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Giambattista Salinari and Gustavo De Santis

A third form of distortion can be generated by a change in the frailty of the cohorts un-
der scrutiny (Salinari and De Santis, 2015). The progressive reduction in infant, child and
juvenile mortality may have weakened the selection process that takes place at very young
ages. If frailer individuals are systematically associated with an earlier onset of ageing,
their increased proportions among the adults observed in this study (aged 25 years and
over) may be responsible for the earlier onset of ageing that has been observed. However,
the few estimates produced on this issue demonstrated that the variance of frailty declined
instead of increasing in more recent cohorts (Salinari and De Santis, 2014).
In a Gompertz-Makeham framework, the anticipation of the ageing onset may be ex-
plained by a reduction in “background mortality”. The Gompertz-Makeham model (Ma-
keham, 1860) stems from the Gompertz model where senescent (or age-dependent) mor-
tality is accompanied by an age-independent (or background) component of mortality
(Bongaarts, 2005). In this setting, a decrease in background mortality may seem to trigger
an earlier onset of ageing because senescent mortality becomes stronger than the back-
ground mortality at an earlier age. But the apparently intuitive notion of an age-indepe-
ndent component of mortality has thus far not been supported by the empirical analysis of
the causes of death (Carnes, Holden, Olshansky et al., 2006). Finally, Figure 2 which is a
plain description of what can be observed, with no statistics involved, strongly suggested
that the anticipation of ageing is not a statistical artifact.
Rate of ageing: Several empirical studies showed that in a Gompertzian framework, the
rate of ageing is higher in recent than in older cohorts (Finch, Beltrán-Sánchez and Crim-
mins, 2014). But these results may be partly biased by selection: the more rapid elimina-
tion of the frailest causes cohort mortality to decelerate at older ages (Vaupel, Manton and
Stallard, 1979), an effect that is arguably stronger when mortality is high that is, in older
cohorts.
In order to remove this spurious negative correlation between (initial) mortality and the
rate of ageing we adopted two strategies. First, we estimated the parameters of the Gom-
pertz model in an age range between 75 and 89 years when selection is still weak. This
method, rudimentary as it may be, has a great advantage over all available alternatives as it
does not require any assumptions on the initial distribution of frailty. The second strategy
was by using the Gamma-Gompertz model, where selection is kept under control - under
the hypothesis that frailty is Gamma distributed.
In both cases we obtained similar results, the rate of ageing is higher in recent cohorts.
If we had controlled for period effects as in Salinari and De Santis (2014) for instance, our
conclusions would have been reinforced because of the strong decline in mortality in the
past decades, thanks to medical innovations.
In short, both results (anticipation and acceleration of ageing) did not seem to depend
on the tools used for the analysis. To the best of our knowledge, the most convincing at-
tempt at an explanation that can be advanced at the moment relates to nutrition – ageing
may be triggered or at least stimulated by an abundance of food as the lab experiments on
animals suggest.
Our results are admittedly preliminary as none of the indicators used in this paper to
measure ageing and its speed is perfect and the association between ageing and nutrition is
only indirectly suggested and were not proven. We offered both conjectures (ageing is ac-
celerating and this acceleration is at least partly due to nutrition) to researchers to carry out
more stringent tests.

Supporting Information

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International Journal of Population Studies | 2015, Volume 1, Issue 1 55