Perturbation analysis of indices of lifespan variability

An Overlapping Cohorts Perspective of Lifespan Inequality

A growing literature investigates the levels, trends, causes, and effects of lifespan inequality. This work is typically based on measures that combine partial cohort histories into a synthetic cohort, most frequently in a period life table, or focus on single (completed) cohort analysis. We introduce a new cohort-based method-the overlapping cohorts perspective-that preserves individual cohort histories and aggregates them in a population-level measure. We apply these new methods to describe levels and trends in lifespan inequality and to assess temporary and permanent mortality changes in several case studies, including the surge of violent deaths in Colombia in the 1990s and 2000s and cause-deleted exercises for top mortality causes such as cardiovascular diseases and cancer. The results from our approach differ from those of existing methods in the timing, trends, and levels of the impact of these mortality developments on lifespan inequality, bringing new insights to the study of lifespan inequality.

Reassessing socioeconomic inequalities in mortality via distributional similarities

Commonly used measures of socioeconomic inequalities in mortality, such as the slope and the relative index of inequality, are based on summary measures of the group-specific age-at-death distributions (e.g. standardized mortality rate or life expectancy). While this approach is informative, it ignores valuable information contained in the group-specific distributions. A recent approach applied a measure of distributional dissimilarity (the non-overlap index) to measure lifespan stratification. In this paper, we rigorously evaluate and further implement the multi-group extension of the non-overlap index ( S P ) to measure socioeconomic inequalities in mortality across a number of groups, and assess whether differences across countries and over time are driven by mortality or compositional changes in two applications with different data availability: educational groups (Sweden and Denmark) and groups defined by an area-level deprivation measure (England). Our findings suggest that the multi-group S P is sensitive not only to changes in the means or variances, but also to broader mortality changes that affect distributional shapes. The method can be employed to any context where mortality rates by age are available by sub-groups. Furthermore, levels and trends in mortality inequalities computed with the multigroup S P often differ compared to other conventional summary-based measures. Moreover, we find that the contribution of mortality changes to changes in inequalities is generally greater than that of the changes in the population composition. Whereas levels and trends of inequalities may depend on whether life expectancy- or lifespan variation-based measures are employed, the multi-group S P provides a holistic perspective by capturing both dimensions simultaneously.

Unpacking occupational and sex divides to understand the moderate progress in life expectancy in recent years (France, 2010's)

PURPOSE

The growth in life expectancy (LE) slows down recently in several high-income countries. Among the underlying dynamics, uneven progress in LE across social groups has been pointed out. However, these dynamics has not been extensively studied, partly due to data limitations. In this paper, we explore this area for the 2010 decade using recent French data.

METHODS

We utilize the recent change in French census mortality follow-up data (EDP) and apply P-spline models to estimate LEs across five occupational classes (OCs) and indicators of lifespan heterogeneity (edagger) within these OCs, for seven triennial periods (2011-2013 to 2017-2019).

RESULTS

First, we found a similar ranking of OCs along the LE gradient over time and across sexes, from manual workers to higher-level OCs. Noteworthy, the lowest LE in women overlaps with the highest one in men drawing a sex-OC gradient. Second, we observe varying progress of LEs. In women, LE increases in higher-level OCs meanwhile it levels off in manual workers, so that the OCs gap widens (up to 3.4 years in 2017-2019). Conversely, in men LE stalls in higher-level OCs and increases in manual workers so that the gap, which is much larger than in women (+5.7 years in 2017-2019), is tending to narrow. Finally, the lifespan homogenizes in OCs only when LE is low.

CONCLUSION

Overall, the limited LE progress in France results from LE stalling in the middle of the sex-OC gradient, though LE increases at both ends. At the lower end, LE progress and lifespan homogenization suggest that laggards benefit recently improvements achieved earlier in other OCs. At the upper end, LE progress may come from a vanguard group within higher-lever OC, benefiting new sources of improvements. These findings underscore the need for further research to explore the diverse mortality dynamics coexisting in the current health landscape.

Contributions of injury deaths to the changes in sex gaps in life expectancy and life disparity in the Nordic countries in the 21st century

OBJECTIVE

The objective of this study was to provide novel comparative insights on the contributions of injury deaths to the changes in sex gaps in life expectancy (SGLE) and sex gaps in life disparity (SGLD) across Nordic countries.

STUDY DESIGN

Retrospective demographic analysis of aggregated mortality data.

METHODS

To compute life expectancy (LE)/life disparity (LD), annual data on age- and sex-specific causes of death from the World Health Organization mortality database were used to construct abridged life tables for two periods: 2000-2002 and 2016-2018 (2014-2016 for Norway). The contributions of injury deaths to the changes in the SGLE and SGLD between these two periods were decomposed by age and cause using a continuous-change model.

RESULTS

Females' LE and LD advantages due to injury deaths narrowed by 0.16-0.44 (0.06-0.35) years for LE (LD) over time. While self-inflicted injuries consistently played a predominant role in contributing to the SGLE/SGLD in all countries in both periods, in all countries but Finland, transport accidents had the greatest contributions to the narrowing SGLE/SGLD. Widening SGLE due to self-inflicted injuries in Iceland and due to falls in Sweden were unique to these countries. Accounting for >20% of total contributions of injury deaths, the age group of 20-24 years had the greatest contributions to the narrowing SGLE/SGLD. Deaths due to falls in older ages and assault in younger ages generally contributed to the widening SGLE/SGLD.

CONCLUSIONS

Injury deaths, particularly transport accidents, contributed significantly to the narrowing SGLE and SGLD across Nordic countries, with cross-country variations in age- and cause-specific patterns. The results suggest the need for injury prevention policies targeting self-inflicted injuries in younger and falls in older males.

Flexible transition timing in discrete-time multistate life tables using Markov chains with rewards

Discrete-time multistate life tables are attractive because they are easier to understand and apply in comparison with their continuous-time counterparts. While such models are based on a discrete time grid, it is often useful to calculate derived magnitudes (e.g. state occupation times), under assumptions which posit that transitions take place at other times, such as mid-period. Unfortunately, currently available models allow very few choices about transition timing. We propose the use of Markov chains with rewards as a general way of incorporating information on the timing of transitions into the model. We illustrate the usefulness of rewards-based multistate life tables by estimating working life expectancies using different retirement transition timings. We also demonstrate that for the single-state case, the rewards approach matches traditional life-table methods exactly. Finally, we provide code to replicate all results from the paper plus R and Stata packages for general use of the method proposed.

Ranking Age-at-Death Distributions Using Dominance: Robust Evaluation of United States Mortality Trends, 2006-2021

Diverging mortality trends at different ages motivate the monitoring of lifespan inequality alongside life expectancy. Conclusions are ambiguous when life expectancy and lifespan inequality move in the same direction or when inequality measures display inconsistent trends. We propose using nonparametric dominance analysis to obtain a robust ranking of age-at-death distributions. Application to U.S. period life tables for 2006-2021 reveals that, until 2014, more recent years generally dominate earlier years, implying improvement if longer lifespans that are less unequally distributed are considered better. Improvements were more pronounced for non-Hispanic Black and Hispanic individuals than for non-Hispanic White individuals. Since 2014, for all subpopulations-particularly Hispanics-earlier years often dominate more recent years, indicating worsening age-at-death distributions if shorter and more unequal lifespans are considered worse. Dramatic deterioration of the distributions in 2020-2021 during the COVID-19 pandemic is most evident for Hispanic individuals.

Cross-sectional Average Length of Life Entropy ( H CAL ): International Comparisons and Decompositions

Keyfitz and Leser's life table entropy was proposed to serve as a relative inequality in mortality measure. Entropy considers the variation around the age at death relative to the length of lifespan in a population, allowing comparisons across time and populations. It is used widely in period and cohort applications. Here, we propose extending this measure and present an index that incorporates the history of survival of all cohorts present at a given time, namely the cross-sectional average length of life entropy, or CAL-entropy ( H CAL ). We decompose cross-population differences of CAL-entropy into the contribution of longevity and lifespan variation, and the change of those differences across time. Our illustrations show that populations are converging regarding lifespan inequality. Lifespan variation holds a noticeable share in the CAL-entropy gap among selected European populations. Longevity held once a pronounced share in CAL-entropy differences and their change, but its influence has receded over the years. The US demonstrates a unique trend where it performs worse across time compared to the selected European populations, and lifespan variation has played a major role in this process. This study signals the importance of lifespan variation in reducing inequality in mortality among developed and longevous populations.

The Lifespan Disparity Dataset: An open repository on inequality and polarization in length of life (1950-2021)

Monitoring health is key for identifying priorities in public health planning and improving healthcare services. Life expectancy has conventionally been regarded as a valuable indicator to compare the health status of different populations. However, this measure is simply the mean of the distribution of the length of life and, as such, neglects individual disparities in health outcomes. In this paper, we use life tables from the UN World Population Prospects to develop the most comprehensive dataset of lifespan inequality and polarization for 258 countries and areas for the period 1950-2021. These extensive series on lifespan distributions provide access to crucial information for researchers, practitioners, and the general public, thus contributing to a better understanding of health differences within and between nations.

Premature Death as a Normative Concept

The practical goal of preventing premature death seems uncontroversial. But the term 'premature death' is vague with several, sometimes conflicting definitions. This ambiguity results in several conceptions with which not all will agree. Moreover, the normative rationale behind the goal of preventing premature deaths is masked by the operational definition of existing measures. In this article, we argue that 'premature death' should be recognized as a normative concept. We propose that normative theories should be used to justify measures of premature death to provide them with normative validity and public legitimacy.

Forecasting Inequalities in Survival to Retirement Age by Socioeconomic Status in Denmark and Sweden

In Denmark and Sweden, statutory retirement age is indexed to life expectancy to account for mortality improvements in their populations. However, mortality improvements have not been uniform across different sub-populations. Notably, in both countries, individuals of lower socioeconomic status (SES) have experienced slower mortality improvements. As a result, a uniform rise in the statutory retirement age could disproportionally affect these low-SES groups and may unintentionally lead to a reverse redistribution effect, shifting benefits from short-lived low-SES individuals to long-lived high-SES individuals. The aim of this study is twofold: to quantify and contextualise mortality inequalities by SES in Denmark and Sweden, and to assess how indexing retirement age will affect future survival to retirement age by SES in these countries. We used Danish and Swedish registry data (1988-2019), to aggregate individuals aged 50 + based on their demographic characteristics and SES. We computed period life tables by year, sex, and SES to estimate the difference in survival across different SES groups. We then forecast mortality across SES groups to assess how indexing retirement age will affect survival inequalities to retirement age, using two forecasting models-the Mode model and the Li-Lee model. Mortality inequalities are comparable in Denmark and Sweden, even though the latter generally has higher survival. We also find that indexing retirement age to life expectancy will have two main consequences: it will reduce the probability of reaching retirement for all SES groups, particularly those of low SES, and time spent in retirement will be reduced, particularly for those of high SES.

Global health inequality: analyses of life disparity and healthy life disparity

BACKGROUND

Alongside average health measures, namely, life expectancy (LE) and healthy life expectancy (HLE), we sought to investigate the inequality in lifespan and healthy lifespan at the worldwide level with an alternative indicator.

METHODS

Using data from the Global Burden of Diseases, Injuries, and Risk Factors Study 2019, we evaluated the global distribution of life disparity (LD) and healthy life disparity (HLD) for 204 countries and territories in 2019 by sex and socio-demographic index (SDI), and also explored the relationships between average and variation health indicators.

RESULTS

Substantial gaps in all observed health indicators were found across SDI quintiles. For instance, in 2019, for low SDI, female LE and HLE were 67.3 years (95% confidence interval 66.8, 67.6) and 57.4 years (56.6, 57.9), and their LD and HLD were 16.7 years (16.5, 17.0) and 14.4 years (14.1, 14.7). For high SDI, female LE and HLE were greater [83.7 years (83.6, 83.7) and 70.2 years (69.3, 70.7)], but their LD and HLD were smaller [10.4 years (10.3, 10.4) and 7.9 years (7.7, 8.0)]. Besides, all estimates varied across populations within each SDI quintile. There were also gaps in LD and HLD between males and females, as those found in LE and HLE.

CONCLUSION

In addition to the disadvantaged LE and HLE, greater LD and HLD were also found in low SDI countries and territories. This reveals the serious challenge in achieving global health equality. Targeted policies are thus necessary for improving health performance among these populations.

Cause-of-Death Determinants of Lifespan Inequality

We propose a novel decomposition approach that breaks down the levels and trends of lifespan inequality as the sum of cause-of-death contributions. The suggested method shows whether the levels and changes in lifespan inequality are attributable to the levels and changes in (1) the extent of inequality in the cause-specific age-at-death distribution (the "Inequality" component), (2) the total share of deaths attributable to each cause (the "Proportion" component), or (3) the cause-specific mean age at death (the "Mean" component). This so-called Inequality-Proportion-Mean (or IPM) method is applied to 10 low-mortality countries in Europe. Our findings suggest that the most prevalent causes of death (in our setting, "circulatory system" and "neoplasms") do not necessarily contribute the most to overall levels of lifespan inequality. In fact, "perinatal and congenital" causes are the strongest drivers of lifespan inequality declines. The contribution of the IPM components to changes in lifespan inequality varies considerably across causes, genders, and countries. Among the three components, the Mean one explains the least lifespan inequality dynamics, suggesting that shifts in cause-specific mean ages at death alone contributed little to changes in lifespan inequality.

Contributions of age groups and causes of death to the sex gap in lifespan variation in Europe

Much less is known about the sex gap in lifespan variation, which reflects inequalities in the length of life, than about the sex gap in life expectancy (average length of life). We examined the contributions of age groups and causes of death to the sex gap in lifespan variation for 28 European countries, grouped into five European regions. In 2010-15, males in Europe displayed a 6.8-year-lower life expectancy and a 2.3-year-higher standard deviation in lifespan than females, with clear regional differences. Sex differences in lifespan variation are attributable largely to higher external mortality among males aged 30-39, whereas sex differences in life expectancy are due predominantly to higher smoking-related and cardiovascular disease mortality among males aged 60-69. The distinct findings for the sex gap in lifespan variation and the sex gap in life expectancy provide additional insights into the survival differences between the sexes.

Contributions of avoidable mortality to the sex gap in life expectancy and life disparity in Iran

BACKGROUND

Public health policies and healthcare quality play a pivotal role on the health outcome level and disparities across sociodemographic groups. However, there is little evidence on their role on disparities in life expectancy (LE) and life disparity (LD) in low and middle income countries. The present study aimed to assess the contributions of avoidable mortality, as a measure of inter-sectoral public health policies and healthcare quality, into the sex gap in LE (SGLE) and LD (SGLD) in Iran.

METHODS

Latest available data of death causes, according to the ICD codes, for Iran was obtained from the WHO mortality database for the period 2015-2016. An upper age limit of 75 years was applied to define avoidable causes of death. LD was measured as the average years of life lost at birth. The SGLE and SGLD (both females minus males) were decomposed by age and cause of death using a continuous-change model.

RESULTS

Females, on average, outlived males for 3.8 years (80.0 vs. 76.2 years) with 1.9 lower life years lost (12.6 vs. 14.4 years). Avoidable causes accounted for 2.5 (67%) and 1.5 (79%) years of the SGLE and SGLD, respectively. Among avoidable causes, injury-related deaths followed by ischaemic heart disease had the greatest contributions to both SGLE and SGLD. Across age groups, the age groups 55-59 and 60-64 accounted for the greatest contributions of avoidable causes to SGLE (0.3 years each), while age groups 20-24 and 55-59 had the greatest contributions to SGLD (0.15 years each). Lower mortality rates for females than males in age groups 50-74 years accounted for about half of the SGLE, while age groups 20-29 and 50-64 years accounted for around half of SGLD.

CONCLUSION

More than two third of the SGLE and SGLD in Iran were attributed to the avoidable mortality, particularly preventable causes. Our results suggest the need for public health policies targeting injuries in young males as well as lifestyle risk factors including smoking in middle aged males in Iran.

Reducing socioeconomic health inequalities? A questionnaire study of majorization and invariance conditions

We study the appeal of basic preference conditions that underpin health inequality indices, including the widely used concentration index. We did a lab experiment in which 349 respondents had to choose repeatedly between two policies that generated a distribution of income and health among five groups in society. We found stronger support for preference conditions that focus on inequality in the marginal distribution of health (and income) than for preference conditions that favor reduced correlation between both dimensions. Respondents' choices were more in line with the principle of income related health transfers when policies did not affect the ranking of groups in terms of health. Respondents also expressed more concern about the correlation between income and health when health was expressed as a shortfall rather than an attainment. Support for the preference conditions was unaffected when all groups in society experienced the same absolute or relative health change.

Trends in mortality patterns in two countries with different welfare models: comparisons between CUBA and Denmark 1955–2020

Cuba and Denmark represent states with different welfare models that have reached the same level of life expectancy. The purpose was to investigate and compare mortality changes in the two countries. Systematically collected information on population numbers and deaths for the entire Cuban and Danish populations was the basis of life table data used to quantify differences in the change in age-at-death distributions since 1955, age-specific contributions to differences in life expectancy, lifespan variation, and other changes in mortality patterns in Cuba and Denmark. Life expectancy in Cuba and Denmark converged until 2000, when the increase in life expectancy for Cuba slowed down. Since 1955, infant mortality has fallen in both countries but mostly in Cuba. Both populations experienced compression of mortality as lifespan variation decreased markedly, primarily due to postponement of early deaths. Given the different starting point in the mid-1900s and living conditions for Cubans and Danes, health status achieved among Cubans is striking. A rapidly ageing population is challenging both countries, but Cuban health and welfare are further burdened by a deteriorating economy in recent decades.

A distributional approach to measuring lifespan stratification

The study of the mortality differences between groups has traditionally focused on metrics that describe average levels of mortality, for example life expectancy and standardized mortality rates. Additional insights can be gained by using statistical distance metrics to examine differences in lifespan distributions between groups. Here, we use a distance metric, the non-overlap index, to capture the sociological concept of stratification, which emphasizes the emergence of unique, hierarchically layered social strata. We show an application using Finnish registration data that cover the entire population over the period from 1996 to 2017. The results indicate that lifespan stratification and life-expectancy differences between income groups both increased substantially from 1996 to 2008; subsequently, life-expectancy differences declined, whereas stratification stagnated for men and increased for women. We conclude that the non-overlap index uncovers a unique domain of inequalities in mortality and helps to capture important between-group differences that conventional approaches miss.

A global assessment of the impact of violence on lifetime uncertainty

Uncertainty around age at death, or lifetime uncertainty, is a key public health indicator and a marker of inequality in survival. How does the extent of violence affect lifetime uncertainty? We address this question by quantifying the impact of violence on dispersion in the ages at death, the metric most used to measure lifetime uncertainty. Using mortality data from the Global Burden of Disease Study and the Internal Peace Index between 2008 and 2017, we find that the most violent countries are also those with the highest lifetime uncertainty. In the Middle East, conflict-related deaths are the largest contributor to lifetime uncertainty. In Latin America, a similar pattern is attributable to homicides. The effects are larger in magnitude for men, but the consequences remain considerable for women. Our study points to a double burden of violence on longevity: Not only does violence shorten individual lives, but it also makes the length of life less predictable.

State-Level Trends in Lifespan Variability in the United States, 1960-2019: A Research Note

State-level disparities in life expectancy are wide, persistent, and potentially growing in the United States. However, the extent to which differences in lifespan variability by state have changed over time is unclear. This research note describes trends in lifespan variability for the United States overall and by state from 1960 to 2019 using period life table data from the United States Mortality Database. Lifespan disparity at birth (e0†) decreased over time in the United States overall from 14.0 years in 1960-1964 to 12.2 in 2015-2019. Lifespan variability decreased in all states, but states differed in the level and pace with which these changes occurred. Southern states and the District of Columbia exhibited consistently higher (i.e., less equitable) levels of lifespan variability than the nation overall. Conversely, lifespan variability was lower among several states in the Northeast (e.g., Connecticut and Massachusetts), Upper Midwest (e.g., Iowa, Minnesota, and Wisconsin), and West (e.g., California, Oregon, Utah, and Washington). We observe a particularly worrisome trend of increasing lifespan variability for the United States overall and for most states from 2010-2014 to 2015-2019. Monitoring state-level trends in lifespan variability has the potential to inform policies designed to ameliorate population health disparities.

The contributions of injury deaths to the gender gap in life expectancy and life disparity in Eastern Mediterranean Region

BACKGROUND

Injury deaths constitute a major avoidable cause of death affecting life expectancy to a different degree in men and women. This study quantified the contributions of injury deaths to the gender gap in life expectancy (GGLE) and life disparity (GGLD) in nine Eastern Mediterranean Region (EMR) countries.

METHODS

We retrieved annual data on age-sex specific causes of death from the World Health Organization mortality database for EMR countries with at least 2-year consecutive data during 2010-2019. The injury-related deaths were categorized into five groups: transport accidents, other accidental injuries, intentional self-harm, assault and events of undetermined intent. Considering women as the reference, the GGLE and GGLD were decomposed by age and causes of death, using a continuous-change model.

RESULTS

The largest and smallest GGLE were observed in Kuwait (5.2 years) and Qatar (- 1.2 years), respectively. Qatar (- 2.2 years) and Oman (0.2 years) had the highest and lowest GGLD. The highest contributions of injury deaths to the GGLE/GGLD were seen in Libya (1.8/- 1.2 years), followed by Iran (1.2/- 0.8 years). Among injury causes, transport accidents were the leading cause of GGLE in all countries but Libya and Morocco, with Iran having the greatest contributions (0.6 years). Injury deaths in men aged 15-29 years accounted for 33% [41%] (Kuwait) to 55% [65%] (Oman) of total GGLE [GGLD] attributable to injury deaths.

CONCLUSIONS

High injury deaths, particularly transport accidents, among young men contributed substantially to the GGLE and GGLD across nine EMR countries in this study. This highlights the need for implementing preventing policies to reduce the burden of injury deaths specifically in young men.

The role of age inequalities in cause of death in the slow pace of epidemiological transition in India

In developed countries, low disparity in lifespan contributed by the reduction in the burden of noncommunicable diseases (NCDs) is the key to advances in epidemiological transition. Contrarily, India passing through a phase of the dual burden of CDs and NCDs shows a heavy burden of NCDs responsible for the high disparity in lifespan. The Gini coefficient was decomposed for examining the contribution of 22 causes of death and their repercussions for inequality in age at death for 30 years between 1990-1994 and 2015-2019, using Global Burden of Disease data. The outcomes of the study reveal that India's epidemiological transition has been just modest on account of high inequality in mortality by NCDs emplaced in the middle through old age despite a consistent mortality decline at infant through old age for communicable diseases (CDs). The structural changes in causes of death structure is shaped by CDs rather than NCDs, but overall bolstered by the adult mortality decline, especially in women. However, the process is restrained by the small contribution of the middle age group and a benign contribution of old mortality decline owing to the low threshold age. India needs to target health interventions in seeking significant mortality decline in the middle age group of 50-69 years that is warranted for epidemiological transition apace as evident in the developed nations.

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.

Trends in lifespan variation across the spectrum of rural and urban places in the United States, 1990-2017

Mortality disparities between urban and rural areas in the United States widened in recent decades as mortality improvements in rural areas slowed. Although the existence of a rural mortality penalty is well-documented, previous research in this area has focused almost exclusively on differences in average levels of mortality between rural and urban areas rather than differences in levels of lifespan variation within rural and urban areas. This oversight is important because monitoring trends in lifespan variation provides unique insights into levels of inequality in the age-at-death distribution within a population. Does the rural mortality penalty in life expectancy extend to lifespan variation? We used U.S. Multiple Cause of Death data files to measure life disparity at birth (e 0 † ) from 1990 to 2017. We found that the rural mortality penalty extends to lifespan variation as large metropolitan areas had greater improvements in life disparity than nonmetropolitan areas. Beginning around 2011, all areas began to show increased life disparity with the largest increases occurring in nonmetropolitan areas. Age decomposition results showed that the nonmetropolitan increases were due to rising working-age mortality. Greater variability in the age-at-death distribution represents an additional dimension of inequality for Americans living in rural places.

Significant impacts of the COVID-19 pandemic on race/ethnic differences in US mortality

The coronavirus 2019 (COVID-19) pandemic triggered global declines in life expectancy. The United States was hit particularly hard among high-income countries. Early data from the United States showed that these losses varied greatly by race/ethnicity in 2020, with Hispanic and Black Americans suffering much larger losses in life expectancy compared with White people. We add to this research by examining trends in lifespan inequality, average years of life lost, and the contribution of specific causes of death and ages to race/ethnic life-expectancy disparities in the United States from 2010 to 2020. We find that life expectancy in 2020 fell more for Hispanic and Black males (4.5 and 3.6 y, respectively) compared with White males (1.5 y). These drops nearly eliminated the previous life-expectancy advantage for the Hispanic compared with the White population, while dramatically increasing the already large gap in life expectancy between Black and White people. While the drops in life expectancy for the Hispanic population were largely attributable to official COVID-19 deaths, Black Americans saw increases in cardiovascular diseases and "deaths of despair" over this period. In 2020, lifespan inequality increased slightly for Hispanic and White populations but decreased for Black people, reflecting the younger age pattern of COVID-19 deaths for Hispanic people. Overall, the mortality burden of the COVID-19 pandemic hit race/ethnic minorities particularly hard in the United States, underscoring the importance of the social determinants of health during a public health crisis.

The gap in life expectancy and lifespan inequality between Iran and neighbour countries: the contributions of avoidable causes of death

Background

Healthcare system and intersectoral public health policies play a crucial role in improving population health and reducing health inequalities. This study aimed to quantify their impact, operationalized as avoidable deaths, on the gap in life expectancy (LE) and lifespan inequality (LI) between Iran and three neighbour countries viz., Turkey, Qatar, and Kuwait in 2015–2016.

Methods

Annual data on population and causes of deaths by age and sex for Iran and three neighbour countries were obtained from the World Health Organization mortality database for the period 2015–2016. A recently developed list by the OECD/Eurostat was used to identify avoidable causes of death (with an upper age limit of 75). The cross-country gaps in LE and LI (measured by standard deviation) were decomposed by age and cause of death using a continuous-change model.

Results

Iranian males and females had the second lowest and lowest LE, respectively, compared with their counterparts in the neighbour countries. On the other hand, the highest LIs in both sexes (by 2.3 to 4.5 years in males and 1.1 to 3.3 years in females) were observed in Iran. Avoidable causes contributed substantially to the LE and LI gap in both sexes with injuries and maternal/infant mortality represented the greatest contributions to the disadvantages in Iranian males and females, respectively.

Conclusions

Higher mortality rates in young Iranians led to a double burden of inequality –shorter LE and greater uncertainty at timing of death. Strengthening intersectoral public health policies and healthcare quality targeted at averting premature deaths, especially from injuries among younger people, can mitigate this double burden.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12939-022-01683-8.

Representativeness is crucial for inferring demographic processes from online genealogies: Evidence from lifespan dynamics

Crowdsourced online genealogies have an unprecedented potential to shed light on long-run population dynamics, if analyzed properly. We investigate whether the historical mortality dynamics of males in familinx, a popular genealogical dataset, are representative of the general population, or whether they are closer to those of an elite subpopulation in two territories. The first territory is the German Empire, with a low level of genealogical coverage relative to the total population size, while the second territory is The Netherlands, with a higher level of genealogical coverage relative to the population. We find that, for the period around the turn of the 20th century (for which benchmark national life tables are available), mortality is consistently lower and more homogeneous in familinx than in the general population. For that time period, the mortality levels in familinx resemble those of elites in the German Empire, while they are closer to those in national life tables in The Netherlands. For the period before the 19th century, the mortality levels in familinx mirror those of the elites in both territories. We identify the low coverage of the total population and the oversampling of elites in online genealogies as potential explanations for these findings. Emerging digital data may revolutionize our knowledge of historical demographic dynamics, but only if we understand their potential uses and limitations.

Normalized lifespan inequality: disentangling the longevity-lifespan variability nexus

Previous studies have documented a historically strong and negative association between countries’ life expectancy (i.e., average longevity) and length-of-life inequality (i.e., variability in ages at death). The relationship between both variables might be partially explained by life expectancy increasing at a faster pace than maximal length of life, a phenomenon that mechanically compresses the age-at-death distribution and has not been taken into consideration in previous studies. In this paper, we propose a new approach to lifespan inequality measurement that accounts for the (uncertainly) bounded nature of length-of-life. Applying the new approach to the countries of the Human Mortality Database, we observe that the decline in overall lifespan variability typically associated with increases in longevity seems to stop and even reverse at higher levels of life expectancy. This suggests the emergence of worrying ethical dilemmas, whereby higher achievements in longevity would only be possible at the expense of higher lifespan variability.

What have we learned about mortality patterns over the past 25 years?

In this paper, I examine progress in the field of mortality over the past 25 years. I argue that we have been most successful in taking advantage of an increasingly data-rich environment to improve aggregate mortality models and test pre-existing theories. Less progress has been made in relating our estimates of mortality risk at the individual level to broader mortality patterns at the population level while appropriately accounting for contextual differences and compositional change. Overall, I find that the field of mortality continues to be highly visible in demographic journals, including Population Studies. However much of what is published today in field journals could just as easily appear in neighbouring disciplinary journals, as disciplinary boundaries are shrinking.

From convergence to divergence: Lifespan variation in US states, 1959-2017

BACKGROUND

Large disparities in life expectancy exist across US states and the gaps have been widening in recent decades. Less is known about the lifespan variability - a measure that can provide important insights into mortality inequalities both between and within states.

METHOD

Using yearly lifetables from the United States Mortality Database, we explore geographic and temporal patterns in lifespan variation (unconditional and conditional on survival to age 10, 35 and 65) across US states between 1959 and 2017. We also examine the contribution of state differences in life expectancy to overall lifespan variation using standard decomposition techniques.

RESULTS

Despite overall convergence in lifespan variation across states over the last six decades, in more recent years there has been notable divergence. Gender-specific analyses show that lifespan variation was generally greater among males than among females; but this pattern reverses for mortality past age 65. Much of the state disparities in lifespan variation, unconditional and conditional on survival to age 10 and 35, were due to mortality differences under the age 65. Decomposition analysis shows that while within-state variability remains the primary driver of overall lifespan variation, the contribution of cross-state differences in life expectancy is growing.

CONCLUSIONS

Variation in longevity is greater within US States than between them, yet cross-states disparities in mortality are increasing. This likely reflects the long-term consequences of rising social, economic, and political stratification for health inequalities both within and across states.

The Cross-sectional Average Inequality in Lifespan (CAL†): A Lifespan Variation Measure That Reflects the Mortality Histories of Cohorts

Lifespan variation is a key metric of mortality that describes both individual uncertainty about the length of life and heterogeneity in population health. We propose a novel and timely lifespan variation measure, which we call the cross-sectional average inequality in lifespan, or CAL†. This new index provides an alternative perspective on the analysis of lifespan inequality by combining the mortality histories of all cohorts present in a cross-sectional approach. We demonstrate how differences in the CAL† measure can be decomposed between populations by age and cohort to explore the compression or expansion of mortality in a cohort perspective. We apply these new methods using data from 10 low-mortality countries or regions from 1879 to 2013. CAL† reveals greater uncertainty in the timing of death than the period life table-based indices of variation indicate. Also, country rankings of lifespan inequality vary considerably between period and cross-sectional measures. These differences raise intriguing questions as to which temporal dimension is the most relevant to individuals when considering the uncertainty in the timing of death in planning their life courses.

Changes in life expectancy and lifespan variability by income quartiles in four Nordic countries: a study based on nationwide register data

OBJECTIVES

Levels, trends or changes in socioeconomic mortality differentials are typically described in terms of means, for example, life expectancies, but studies have suggested that there also are systematic social disparities in the dispersion around those means, in other words there are inequalities in lifespan variation. This study investigates changes in income inequalities in mean and distributional measures of mortality in Denmark, Finland, Norway, and Sweden over two decades.

DESIGN

Nationwide register-based study.

SETTING

The Danish, Finnish, Norwegian and Swedish populations aged 30 years or over in 1997 and 2017.

MAIN OUTCOME MEASURES

Income-specific changes in life expectancy, lifespan variation and the contribution of 'early' and 'late' deaths to increasing life expectancy.

RESULTS

Increases in life expectancy has taken place in all four countries, but there are systematic differences across income groups. In general, the largest gains in life expectancy were observed in Denmark, and the smallest increase among low-income women in Sweden and Norway. Overall, life expectancy increased and lifespan variation decreased with increasing income level. These differences grew larger over time. In all countries, a marked postponement of early deaths led to a compression of mortality in the top three income quartiles for both genders. This did not occur for the lowest income quartile.

CONCLUSION

Increasing life expectancy is typically accompanied by postponement of early deaths and reduction of lifespan inequality in the higher-income groups. However, Nordic welfare societies are challenged by the fact that postponing premature deaths among people in the lowest-income groups is not taking place.

Entropy analysis of human death uncertainty

Uncertainty about the time of death is part of one's life, and plays an important role in demographic and actuarial sciences. Entropy is a measure useful for characterizing complex systems. This paper analyses death uncertainty through the concept of entropy. For that purpose, the Shannon and the cumulative residual entropies are adopted. The first may be interpreted as an average information. The second was proposed more recently and is related to reliability measures such as the mean residual lifetime. Data collected from the Human Mortality Database and describing the evolution of 40 countries during several decades are studied using entropy measures. The emerging country and inter-country entropy patterns are used to characterize the dynamics of mortality. The locus of the two entropies gives a deeper insight into the dynamical evolution of the human mortality data series.

Time and Chance: Using Age Partitioning to Understand How Luck Drives Variation in Reproductive Success

AbstractOver the course of individual lifetimes, luck usually explains a large fraction of the between-individual variation in life span or lifetime reproductive output (LRO) within a population, while variation in individual traits or "quality" explains much less. To understand how, where in the life cycle, and through which demographic processes luck trumps trait variation, we show how to partition by age the contributions of luck and trait variation to LRO variance and how to quantify three distinct components of luck. We apply these tools to several empirical case studies. We find that luck swamps effects of trait variation at all ages, primarily because of randomness in individual state dynamics ("state trajectory luck"). Luck early in life is most important. Very early state trajectory luck generally determines whether an individual ever breeds, likely by ensuring that they are not dead or doomed quickly. Less early luck drives variation in success among those breeding at least once. Consequently, the importance of luck often has a sharp peak early in life or it has two peaks. We suggest that ages or stages where the importance of luck peaks are potential targets for interventions to benefit a population of concern, different from those identified by eigenvalue elasticity analysis.

Black-white disparities during an epidemic: Life expectancy and lifespan disparity in the US, 1980-2000

Covid-19 has demonstrated again that epidemics can affect minorities more than the population in general. We consider one of the last major epidemics in the United States: HIV/AIDS from ca. 1980-2000. We calculate life expectancy and lifespan disparity (a measure of variance in age at death) for thirty US states, finding noticeable differences both between states and between the black and white communities. Lifespan disparity allows us to examine distributional effects, and, using decomposition methods, we find that for six states lifespan disparity for blacks increased between 1980 and 1990, while life expectancy increased less than for whites. We find that we can attribute most of this to the impact of HIV/AIDS.

The ratio of expansion to compression: A new measure of lifespan disparity

Numerous studies have shown that high life expectancy is closely related to low life disparity. Unlike life expectancy, which can be increased by mortality decline at any age, life disparity can either increase or decrease in response to mortality decline. Disparity can thus be decomposed into two opposite components, called compression and expansion, depending on the effect of mortality decline on the age distribution of mortality. Without specifying the two components, various conventional measures of disparity may provide misleading information relating to how life chances in society can be equalized. Based on the relevant properties of changes in disparity, we develop a new measure of disparity—the ratio of expansion to compression—that can account for the relative importance of the two components. This simple measure not only provides a clear view of the evolution of disparity, but also permits changes in disparity related to mortality decline to be interpreted in a consistent manner similar to life expectancy. Simulations and an empirical analysis demonstrated the advantages of this new measure over conventional measures of disparity.

Rethinking morbidity compression

Studies of morbidity compression routinely report the average number of years spent in an unhealthy state but do not report variation in age at morbidity onset. Variation was highlighted by Fries (1980) as crucial for identifying disease postponement. Using incidence of first hospitalization after age 60, as one working example, we estimate variation in morbidity onset over a 27-year period in Denmark. Annual estimates of first hospitalization and the population at risk for 1987 to 2014 were identified using population-based registers. Sex-specific life tables were constructed, and the average age, the threshold age, and the coefficient of variation in age at first hospitalization were calculated. On average, first admissions lasting two or more days shifted towards older ages between 1987 and 2014. The average age at hospitalization increased from 67.8 years (95% CI 67.7-67.9) to 69.5 years (95% CI 69.4-69.6) in men, and 69.1 (95% CI 69.1-69.2) to 70.5 years (95% CI 70.4-70.6) in women. Variation in age at first admission increased slightly as the coefficient of variation increased from 9.1 (95% CI 9.0-9.1) to 9.9% (95% CI 9.8-10.0) among men, and from 10.3% (95% CI 10.2-10.4) to 10.6% (95% CI 10.5-10.6) among women. Our results suggest populations are ageing with better health today than in the past, but experience increasing diversity in healthy ageing. Pensions, social care, and health services will have to adapt to increasingly heterogeneous ageing populations, a phenomenon that average measures of morbidity do not capture.

The impact of violence on Venezuelan life expectancy and lifespan inequality

BACKGROUND

Venezuela is one of the most violent countries in the world. According to the United Nations, homicide rates in the country increased from 32.9 to 61.9 per 100 000 people between 2000 and 2014. This upsurge coincided with a slowdown in life expectancy improvements. We estimate mortality trends and quantify the impact of violence-related deaths and other causes of death on life expectancy and lifespan inequality in Venezuela.

METHODS

Life tables were computed with corrected age-specific mortality rates from 1996 to 2013. From these, changes in life expectancy and lifespan inequality were decomposed by age and cause of death using a continuous-change model. Lifespan inequality, or variation in age at death, is measured by the standard deviation of the age-at-death distribution.

RESULTS

From 1996 to 2013 in Venezuela, female life expectancy rose 3.57 [95% confidence interval (CI): 3.08-4.09] years [from 75.79 (75.98-76.10) to 79.36 (78.97-79.68)], and lifespan inequality fell 1.03 (-2.96 to 1.26) years [from 18.44 (18.01-19.00) to 17.41 (17.30-18.27)]. Male life expectancy increased 1.64 (1.09-2.25) years [from 69.36 (68.89-59.70) to 71.00 (70.53-71.39)], but lifespan inequality increased 0.95 (-0.80 to 2.89) years [from 20.70 (20.24-21.08) to 21.65 (21.34-22.12)]. If violence-related death rates had not risen over this period, male life expectancy would have increased an additional 1.55 years, and lifespan inequality would have declined slightly (-0.31 years).

CONCLUSIONS

As increases in violence-related deaths among young men (ages 15-39) have slowed gains in male life expectancy and increased lifespan inequality, Venezuelan males face more uncertainty about their age at death. There is an urgent need for more accurate mortality estimates in Venezuela.

Dietary macronutrient content, age-specific mortality and lifespan

Protein and calorie restrictions extend median lifespan in many organisms. However, studies suggest that among-individual variation in the age at death is also affected. Ultimately, both of these outcomes must be caused by effects of nutrition on underlying patterns of age-specific mortality (ASM). Using model life tables, we tested for effects of dietary macronutrients on ASM in mice ( Mus musculus). High concentrations of protein and fat relative to carbohydrates were associated with low life expectancy and high variation in the age at death, a result caused predominantly by high mortality prior to middle age. A lifelong diet comprising the ratio of macronutrients self-selected by mouse (in early adulthood) was associated with low mortality up until middle age, but higher late-life mortality. This pattern results in reasonably high life expectancy, but very low variation in the age at death. Our analyses also indicate that it may be possible to minimize ASM across life by altering the ratio of dietary protein to carbohydrate in the approach to old age. Mortality in early and middle life was minimized at around one-part protein to two-parts carbohydrate, whereas in later life slightly greater than equal parts protein to carbohydrate reduced mortality.

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.

Longevity and Lifespan Variation by Educational Attainment in Spain: 1960-2015

For a long time, studies of socioeconomic gradients in health have limited their attention to between-group comparisons. Yet, ignoring the differences that might exist within groups and focusing on group-specific life expectancy levels and trends alone, one might arrive at overly simplistic conclusions. Using data from the Spanish Encuesta Sociodemográfica and recently released mortality files by the Spanish Statistical Office (INE), this is the first study to simultaneously document (1) the gradient in life expectancy by educational attainment groups, and (2) the inequality in age-at-death distributions within and across those groups for the period between 1960 and 2015 in Spain. Our findings suggest that life expectancy has been increasing for all education groups but particularly among the highly educated. We observe diverging trends in life expectancy, with the differences between the low- and highly educated becoming increasingly large, particularly among men. Concomitantly with increasing disparities across groups, length-of-life inequality has decreased for the population as a whole and for most education groups, and the contribution of the between-group component of inequality to overall inequality has been extremely small. Even if between-group inequality has increased over time, its contribution has been too small to have sizable effects on overall inequality. In addition, our results suggest that education expansion and declining within-group variability might have been the main drivers of overall lifespan inequality reductions. Nevertheless, the diverging trends in longevity and lifespan inequality across education groups represent an important phenomenon whose underlying causes and potential implications should be investigated in detail.

The increasing lifespan variation gradient by area-level deprivation: A decomposition analysis of Scotland 1981-2011

Life expectancy inequalities are an established indicator of health inequalities. More recent attention has been given to lifespan variation, which measures the amount of heterogeneity in age at death across all individuals in a population. International studies have documented diverging socioeconomic trends in lifespan variation using individual level measures of income, education and occupation. Despite using different socioeconomic indicators and different indices of lifespan variation, studies reached the same conclusion: the most deprived experience the lowest life expectancy and highest lifespan variation, a double burden of mortality inequality. A finding of even greater concern is that relative differences in lifespan variation between socioeconomic group were growing at a faster rate than life expectancy differences. The magnitude of lifespan variation inequalities by area-level deprivation has received limited attention. Area-level measures of deprivation are actively used by governments for allocating resources to tackle health inequalities. Establishing if the same lifespan variation inequalities emerge for area-level deprivation will help to better inform governments about which dimension of mortality inequality should be targeted. We measure lifespan variation trends (1981-2011) stratified by an area-level measure of socioeconomic deprivation that is applicable to the entire population of Scotland, the country with the highest level of variation and one of the longest, sustained stagnating trends in Western Europe. We measure the gradient in variation using the slope and relative indices of inequality. The deprivation, age and cause specific components driving the increasing gradient are identified by decomposing the change in the slope index between 1981 and 2011. Our results support the finding that the most advantaged are dying within an ever narrower age range while the most deprived are facing greater and increasing uncertainty. The least deprived group show an increasing advantage, over the national average, in terms of deaths from circulatory disease and external causes.

Global trends in lifespan inequality: 1950-2015

Using data from the UN World Population Prospects, we document global trends in lifespan inequality from 1950 until 2015. Our findings indicate that (i) there has been a sustained decline in overall lifespan inequality, (ii) adult lifespan variability has also declined, but some plateaus and trend reversals have been identified, (iii) lifespan inequality among the elderly has increased virtually everywhere, and (iv) most of the world variability in age-at-death can be attributed to within-country variability. Such changes have occurred against a backdrop of generalized longevity increases. Our analyses suggest that the world is facing a new challenge: the emergence of diverging trends in longevity and age-at-death inequality among the elderly around the globe-particularly in high-income areas. As larger fractions of the world population survive to more advanced ages, it will be necessary for national and international health planners to recognize the growing heterogeneity that characterizes older populations.

Changing contribution of area-level deprivation to total variance in age at death: a population-based decomposition analysis

OBJECTIVES

Two processes generate total variance in age at death: heterogeneity (between-group variance) and individual stochasticity (within-group variance). Limited research has evaluated how these two components have changed over time. We quantify the degree to which area-level deprivation contributed to total variance in age at death in Scotland between 1981 and 2011.

DESIGN

Full population and mortality data for Scotland were obtained and matched with the Carstairs score, a standardised z-score calculated for each part-postcode sector that measures relative area-level deprivation. A z-score above zero indicates that the part-postcode sector experienced higher deprivation than the national average. A z-score below zero indicates lower deprivation. From the aggregated data we constructed 40 lifetables, one for each deprivation quintile in 1981, 1991, 2001 and 2011 stratified by sex.

PRIMARY OUTCOME MEASURES

Total variance in age at death and the proportion explained by area-level deprivation heterogeneity (between-group variance).

RESULTS

The most deprived areas experienced stagnating or slightly increasing variance in age at death. The least deprived areas experienced decreasing variance. For males, the most deprived quintile life expectancy was between 7% and 11% lower and the SD is between 6% and 25% higher than the least deprived. This suggests that the effect of deprivation on the SD of longevity is comparable to its effect on life expectancy. Decomposition analysis revealed that contributions from between-group variance doubled between 1981 and 2011 but at most only explained 4% of total variance.

CONCLUSIONS

This study adds to the emerging body of literature demonstrating that socio-economic groups have experienced diverging trends in variance in age at death. The contribution from area-level deprivation to total variance in age at death, which we were able to capture, has doubled since 1981. Area-level deprivation may play an increasingly important role in mortality inequalities.

Modelling and forecasting adult age-at-death distributions

Age-at-death distributions provide an informative description of the mortality pattern of a population but have generally been neglected for modelling and forecasting mortality. In this paper, we use the distribution of deaths to model and forecast adult mortality. Specifically, we introduce a relational model that relates a fixed 'standard' to a series of observed distributions by a transformation of the age axis. The proposed Segmented Transformation Age-at-death Distributions (STAD) model is parsimonious and efficient: using only three parameters, it captures and disentangles mortality developments in terms of shifting and compression dynamics. Additionally, mortality forecasts can be derived from parameter extrapolation using time-series models. We illustrate our method and compare it with the Lee-Carter model and variants for females in four high-longevity countries. We show that the STAD fits the observed mortality pattern very well, and that its forecasts are more accurate and optimistic than the Lee-Carter variants.