How Has the Lower Boundary of Human Mortality Evolved, and Has It Already Stopped Decreasing?

Grace period of human mortality has declined for over a century

OBJECTIVES

Human mortality is U-shaped and, therefore, defines an agex * $$ {x}^{\ast } $$ separating lives with an overall negative net change in mortality from lives with an overall positive net change in mortality. How has agex * $$ {x}^{\ast } $$ changed, also relatively to life expectancy, over recent human history? And how doesx * $$ {x}^{\ast } $$ compare between humans and other primates, the mortality of which is also U-shaped?

METHODS

Modeling data from the Human Mortality Database, the historical change ofx * $$ {x}^{\ast } $$ in advanced economies is reported and compared with that of primates in wild and captive conditions the demography of which was already modeled in the literature.

RESULTS

In humans, a marked decline inx * $$ {x}^{\ast } $$ for both sexes, also relatively to their life expectancy, is associated with medical and economic progress. Comparing wild with captive conditions in nonhuman primates, magnitude, and direction of the change inx * $$ {x}^{\ast } $$ , both relatively to life expectancy and absolutely, can depend on genus and sex.

CONCLUSIONS

With medical and economic progress, human lives have transitioned from a negative to a positive net change in mortality independently of sex. There is no evidence of an analogous transition occurring in other primates when their environment is made more benign.

Mortality as a Function of Survival

Everyone has a chronological age. Because survivorship declines relentlessly in populations with age-specific death rates greater than zero, everyone also has a survivorship age ("s-age"), the age at which a proportion s of the population is still alive. S-ages can be estimated for both periods and cohorts. While trajectories of mortality over chronological ages differ (e.g., across populations, over time, by sex, or by any subpopulation), mortality trajectories over s-ages are similar, a sign that populations experience similar mortality dynamics at specific levels of survivorship. We show that this important demographic regularity holds for 23 sex-specific populations analyzed during a period comprising more than 100 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.

A Mixture-Function Mortality Model: Illustration of the Evolution of Premature Mortality

Premature mortality is often a neglected component of overall deaths, and the most difficult to identify. However, it is important to estimate its prevalence. Following Pearson's theory about mortality components, a definition of premature deaths and a parametric model to study its transformations are introduced. The model is a mixture of three distributions: a Half Normal for the first part of the death curve and two Skew Normals to fit the remaining pieces. One advantage of the model is the possibility of obtaining an explicit equation to compute life expectancy at birth and to break it down into mortality components. We estimated the mixture model for Sweden, France, East Germany and Czech Republic. In addition, to the well-known reduction in infant deaths, and compression and shifting trend of adult mortality, we were able to study the trend of the central part of the distribution of deaths in detail. In general, a right shift of the modal age at death for young adults is observed; in some cases, it is also accompanied by an increase in the number of deaths at these ages: in particular for France, in the last twenty years, premature mortality increases.