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Giambattista Salinari and Gustavo De Santis

senescence is not the only factor and it is not necessarily the most important.
In order to indirectly gauge physiological ageing, biologists, gerontologists and demo-
graphers commonly use other measures. The most frequent among these is probably the
mortality rate doubling time (MRDT) or its equivalent, the rate of ageing. The general idea
behind it is that the pace at which mortality increases with age reflects the pace of the un-
derlying physiological process of molecular deterioration. Strehler and Mildvan (1960),
two forerunners in this line of thinking, indicated that the MRDT was shorter where life
expectancy at birth was higher or in other words, that modern populations age faster. This
empirical regularity also known as the “compensation” or Strehler-Mildvan law has sub-
sequently been confirmed by several other studies (Zheng, Yang and Land, 2011).
However, the MRDT has its drawbacks. Its estimates derive from aggregate (preferably
cohort) life tables but individuals are not homogeneous and as the frailest tend to die earli-
er, the composition of the group under observation changes over time. At advanced ages,
for example 90 years and over, this selection causes a detectable deceleration in the evolu-
tion of aggregate mortality with age (Vaupel, Manton and Stallard, 1979; Vaupel, Carey,
Christensen et al., 1998) which biases the estimated MRDT upwards. Populations with
shorter average life spans tend to display stronger mortality deceleration and therefore also
higher MRDT. In other words, the “compensation law” may be nothing more than an arti-
fact caused by selection.
To keep selection under control one needs sophisticated statistical models, a specific
definition of frailty and several assumptions, both about the functional form of the indi-
vidual hazard functions and on the distribution of frailty in the population. Unfortunately,
most of these assumptions refer to non-observable variables and cannot be tested directly
which undermines confidence in MRDT estimates.
In 2010, Gampe ventured that at very advanced ages (110+), human mortality may level
off producing what is generally known as the “mortality plateau” which turns out to be
consistent with only a few mortality models. It is not for instance, compatible with the ac-
celerated-life models (Finkelstein and Esaulova, 2006) or with the assumption that frailty
is log-normally distributed (Missov and Finkelstein, 2011). If a mortality plateau really
exists, the only meaningful way of describing human mortality seems to be the Gam-
ma-Gompertz model where the individual rate of ageing is constant, the hazards evolve
exponentially (à la Gompertz) and frailty is Gamma distributed (Missov and Vaupel,
2015).
In 2010, Vaupel conjectured that the individual rate of ageing might be constant in all
human populations but this “constant senescence hypothesis” has thus far received only
partial empirical corroboration (Salinari and De Santis, 2014; Zarulli, 2013). This paper
carefully studied the question of whether the rate of ageing is a constant together with a set
of related questions: at what age does the force of mortality begin to increase with age?
Why not earlier? Has this threshold age remained constant over time?
Our analysis encompassed seven European countries (Finland, France, Italy, the Neth-
erlands, Norway, Sweden and Switzerland) with good cohort data in the Human Mortality
Database (HMD). Salinari and De Santis (2014) had previously identified the series of
Nordic countries and those of Switzerland as the best for this type of analysis because
deaths were originally classified by single year of age and could be represented in paralle-
lograms on a Lexis diagram. This paper however, also uses mortality data from France and
Italy, albeit of somewhat lower quality, in order to exclude the possibility that the conclu-
sions apply only to the specific dietary regimes of selected countries.
For each of these countries, we analyzed the evolution of female mortality in the age
range of 25 to 99 years in the cohorts born between 1890 and 1919. We preferred females

International Journal of Population Studies | 2015, Volume 1, Issue 1 43