How life expectancy varies with perturbations in age-specific mortality

Death rates at specific life stages mold the sex gap in life expectancy

Why do women live longer than men? Here, we mine rich lodes of demographic data to reveal that lower female mortality at particular ages is decisive-and that the important ages changed around 1950. Earlier, excess mortality among baby boys was crucial; afterward, the gap largely resulted from elevated mortality among men 60+. Young males bear modest responsibility for the sex gap in life expectancy: Depending on the country and time, their mortality accounts for less than a quarter and often less than a 10th of the gap. Understanding the impact on life expectancy of differences between male and female risks of death by age, over time, and across populations yields insights for research on how the lives of men and women differ.

Demographic perspectives on the rise of longevity

This article reviews some key strands of demographic research on past trends in human longevity and explores possible future trends in life expectancy at birth. Demographic data on age-specific mortality are used to estimate life expectancy, and validated data on exceptional life spans are used to study the maximum length of life. In the countries doing best each year, life expectancy started to increase around 1840 at a pace of almost 2.5 y per decade. This trend has continued until the present. Contrary to classical evolutionary theories of senescence and contrary to the predictions of many experts, the frontier of survival is advancing to higher ages. Furthermore, individual life spans are becoming more equal, reducing inequalities, with octogenarians and nonagenarians accounting for most deaths in countries with the highest life expectancy. If the current pace of progress in life expectancy continues, most children born this millennium will celebrate their 100th birthday. Considerable uncertainty, however, clouds forecasts: Life expectancy and maximum life span might increase very little if at all, or longevity might rise much faster than in the past. Substantial progress has been made over the past three decades in deepening understanding of how long humans have lived and how long they might live. The social, economic, health, cultural, and political consequences of further increases in longevity are so significant that the development of more powerful methods of forecasting is a priority.

The Mechanism Underlying Change in the Sex Gap in Life Expectancy at Birth: An Extended Decomposition

The relationship between differential mortality rates and differences in life expectancy is well understood, but how changing differential rates translate into changing differences in life expectancy has not been fully explained. To elucidate the mechanism involved, this study extends existing decomposition methods. The extended method decomposes change in the sex gap in life expectancy at birth into three components capturing the effects of the sex difference in mortality improvement (ρ-effect), life table deaths density by age (f-effect), and remaining life expectancy by age (e-effect). These three effects oppose and augment each other, depending on relative change in sex-differential mortality rates. The new method is applied to period data for 35 countries and cohort data for 25 countries. The results demonstrate how the mechanism, involving the three effects, operates to determine change in the sex difference in life expectancy. We observe the pivotal importance of the f-effect, which is predominantly negative because of lower female mortality, in favoring narrowing rather than widening of the sex gap, in shifting the overall effect to younger ages, and in exaggerating fluctuations due to crisis mortality. The new decomposition provides a more detailed basis for substantive analyses examining change in differences in life expectancy.

Trends in the Quantiles of the Life Table Survivorship Function

We offer a new approach for modeling past trends in the quantiles of the life table survivorship function. Trends in the quantiles are estimated, and the extent to which the observed patterns fit the unit root hypothesis or, alternatively, an innovative outlier model, are conducted. Then a factor model is applied to the detrended data, and it is used to construct quantile cycles. We enrich the ongoing discussion about human longevity extension by calculating specific improvements in the distribution of the survivorship function, across its full range, and not only at the central-age ranges. To illustrate our proposal, we use data for the UK from 1922 to 2013. We find that there is no sign in the data of any reduction in the pace of longevity extension during the last decades.

Quantifying the shape of aging

In Biodemography, aging is typically measured and compared based on aging rates. We argue that this approach may be misleading, because it confounds the time aspect with the mere change aspect of aging. To disentangle these aspects, here we utilize a time-standardized framework and, instead of aging rates, suggest the shape of aging as a novel and valuable alternative concept for comparative aging research. The concept of shape captures the direction and degree of change in the force of mortality over age, which—on a demographic level—reflects aging. We 1) provide a list of shape properties that are desirable from a theoretical perspective, 2) suggest several demographically meaningful and non-parametric candidate measures to quantify shape, and 3) evaluate performance of these measures based on the list of properties as well as based on an illustrative analysis of a simple dataset. The shape measures suggested here aim to provide a general means to classify aging patterns independent of any particular mortality model and independent of any species-specific time-scale. Thereby they support systematic comparative aging research across different species or between populations of the same species under different conditions and constitute an extension of the toolbox available to comparative research in Biodemography.

Why do lifespan variability trends for the young and old diverge? A perturbation analysis

BACKGROUND

Variation in lifespan has followed strikingly different trends for the young and old: while total lifespan variability has decreased as life expectancy at birth has risen, the variability conditional on survival to older ages has increased. These diverging trends reflect changes in the underlying demographic parameters determining age-specific mortality.

OBJECTIVE

We ask why the variation in the ages at death after survival to adult ages has followed a different trend than the variation at younger ages, and aim to explain the divergence in terms of the age pattern of historical mortality changes.

METHODS

Using simulations, we show that the empirical trends in lifespan variation are well characterized using the Siler model, which describes the mortality trajectory using functions representing early-life, later-life, and background mortality. We then obtain maximum likelihood estimates of the Siler parameters for Swedish females from 1900 to 2010. We express mortality in terms of a Markov chain model, and apply matrix calculus to compute the sensitivity of age-specific variance trends to the changes in Siler model parameters.

RESULTS

Our analysis quantifies the influence of changing demographic parameters on lifespan variability at all ages, highlighting the influence of declining childhood mortality on the reduction of lifespan variability, and the influence of subsequent improvements in adult survival on the rising variability of lifespans at older ages.

CONCLUSIONS

These findings provide insight into the dynamic relationship between the age pattern of survival improvements and time trends in lifespan variability.

Tempo effects may distort the interpretation of trends in life expectancy

OBJECTIVES

Recently, a new interpretation problem of trends in period life expectancy has been discussed in the demographic literature. The so-called tempo effects arise if large numbers of deaths are suddenly postponed. In such conditions, the life table inflates longevity gains in the population because it weights avoided deaths with the full remaining life expectancy. This article explains how such effects occur and indicates their relevance using an illustrative example.

STUDY DESIGN AND SETTING

Data of East and West Germany from the Human Mortality Database for the years 1990-2009 were used. We simulated a scenario that contrasts the observed life expectancy in West and East Germany with an alternative one based on the assumption of short-term postponements of deaths.

RESULTS

Our example demonstrates that if tempo effects have distorted changes in life expectancy, the pace of improvement in underlying mortality conditions could be over- and underestimated.

CONCLUSION

We recommend that the assumptions of the life table, in this case about the remaining life expectancy of avoided deaths, are carefully evaluated in all applications. Interdisciplinary efforts to develop models to detect and quantify tempo effects from life expectancy calculations should be put on the research agenda.

Perturbation analysis of indices of lifespan variability

A number of indices exist to calculate lifespan variation, each with different underlying properties. Here, we present new formulae for the response of seven of these indices to changes in the underlying mortality schedule (life disparity, Gini coefficient, standard deviation, variance, Theil's index, mean logarithmic deviation, and interquartile range). We derive each of these indices from an absorbing Markov chain formulation of the life table, and use matrix calculus to obtain the sensitivity and the elasticity (i.e., the proportional sensitivity) to changes in age-specific mortality. Using empirical French and Russian male data, we compare the underlying sensitivities to mortality change under different mortality regimes to determine the conditions under which the indices might differ in their conclusions about the magnitude of lifespan variation. Finally, we demonstrate how the sensitivities can be used to decompose temporal changes in the indices into contributions of age-specific mortality changes. The result is an easily computable method for calculating the properties of this important class of longevity indices.