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Several Organisation for Economic Co-operation and Development countries have recently implemented an automatic link between the statutory retirement age and life expectancy for the total population to ensure sustainability in their pension systems due to increasing life expectancy. As significant mortality differentials are observed across socio-economic groups, future changes in these differentials will determine whether some socio-economic groups drive increases in the retirement age, leaving other groups with fewer pensionable years. We forecast life expectancy by socio-economic groups and compare the forecast performance of competing models by using Danish mortality data and find that the most accurate model assumes a common mortality trend. Life expectancy forecasts are used to analyse the consequences of a pension system where the statutory retirement age is increased when total life expectancy is increasing.

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.

ObjectiveTo quantify inequalities in lifespan across multiple social determinants of health, how they act in tandem with one another, and to create a scoring system that can accurately identify subgroups of the population at high risk of mortality.DesignComparison of life tables across 54 subpopulations defined by combinations of four social determinants of health: sex, marital status, education and race, using data from the Multiple Cause of Death dataset and the American Community Survey.SettingUnited States, 2015–2019.Main outcome measuresWe compared the partial life expectancies (PLEs) between age 30 and 90 years of all subpopulations. We also developed a scoring system to identify subgroups at high risk of mortality.ResultsThere is an 18.0-year difference between the subpopulations with the lowest and highest PLE. Differences in PLE between subpopulations are not significant in most pairwise comparisons. We visually illustrate how the PLE changes across social determinants of health. There is a complex interaction among social determinants of health, with no single determinant fully explaining the observed variation in lifespan. The proposed scoring system adds clarification to this interaction by yielding a single score that can be used to identify subgroups that might be at high risk of mortality. A similar scoring system by cause of death was also created to identify which subgroups could be considered at high risk of mortality from specific causes. Even if subgroups have similar mortality levels, they are often subject to different cause-specific mortality risks.ConclusionsHaving one characteristic associated with higher mortality is often not sufficient to be considered at high risk of mortality, but the risk increases with the number of such characteristics. Reducing inequalities is vital for societies, and better identifying individuals and subgroups at high risk of mortality is necessary for public health policy.

Mortality trends for subpopulations, e.g., countries in a region or provinces in a country, tend to change similarly over time. However, when forecasting subpopulations independently, the forecast mortality trends often diverge. These divergent trends emerge from an inability of different forecast models to offer population-specific forecasts that are consistent with one another. Nondivergent forecasts between similar populations are often referred to as \"coherent.\" We propose a new forecasting method that addresses the coherence problem for subpopulations, based on Compositional Data Analysis (CoDa) of the life table distribution of deaths. We adapt existing coherent and noncoherent forecasting models to CoDa and compare their results. We apply our coherent method to the female mortality of 15 Western European countries and show that our proposed strategy would have improved the forecast accuracy for many of the selected countries. The results also show that the CoDa adaptation of commonly used models allows the rates of mortality improvements (RMIs) to change over time.

The modal age at death (or mode) is an important indicator of longevity associated with different mortality regularities. Accurate estimates of the mode are essential, but existing methods are not always able to provide them. Our objective is to develop a method to estimate the modal age at death, which is purely based on its mathematical properties. The mode maximizes the density of the age-at-death distribution. In addition, at the mode, the rate of aging equals the force of mortality. Using these properties, we develop a novel discrete estimation method for the mode, the discretized derivative tests (DDT) method, and compare its outcomes to those of other existing models. Both the modal age at death and the rate of aging have been increasing since 1960 in low-mortality countries. The DDT method produces close estimates to the ones generated by the P-spline smoothing. The modal age at death plays a central role in estimating longevity advancement, quantifying mortality postponement, and estimating the rate of aging. The novel DDT method proposed here provides a simple and mathematically based estimation of the modal age at death. The method accounts for the mathematical properties of the mode and is not computationally demanding.

ObjectiveTo measure sex differences in lifespan based on the probability of males to outlive females.DesignInternational comparison of national and regional sex-specific life tables from the Human Mortality Database and the World Population Prospects.Setting199 populations spanning all continents, between 1751 and 2020.Primary outcome measureWe used the outsurvival statistic ( φ ) to measure inequality in lifespan between sexes, which is interpreted here as the probability of males to outlive females.ResultsIn random pairs of one male and one female at age 0, the probability of the male outliving the female varies between 25% and 50% for life tables in almost all years since 1751 and across almost all populations. We show that φ is negatively correlated with sex differences in life expectancy and positively correlated with the level of lifespan variation. The important reduction of lifespan inequality observed in recent years has made it less likely for a male to outlive a female.ConclusionsAlthough male life expectancy is generally lower than female life expectancy, and male death rates are usually higher at all ages, males have a substantial chance of outliving females. These findings challenge the general impression that ‘men do not live as long as women’ and reveal a more nuanced inequality in lifespans between females and males.

Inequality in lifespans between two populations, e.g., males and females or people with low and high socioeconomic status, is a focus of demographic, economic, and sociological research and of public policy analysis. Such inequality is usually measured by differences in life expectancy. We aim to devise a cogent measure of how much distributions of lifespans differ between two populations. We propose an outsurvival statistic,