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

Thatcher, Kannisto and Andreev, 2002). In doing so, researchers have used various mathematic func-
tions to simulate age trajectories of mortality at oldest-old ages. Based on age-specific mortality da-
ta between the ages of 80 and 98 from 1960 to 1990 in 13 countries with the world's highest quality
of mortality data (Austria, Denmark, United Kingdom (England and Wales), Finland, France, Ger-

many (West), Iceland, Italy, Japan, the Netherlands, Norway, Sweden, and Switzerland ), Thatcher,
Kannisto, and Vaupel (1998) showed that mortality estimates from ages 80 to 120 derived from the
Kannisto model fit the data best compared with those from Gompertz, Weibull, Heligman-Pollard,
Quadratic, and Logistic models. The Human Mortality Database (HMD) uses the Kannisto model to
adjust mortality from ages 80 to 110 for its included countries (Wilmoth, Andreev, Jdanov et al.,
2007). The United Nations Population Division (UNPD) also uses the Kannisto model in its biennial
World Population Prospects (UNPD, 2015). One reason that the Gompertz model fails to accurate-
ly capture mortality rates at oldest-old ages is possibly because it does not account for the decelera-
tion in death rates at advanced ages (Horiuchi and Wilmoth, 1998). The wide recognition of the
Kannisto model and its broad application in estimating human mortality at oldest-old ages clearly
establishes it as a relatively standard model to assess whether the trajectory of age-specific mortality
at oldest-old ages in a given population follows the Kannisto function. Moreover, the increasing rate
of mortality with age embedded in the Kannisto model serves as an important indicator to assess
discrepancies in age trajectories of death rates between the expected trajectory and the observed tra-
jectory. In other words, the quality of mortality data is likely to be problematic if the age-specific
death rates at oldest-old ages do not follow the Kannisto model.
It is problematic to study mortality at oldest-old ages without reliable data; however, obtaining
accurate data on deaths at advanced ages is challenging, even in many developed countries. For ex-
ample, Andreev and Gu (2017) recently examined the accuracy of death rates at oldest-old ages in
the United States in 1959–1969 and 2001–2011 using the rate of mortality increase with age in oc-
togenarians (aged 80–89), nonagenarians (aged 90–99), and centenarians (aged 100+) in comparison
with the 13 countries with world's highest quality of mortality data used by Thatcher and colleagues
(1998). They found that the United States had very low growth rates in all three age groups in the
period 1959–1969 compared with those in the 13 countries. Together with other evidence, Andreev
and Gu concluded that U.S. death rates for overall mortality of aged 80 and over in the period
1959–1969 were not reliable. However, they found that the quality of death rates in 2001–2011 had
greatly improved. These conclusions are further substantiated by the fact that birth registration was
not complete in the United States before the 1930s.
In studying mortality at older or oldest-old ages in populations where data at these ages are not
available or reliable, the relational logit system can be applied to obtain indirect estimates (Brass,
1971). The purpose of the relational logit system is to find a regression-based relationship between a
study population and a standard mortality scheme (normally from a model life table or a
scheme based on reliable data) by linking some reliable logit-transformed mortality indicators (nor-
mally two of three indicators: infant/child mortality, adult mortality, or life expectancy) of the study
population with the corresponding indicators in a standard scheme (see Murray, Ferguson, Lopez et
al., 2003; Rob, 2013; Wilmoth, Zureick, Canudas-Romo et al., 2012).
In China, some scholars have applied the abovementioned methods to census data. For example,
Zeng and Vaupel (2003) applied a similar approach with six models used by Thatcher and col-
leagues (1998) to oldest-old mortality data in the 1990 census — for Han Chinese who have the
highest quality of age-reporting data in China because they use a lunar calendar to accurately re-
member their dates of birth (Coale and Li, 1991; Zeng and Gu, 2008). Zeng and Vaupel demon-
strated that the Kannisto function fit the observed data best from ages 80 to 96 compared with five
other models. However, they also found that the death rates among Han Chinese were not reliable
after age 96 in the 1990 census. Duan and Shi (2015) applied Gompertz, Makeham, Beard, Kannisto,
and Logistic functions to data in the 2000 and 2010 Chinese censuses and concluded that the logistic

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