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

investigated the possible underestimation of mortality at oldest-old ages and discrepancies from an
established age-trajectory of mortality. Following a similar approach used by Coale and Kisker
(1986), we examined the ratio of the probability of dying at ages 60–70. We further estimated the
q
regression-based linear relationships between logit-transformed 10 60 and 25 70 and between
q
q and q from 13 countries together with the confidence ellipses that in-
logit-transformed 10 70 15 80
cludes 95% of data points in these 13 HMD countries. Given the high quality of demographic data
2
(and high R ) in the 13 HMD countries, the established regression relationship and the confidence
ellipse are effective comparisons to assess the reliability of mortality estimates at oldest-old ages for
q or the probabilities of
other countries, such as China. If the probabilities of dying q and 25 70
10 60
dying q and q for a country under study do not fall into the ellipse, there is evidence to suggest
15 80
10 70
that the death rates calculated from enumerated population and deaths in the census(es) for a giv-
en country could suffer from age-misreporting or death undercounts.
q
By comparisons with the regression-based linear relationship between logit-transformed 10 60
q from the 13 HMD countries (the strict criterion) — and the relationship implied by the
and 25 70
lower boundaries of their confidence ellipses (the lenient criterion) — we found that many Chinese
provinces in general had at least a 10% rate of underestimation in mortality at ages 70 or older in the
2000 and 2010 censuses if the death rates at ages 60 to 70 were accurate. Some western provinces
had more than a 40% rate of underestimation in the regression-based scenario. The rates of underes-
timation at oldest-old ages would be greater if underestimations at ages 60 to 70 were also taken into
account. Rates of underestimation were slightly smaller for probabilities of dying at ages 80–95.
For age trajectories of mortality, when the underestimation of mortality at ages 60–70 was not
taken into account, our findings revealed that death rates after age 90 were not reliable in most
provinces in the 2000 and 2010 Chinese censuses because the observed death rates after age 90 ei-
ther plateaued or declined with age, which is off the Kannisto curve. This distortion in mortality
rates increased with age for both sexes and for all provinces. Simply put, death rates are progres-
sively more unreliable with advancing age. Furthermore, if the rate of underestimation in mortality at
ages 60–70 was taken into consideration, the distortion would be even more severe.
Our conclusions about the underestimation and inaccuracy of age-trajectories of mortality at old-
est-old ages in China are strongly supported by the fact that death rates for China (overall and for
each province) began to decline at ages 90 to 95, which is implausible. In fact, there is no evidence
in the literature to suggest that human mortality declines after age 90 if the data on deaths and popu-
lation counts are accurate (Andreev and Gu, 2017). The decline in death rates after age 95 was only
found in HMD countries with lower-quality data and/or HMD countries at periods when their regis-
tration systems were incomplete and age exaggerations were documented (i.e., before 1900 or 1950).
For example, death rates in the United States declined at ages 98 and older in the 1950s and 1960s.
Nowadays, such declines are not observed because of improvements in vital registration systems;
and death rates are shown to increase continuously with age when based on death records with ex-
tensive age validation (see Bayo and Faber, 1983; Kestenbaum, 1992). Accordingly, Andreev and Gu
(2017) showed that mortality declines after age 100 disappeared in the United States by 2001–2011.
With regard to China, Gu and Dupre (2008) showed that observed mortality rates continued to in-
crease with age beyond age 100 in the 1998, 2000, and 2002 waves of the Chinese Longitudinal
Healthy Longevity Survey (CLHLS). In the 2000 Chinese census, however, death rates decreased
after age 95 (Gu and Dupre, 2008). The CLHLS is a nationwide survey focusing on oldest-old adults
and includes approximately 2,500–3,000 centenarians in each wave. Death rates were further calcu-
lated in later waves of the CLHLS (in 2005, 2008, and 2011) and it was shown that death rates con-
tinued to increase after age 95 to age 110 and beyond. The discrepancy is because age validation in
the CLHLS is much more restricted than in the Chinese census (Gu and Dupre, 2008); and therefore,
death rates calculated from the CLHLS are more reliable than those from the Chinese census.

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