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

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.

Average lifespan variation among people with mental disorders in Denmark: a nationwide, register-based cohort study

AIMS

Mortality associated with mental disorders has been estimated using metrics such as mortality rate ratios and life expectancy. However, the variation around the average life expectancy has never been quantified. The main aim of this study was to measure life disparity for people with mental disorders as a measure of inequality at the time of death.

METHODS

Using data from Danish registries, average life disparity was introduced and calculated to measure the lifespan variation associated with major types of mental disorders. Average life expectancy is also reported for completeness.

RESULTS

Compared with the general population, people with mental disorders not only had shorter average life expectancy, but experienced larger average life disparity. For those diagnosed with a mental disorder, average life expectancy increased between 1995 and 2021; however, average life disparity declined in women only, and did not change for men. In addition, the differences in both metrics between those with mental disorders and the general population were largest for substance use disorders and schizophrenia spectrum disorders. For these disorders, the differences even increased during the study period.

CONCLUSIONS

Mortality rates for individuals with mental disorders have been declining in recent decades in Denmark; however, the increase in the average life disparity emphasizes the increasing heterogeneity and inequality in lifespans within this group, which requires measures to promote a longer and more equal life for those with mental disorders.

Convergence and divergence in mortality: A global study from 1990 to 2030

An empirical question that has motivated demographers is whether there is convergence or divergence in mortality/longevity around the world. The epidemiological transition is the starting point for studying a global process of mortality convergence. This manuscript aims to provide an update on the concept of mortality convergence/divergence. We perform a comprehensive examination of nine different mortality indicators from a global perspective using clustering methods in the period 1990-2030. In addition, we include analyses of projections to provide insights into prospective trajectories of convergence clubs, a dimension unexplored in previous work. The results indicate that mortality convergence clubs of 194 countries by sex resemble the configuration of continents. These five clubs show a common steady upward trend in longevity indicators, accompanied by a progressive reduction in disparities between sexes and between groups of countries. Furthermore, this paper shows insights into the historical evolution of the convergence clubs in the period 1990-2020 and expands their scope to include projections of their expected future evolution in 2030.

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.

Lifespan variation among people with a given disease or condition

In addition to fundamental mortality metrics such as mortality rates and mortality rate ratios, life expectancy is also commonly used to investigate excess mortality among a group of individuals diagnosed with specific diseases or conditions. However, as an average measure, life expectancy ignores the heterogeneity in lifespan. Interestingly, the variation in lifespan-a measure commonly used in the field of demography-has not been estimated for people with a specific condition. Based on recent advances in methodology in research within epidemiology and demography, we discuss two metrics, namely, the average life disparity and average lifetable entropy after diagnosis, which estimate the variation in lifespan for time-varying conditions in both absolute and relative aspects. These metrics are further decomposed into early and late components, separated by their threshold ages. We use mortality data for women with mental disorders from Danish registers to design a population-based study and measure such metrics. Compared with women from the general population, women with a mental disorder had a shorter average remaining life expectancy after diagnosis (37.6 years vs. 44.9 years). In addition, women with mental disorders also experienced a larger average lifespan variation, illustrated by larger average life disparity (9.5 years vs 9.1 years) and larger average lifetable entropy (0.33 vs 0.27). More specifically, we found that women with a mental disorder had a larger early average life disparity but a smaller late average life disparity. Unlike the average life disparity, both early and late average lifetable entropy were higher for women with mental disorders compared to the general population. In conclusion, the metric proposed in our study complements the current research focusing merely on life expectancy and further provides a new perspective into the assessment of people's health associated with time-varying conditions.

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.

Evaluation of age-specific causes of death in the context of the Italian longevity transition

In many low-mortality countries, life expectancy at birth increased steadily over the last century. In particular, both Italian females and males benefited from faster improvements in mortality compared to other high-income countries, especially from the 1960s, leading to an exceptional increase in life expectancy. However, Italy has not become the leader in longevity. Here, we investigate life expectancy trends in Italy during the period 1960-2015 for both sexes. Additionally, we contribute to the existing literature by complementing life expectancy with an indicator of dispersion in ages at death, also known as lifespan inequality. Lifespan inequality underlies heterogeneity over age in populating health improvements and is a marker of uncertainty in the timing of death. We further quantify the contributions of different age groups and causes of death to recent trends in life expectancy and lifespan inequality. Our findings highlight the contributions of cardiovascular diseases and neoplasms to the recent increase in life expectancy but not necessarily to the decrease in lifespan inequality. Our results also uncover a more recent challenge across Italy: worsening mortality from infectious diseases and mortality at older age.

Comparing Cohort Survival in Good Health: A Research Note on Decomposing Sex Differentials in the United States

We introduce a method for decomposing differences in healthy cross-sectional average length of life (HCAL). HCAL provides an alternative to the health expectancy (HE) indicator by including the health and mortality history of all cohorts present at a given time. While decompositions of HE differences account for contributions made by health and mortality, differences in HCAL are further disentangled into cohort-specific contributions. In this research note we illustrate the technique by analyzing the sex gap in health and mortality for the United States. We use the harmonized version of the Health and Retirement Survey data and define the health status in terms of activities of daily living. Our results suggest that the female advantage in cohort survival is partly compensated by women's lower cohort-specific health levels. At older ages, however, the sex differences in health are not large enough to compensate men's disadvantage in cohort survival.