Lifespan Disparity as an Additional Indicator for Evaluating Mortality Forecasts

A modal age at death approach to forecasting adult mortality

Recent studies have shown that there are some advantages to forecasting mortality with indicators other than age-specific death rates. The mean, median, and modal ages at death can be directly estimated from the age-at-death distribution, as can information on lifespan variation. The modal age at death has been increasing linearly since the second half of the twentieth century, providing a strong basis from which to extrapolate past trends. The aim of this paper is to develop a forecasting model that is based on the regularity of the modal age at death and that can also account for changes in lifespan variation. We forecast mortality at ages 40 and above in 10 West European countries. The model we introduce increases forecast accuracy compared with other forecasting models and provides consistent trends in life expectancy and lifespan variation at age 40 over time.

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 Can We Learn from the Functional Clustering of Mortality Data? An Application to the Human Mortality Database

This study analyzed whether there are different patterns of mortality decline among low-mortality countries by identifying the role played by all the mortality components. We implemented a cluster analysis using a functional data analysis (FDA) approach, which allowed us to consider age-specific mortality rather than summary measures, as it analyses curves rather than scalar data. Combined with a functional principal component analysis, it can identify what part of the curves is responsible for assigning one country to a specific cluster. FDA clustering was applied to the data from 32 countries in the Human Mortality Database from 1960 to 2018 to provide a comprehensive understanding of their patterns of mortality. The results show that the evolution of developed countries followed the same pattern of stages (with different timings): (1) a reduction of infant mortality, (2) an increase of premature mortality and (3) a shift and compression of deaths. Some countries were following this scheme and recovering the gap with precursors; others did not show signs of recovery. Eastern European countries were still at Stage (2), and it was not clear if and when they will enter Stage 3. All the country differences related to the different timings with which countries underwent the stages, as identified by the clusters.

Progress of Inequality in Age at Death in India: Role of Adult Mortality

India has seen a reduction in infant and child mortality rates for both the sexes since the early 1980s. However, a decline in mortality at adult ages is marked by significant differences in the subgroups of sex and regions. This study assesses the progress of inequality in age at death with the advances in mortality transition during 36 years period between 1981-1985 and 2012-2016 in India, using the Gini coefficients at the age of zero (G ₀ ). The Gini coefficients show that in the mid-2000s, women outpaced men in G ₀ . The reduction in inequality in age at death is a manifestation of the process of homogeneity in mortality. The low G ₀ is concomitant of high life expectancy at birth (e ₀ ) in India. The results show the dominance of adult mortality over child mortality in the medium-mortality and low-mortality regimes. Varying adult mortality in the subgroups of sex and variance in the mortality levels of regions are the predominant factors for the variation in inequality in age at death. By lowering of the mortality rates in the age group of 15-29 years, India can achieve a high e ₀ that appears at high demographic development and the narrow sex differentials in e ₀ and G ₀ in a short time. Men in the age group of 15-29 years are the most vulnerable subgroup with respect to mortality. There is an immediate need for health policies in India to prioritise the aversion of premature deaths in men aged 15-29 years.

Smoothing, Decomposing and Forecasting Mortality Rates

The Lee-Carter (LC) model represents a landmark paper in mortality forecasting. While having been widely accepted and adopted, the model has some limitations that hinder its performance. Some variants of the model have been proposed to deal with these drawbacks individually, none coped with them all at the same time. In this paper, we propose a Three-Component smooth Lee-Carter (3C-sLC) model which overcomes many of the issues simultaneously. It decomposes mortality development into childhood, early-adult and senescent mortality, which are described, individually, by a smooth variant of the LC model. Smoothness is enforced to avoid irregular patterns in projected life tables, and complexity in the forecasting methodology is unaltered with respect to the original LC model. Component-specific schedules are considered in projections, providing additional insights into mortality forecasts. We illustrate the proposed approach to mortality data for ten low-mortality populations. The 3C-sLC captures mortality developments better than a smooth improved version of the LC model, and it displays wider prediction intervals. The proposed approach provides actuaries, demographers, epidemiologists and social scientists in general with a unique and valuable tool to simultaneously smooth, decompose and forecast mortality.

Future life expectancy in Europe taking into account the impact of smoking, obesity, and alcohol

Introduction: In Europe, women can expect to live on average 82 years and men 75 years. Forecasting how life expectancy will develop in the future is essential for society. Most forecasts rely on a mechanical extrapolation of past mortality trends, which leads to unreliable outcomes because of temporal fluctuations in the past trends due to lifestyle 'epidemics'. Methods: We project life expectancy for 18 European countries by taking into account the impact of smoking, obesity, and alcohol on mortality, and the mortality experiences of forerunner populations. Results: We project that life expectancy in these 18 countries will increase from, on average, 83.4 years for women and 78.3 years for men in 2014 to 92.8 years for women and 90.5 years for men in 2065. Compared to others (Lee-Carter, Eurostat, United Nations), we project higher future life expectancy values and more realistic differences between countries and sexes. Conclusions: Our results imply longer individual lifespans, and more elderly in society. Funding: Netherlands Organisation for Scientific Research (NWO) (grant no. 452-13-001).

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.

Mortality Forecasting with the Lee-Carter Method: Adjusting for Smoothing and Lifespan Disparity

Reliable mortality forecasts are an essential component of healthcare policies in ageing societies. The Lee-Carter method and its later variants are widely accepted probabilistic approaches to mortality forecasting, due to their simplicity and the straightforward interpretation of the model parameters. This model assumes an invariant age component and linear time component for forecasting. We apply the Lee-Carter method on smoothed mortality rates obtained by LASSO-type regularization and hence adjust the time component with the observed lifespan disparity. Smoothing with LASSO produces less error during the fitting period than do spline-based smoothing techniques. As a more informative indicator of longevity, matching with lifespan disparity makes the time component more reflective of mortality improvements. The forecasts produced by the new method were more accurate during out-of-sample evaluation and provided optimistic forecasts for many low-mortality countries.

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.