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On the Beginning of Mortality Acceleration

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Demography

Abstract

Physiological senescence is characterized by the increasing limitation of capabilities of an organism resulting from the progressive accumulation of molecular damage, which at group (cohort) level translates into, among other things, an increase in mortality risks with age. Physiological senescence is generally thought to begin at birth, if not earlier, but models of demographic aging (i.e., an increase in mortality risks) normally start at considerably later ages. This apparent inconsistency can be solved by assuming the existence of two mortality regimes: “latent” and “manifest” aging. Up to a certain age, there is only latent aging: physiological senescence occurs, but its low level does not trigger any measurable increase in mortality. Past a certain level (and age), molecular damage is such that mortality risks start to increase. We first discuss why this transition from latent to manifest aging should exist at all, and then we turn to the empirical estimation of the corresponding threshold age by applying Bai’s approach to the estimation of breakpoints in time series. Our analysis, which covers several cohorts born between 1850 and 1938 in 14 of the countries included in the Human Mortality Database, indicates that an age at the onset of manifest aging can be identified. However, it has not remained constant: it has declined from about 43 and 47 years, respectively, for males and females at the beginning of the period (cohorts born in 1850–1869) to about 31 for both males and females toward its end (cohorts born in 1920–1938). A discussion of why this may have happened ensues.

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Notes

  1. In this text, demographic aging denotes the phase when individual mortality risks accelerate irreversibly. Instead, senescence or physiological aging indicates the process characterized by the increasing limitation of capabilities of an organism due to the progressive accumulation of molecular damage.

  2. “Variation in initial cell number and damage rate will in turn affect the time taken before a threshold for dysfunction is crossed,” according to Kirkwood and Austad (2000:237; emphasis added).

  3. Because \( {\overline{k}}_0 \)is the mean age at which manifest (individual) aging begins, some individuals will start aging before or after \( {\overline{k}}_0 \). Thus, the aggregate (cohort) rate of aging will begin to increase some time before \( {\overline{k}}_0 \)and will continue to do so for a while after that, gradually passing from its initial level (supposedly, 0) to its final value: for instance, β = 0.1 in Vaupel’s (2010) hypothesis (see also Baudisch and Vaupel 2010). This is consistent with the empirical estimates of β made by, among others, Horiuchi (1997), Horiuchi et al. (2003), and Li et al. (2013). In short, \( {\overline{k}}_0 \)is not the age when mortality starts increasing following exactly a Gompertz pattern, with a possibly constant rate of β = 0.1.

  4. Noisy series should therefore be treated with special caution.

  5. Bai’s methodology works separately on the log-differentiated hazard functions of each cohort: mortality selection can be thought to operate within each cohort, but not at the group level. Note that \( \widehat{b} \) is calculated on the mean evolution of the rate of aging in each cohort and is therefore not affected by the size of cohorts, who have all the same weight in the procedure.

  6. The distribution of the error terms, however, can be proved to be approximately normal.

  7. Period effects can also be negative: wars and epidemics are the most relevant examples. In this context, we consider only positive period effects, such as medical breakthroughs, because we focus on mortality reduction.

  8. In the following, with the exception of Table 3 and Fig. 5, we focus only on women to avoid multiple presentations of parameters, tables, and figures and to minimize the effects of WWI and WWII.

  9. The expected magnitude of the break is β S − β L = 0.1 – 0 = 0.1.

  10. This pioneering analysis follows Finch et al.’s (1990) and Finch’s (1994) suggestion of focusing on intrinsic mortality. It may, however, suffer from a few biases because (1) it is based on period data; (2) it does not account for heterogeneity; and (3) mortality acceleration is supposed to begin when the first individuals of the (fictitious) cohort start aging.

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Acknowledgment

The research work has been financed by the P.O.R. Sardinia F.S.E. 2007–2013 in the context of research project 13/D3-2 developed at the University of Sassari.

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  1. Department of Economics and Business, University of Sassari, Sassari, Italy

    Giambattista Salinari

  2. Department of Statistics, Informatics, Application, University of Firenze, Firenze, Italy

    Gustavo De Santis

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  1. Giambattista Salinari
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Correspondence to Giambattista Salinari.

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Salinari, G., De Santis, G. On the Beginning of Mortality Acceleration. Demography 52, 39–60 (2015). https://doi.org/10.1007/s13524-014-0363-0

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