimates; otherwise, direct estimates of mortality at oldest-old ages —
especially beyond age 95 in the Chinese censuses — should not be used. Improvements in the death
registration system may provide opportunities in the near future to further assess rates of underesti-

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