Elisabetta Barbi

The plateau of human mortality: Demography of longevity pioneers

Mortality rates level off at extreme age The demography of human longevity is a contentious topic. On the basis of high-quality data from Italians aged 105 and older, Barbi et al. show that mortality is constant at extreme ages but at levels that decline somewhat across cohorts. Human death rates increase exponentially up to about age 80, then decelerate, and plateau after age 105. Science, this issue p. 1459 A study of centenarians in Italy suggests that human mortality is approximately constant in extreme old age. Theories about biological limits to life span and evolutionary shaping of human longevity depend on facts about mortality at extreme ages, but these facts have remained a matter of debate. Do hazard curves typically level out into high plateaus eventually, as seen in other species, or do exponential increases persist? In this study, we estimated hazard rates from data on all inhabitants of Italy aged 105 and older between 2009 and 2015 (born 1896–1910), a total of 3836 documented cases. We observed level hazard curves, which were essentially constant beyond age 105. Our estimates are free from artifacts of aggregation that limited earlier studies and provide the best evidence to date for the existence of extreme-age mortality plateaus in humans.

Hétérogénéité des générations et âge extrême de la vie

Recent gains in life expectancy among the elderly have noticeably contributed to increasing average life expectancy in developed countries. The old and oldest old are reaching thresholds that were unthinkable 30 or 40 years ago. Are recent gains due to increased longevity among a growing proportion of the population? Or are such gains the harbinger of new frontiers that may announce the further ?extension? of the survival curve? Deeper comprehension of underlying mechanisms hinges on models that consider the impact of heterogeneity in individual frailty. In this paper, we analyse the mortality trajectories of French women born between 1820 and 1879. We applied a classic frailty model and a mixture frailty model accounting for individual differences both in the level of mortality and in the rate of aging. The survival trajectories obtained with these models were used to estimate the maximum life span. Moreover, a non-parametric approach was applied to female centenarians born in France between 1870 and 1879 to estimate the extreme age at death. Results confirm that population heterogeneity can be an important factor in the dynamics of mortality at the oldest ages. In particular, the mixture frailty model may fit the data better and estimate the possible maximum life span more accurately. A tendency towards an increasing human life span clearly emerges, without however establishing whether a limit in fact exists.

Segmentation of mortality surfaces by hidden Markov models

Abstract Gender-specific mortality surfaces are panels of time series of mortality rates that allow to examine the temporal evolution of male and female mortality across ages. The analysis of these surfaces is often complicated by time-varying effects that reflect the association of age and gender with mortality under unobserved time-varying conditions of the population under study. We propose a hidden Markov model as a simple tool to estimate time-varying effects in mortality surfaces. Under this model, age and gender effects depend on the evolution of an unobserved (hidden) Markov chain, which segments each time series of rates according to time-varying latent classes. We describe the details of an efficient EM algorithm for maximum likelihood estimation of the parameters and suggest a straightforward parametric bootstrap routine to compute standard errors. These methods are illustrated on cardiovascular and cancer mortality rates, observed in Italy during the period 1980–2014.

Response to Comment on “The plateau of human mortality: Demography of longevity pioneers”

Beltrán-Sánchez et al. based their comment on misleading calculations of the maximum survival age. With realistic numbers of people attaining age 105 and the estimated plateau, the Jeanne Calment record is indeed plausible.

Demographic Techniques: Inverse Projection

This article is a revision of the previous edition article by R. McCaa, volume 5, pp. 3464–3471,