How slowing senescence translates into longer life expectancy

Abstract

Mortality decline has historically been largely a result of reductions in the level of mortality at all ages. A number of leading researchers on ageing, however, suggest that the next revolution of longevity increase will be the result of slowing down the rate of ageing. In this paper, we show mathematically how varying the pace of senescence influences life expectancy. We provide a formula that holds for any baseline hazard function. Our result is analogous to Keyfitz's 'entropy' relationship for changing the level of mortality. Interestingly, the influence of the shape of the baseline schedule on the effect of senescence changes is the complement of that found for level changes. We also provide a generalized formulation that mixes level and slope effects. We illustrate the applicability of these models using recent mortality decline in Japan and the problem of period to cohort translation.

An examination of black/white differences in the rate of age-related mortality increase

“…As medical technology begins to make headway against diseases at very old ages (e.g. cancers, dementias), the rate of aging may decline for both blacks and whites (Goldstein and Cassidy 2012). Like the results of this paper, this explanation is also consistent with a top down approach to aging-related mortality.…”

How life expectancy varies with perturbations in age-specific mortality

“…This relationship is a special case of the result derived in Goldstein and Cassidy (2012), where a mortality change of the form µ(x, ϵ) = µ((1 + ϵ)x) is investigated, which in the case of Gompertz-Makeham corresponds to a proportional change in b. iii) Change in the level of age-independent mortality: c(ϵ) = c + ϵ Because c is merely an age-independent additive term, this case is captured by the additive case derived under I),…”

“…Goldstein and Cassidy (2012) investigate the effect of specific mortality changes (level changes and senescence changes, corresponding to Gompertz a and b respectively) and apply their results to human mortality data. Caswell (2008Caswell ( , 2011aCaswell ( , 2011b revisits the question of perturbation analysis from the standpoint of Markov chains and matrix population models, thus complementing the continuous approach discussed here.…”

“…For instance, since Gompertz parameter b is often taken to reflect the rate of aging within the community of Gerontologists and Biodemographers, relationship (11) may support research concerned with changes in the rate of aging (as laid out in Goldstein and Cassidy (2012)). Additive age-independent perturbations in mortality as captured by relationships (2) and (12) may support studying the effect of "extrinsic" or "environmental" mortality, which plays an important role in biological applications, and in particular in evolutionary theories of aging.…”

The timing of the transition from mortality compression to mortality delay in Europe, Japan and the United States

“…Vaupel et al (2011) also emphasised that whereas a reduction in premature deaths diminishes lifespan disparities, a reduction in old-age mortality increases lifespan disparities. Goldstein and Cassidy (2012) showed that slowing of senescence, i.e. more reduction of death rates at older ages than at middle age, results in expansion of mortality, while an equal reduction in death rates across all ages results in a shift of the age-at-death distribution.…”