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 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 emer

In most developed countries, mortality reductions in the first half of the 20th century were highly associated with changes in lifespan disparities. In the second half of the 20th century, changes in mortality are best described by a shift in the mortality

Introduction An important role of public health organisations is to monitor indicators of variation, so as to disclose underlying inequality in health improvement. In industrialised societies, more individuals than ever are reaching older ages and have become more homogeneous in their age at death. This has led to a decrease in lifespan variation, with substantial implications for the reduction of health inequalities. We focus on a new form of variation to shed further light on our understanding of population health and ageing: variation in causes of death. Methods Data from the WHO Mortality Database and the Human Mortality Database are used to estimate cause-of-death distributions and life tables in 15 low-mortality countries. Cause-of-death variation, using 19 groups of causes, is quantified using entropy measures and analysed from 1994 to 2017. Results The last two decades have seen increasing diversity in causes of death in low-mortality countries. There have been important reductions in the share of deaths from diseases of the circulatory system, while the share of a range of other causes, such as diseases of the genitourinary system, mental and behavioural disorders, and diseases of the nervous system, has been increasing, leading to a more complex cause-of-death distribution. Conclusions The diversification in causes of death witnessed in recent decades is most likely a result of the increase in life expectancy, together with better diagnoses and awareness of certain diseases. Such emerging patterns bring additional challenges to healthcare systems, such as the need to research, monitor and treat a wider range of diseases. It also raises new questions concerning the distribution of health resources.

Mortality levels for subpopulations, such as countries in a region or provinces within a country, generally change in a similar fashion over time, as a result of common historical experiences in terms of health, culture, and economics. Forecasting mortality for such populations should consider the correlation between their mortality levels. In this perspective, we suggest using multilinear component techniques to identify a common time trend and then use it to forecast coherently the mortality of subpopulations. Moreover, this multiway approach is performed on life table deaths by referring to Compositional Data Analysis (CoDa) methodology. Compositional data are strictly positive values summing to a constant and represent part of a whole. Life table deaths are compositional by definition because they provide the age composition of deaths per year and sum to the life table radix. In bilinear models the use of life table deaths treated as compositions generally leads to less biased forecasts than other commonly used models by not assuming a constant rate of mortality improvement. As a consequence, an extension of this approach to multiway data is here presented. Specifically, a CoDa adaptation of the Tucker3 model is implemented for life table deaths arranged in three-dimensional arrays indexed by time, age, and population. The proposed procedure is used to forecast the mortality of Canadian provinces in a comparative study. The results show that the proposed model leads to coherent forecasts.

The Lee-Carter (LC) model has been recurrently used to forecast mortality, including by national statistical offices. This model has many advantages, but tends to underpredict life expectancy due to its assumption of constant age-specific response to the time index. Does this bias emerge from all ages or from specific ages only? In this paper, we aim to provide a more detailed evaluation of the model, by evaluating its accuracy, bias and robustness by age. Our analysis is based on 806 out-of-sample forecasts using various different fitting periods and forecast horizons. We focus on age 65 and above, as most deaths occur at older ages nowadays. We showed that the LC model is not fundamentally biased, but its main assumption of constant age-specific response to the time index, often leading to constant rates of mortality improvement, is not appropriate in all populations and at all ages.