Drewnowski's index to measure lifespan variation: revisiting the Gini coefficient of the life table

The Gini coefficient of the life table is a concentration index that provides information on lifespan variation. Originally proposed by economists to measure income and wealth inequalities, it has been widely used in population studies to investigate variation in ages at death. We focus on the complement of the Gini coefficient, Drewnowski's index, which is a measure of equality. We study its mathematical properties and analyze how changes over time relate to changes in life expectancy. Further, we identify the threshold age below which mortality improvements are translated into decreasing lifespan variation and above which these improvements translate into increasing lifespan inequality. We illustrate our theoretical findings simulating scenarios of mortality improvement in the Gompertz model, and showing an example of application to Swedish life table data. Our experiments demonstrate how Drewnowski's index can serve as an indicator of the shape of mortality patterns. These properties, along with our analytical findings, support studying lifespan variation alongside life expectancy trends in multiple species

The linear link: deriving age-specific death rates from life expectancy

The prediction of human longevity levels in the future by direct forecasting of life expectancy offers numerous advantages, compared to methods based on extrapolation of age-specific death rates. However, the reconstruction of accurate life tables starting from a given level of life expectancy at birth, or any other age, is not straightforward. Model life tables have been extensively used for estimating age patterns of mortality in poor-data countries. We propose a new model inspired by indirect estimation techniques applied in demography, which can be used to estimate full life tables at any point in time, based on a given value of life expectancy at birth. Our model relies on the existing high correlations between levels of life expectancy and death rates across ages. The methods presented in this paper are implemented in a publicly available R package

Dynamics of life expectancy and life span equality

As people live longer, ages at death are becoming more similar. This dual advance over the last two centuries, a central aim of public health policies, is a major achievement of modern civilization. Some recent exceptions to the joint rise of life expectancy and life span equality, however, make it difficult to determine the underlying causes of this relationship. Here, we develop a unifying framework to study life expectancy and life span equality over time, relying on concepts about the pace and shape of aging. We study the dynamic relationship between life expectancy and life span equality with reliable data from the Human Mortality Database for 49 countries and regions with emphasis on the long time series from Sweden. Our results demonstrate that both changes in life expectancy and life span equality are weighted totals of rates of progress in reducing mortality. This finding holds for three different measures of the variability of life spans. The weights evolve over time and indicate the ages at which reductions in mortality increase life expectancy and life span equality: the more progress at the youngest ages, the tighter the relationship. The link between life expectancy and life span equality is especially strong when life expectancy is less than 70 y. In recent decades, life expectancy and life span equality have occasionally moved in opposite directions due to larger improvements in mortality at older ages or a slowdown in declines in midlife mortality. Saving lives at ages below life expectancy is the key to increasing both life expectancy and life span equality

Senescent declines in elite tennis players are similar across the sexes

This is the author accepted manuscript. The final version is available from Oxford University Press via the DOI in this record.Note: the title in the document differs from the published titleData accessibility: Analyses reported in this article can be reproduced using the data provided in Sutter A, Barton S, Sharma MD, BaselliniU, Hosken D, Archer CR. Data from: senescent declines in elite tennis players are similar across the sexes. Dryad Digital Repository: http://dx.doi.org/10.5061/dryad.58dm217.Aging is characterized by rising mortality, declining fertility and declines in physiological function with age (functional senescence). Sex differences in the tempo and severity of survival and fertility declines are widespread, but it is less clear how often and how much trajectories of functional senescence diverge between the sexes. We tested how physiological function changed with age in male and female elite tennis players using first-serve speed (power) and first-serve accuracy as performance measures. We found absolute differences between the sexes with men serving faster, but less accurately than women. Both power and accuracy showed senescent declines but these began earlier for power. There were signals of trait-compensation, where players with pronounced power declines showed relative increases in accuracy, which might partially buffer against power deterioration. However, there were no sex differences in how either trait changed with age, contrasting with other sports. Sex differences in functional senescence are probably shaped by interactions between natural and sexual selection, the proximate costs of trait expression and a trait’s genetic architecture, and so are highly trait-specific. We discuss the strengths and potential pitfalls of using data from elite athletes to disentangle these complex interactions.This work was supported by a Swiss National Science Foundation fellowship (Grant P2ZHP3_164990) and a Leverhulme Trust grant awarded to DJH (Grant RF-2015-001)

Alternative Forecasts of Danish Life Expectancy

In the last three decades, considerable progress in mortality forecasting has been achieved, with new and more sophisticated models being introduced. Most of these forecasting models are based on the extrapolation of past trends, often assuming linear (or log-linear) development of mortality indicators, such as death rates or life expectancy. However, this assumption can be problematic in countries where mortality development has not been linear, such as in Denmark. Life expectancy in Denmark experienced stagnation from the 1980s until the mid-1990s. To avoid including the effect of the stagnation, Denmark’s official forecasts are based on data from 1990 only. This chapter is divided into three parts. First, we highlight and discuss some of the key methodological issues for mortality forecasting in Denmark. How many years of data are needed to forecast? Should linear extrapolation be used? Second, we compare the forecast performance of 11 models for Danish females and males and for period and cohort data. Finally, we assess the implications of the various forecasts for Danish society, and, in particular, their implications for future lifespan variability and age at retirement

A three-component approach to model and forecast age-at-death distributions

Mortality forecasting has recently received growing interest, as accurate projections of future lifespans are needed to ensure the solvency of insurance and pension providers. Several innovative stochastic methodologies have been proposed in most recent decades, the majority of them being based on age-specific mortality rates or on summary measures of the life table. The age-at-death distribution is an informative life-table function that provides readily available information on the mortality pattern of a population, yet it has been mostly overlooked for mortality projections. In this chapter, we propose to analyse and forecast mortality developments over age and time by introducing a novel methodology based on age-at-death distributions. Our approach starts from a nonparametric decomposition of the mortality pattern into three independent components corresponding to Childhood, Early-Adulthood and Senescence, respectively. We then model the evolution of each component-specific death density with a relational model that associates a time-invariant standard to a series of observed distributions by means of a transformation of the age axis. Our approach allows us to capture mortality developments over age and time, and forecasts can be derived from parameters’ extrapolation using standard time series models. We illustrate our methods by estimating and forecasting the mortality pattern of females and males in two high-longevity countries using data of the Human Mortality Database. We compare the forecast accuracy of our model and its projections until 2050 with three other forecasting methodologies