The modal age at death and the shifting mortality hypothesis

The modal age at death is used to study the shifting mortality scenario experienced by low mortality countries. The relations of the life table functions at the modal age are analyzed using mortality models. In the models the modal age increases over time, but there is an asymptotic approximation towards a constant number of deaths and standard deviation from the mode. The findings are compared to the changes observed in populations with historical mortality data. During the transition period to a shifting mortality era the population becomes highly heterogeneous and the rate of improvement in mortality is highly sensitive to these changes. By focusing in the modal age at death, a new perspective on the analysis of human longevity is revealed.compression of mortality, distribution of deaths, life table modal age at death, mortality models, shifting mortality

Age-specific contributions to changes in the period and cohort life expectancy

Period life expectancy has increased more slowly than its cohort counterpart. This paper explores the differences between life expectancies at a given time (the gap) and the time required for period life expectancy to reach the current level of cohort life expectancy (the lag). Additionally, to understand the disparity between the two life expectancies we identify and compare age-specific contributions to change in life expectancy. Using mortality models and historical data for Sweden, we examine the effect of mortality changes over time. Our results indicate that the widening of the gap between the two life expectancies is primarily a consequence of the dramatic mortality decline at older ages that occurred during the twentieth century. These results imply that the divergence between the two measures is likely to become even greater in the future as reductions in deaths are concentrated at older ages.age-specific decomposition, cohort life expectancy, gap and lag, life expectancy, mortality models, period life expectancy

Changing mortality and average cohort life expectancy

Period life expectancy varies with changes in mortality, and should not be confused with the life expectancy of those alive during that period. Given past and likely future mortality changes, a recent debate has arisen on the usefulness of the period life expectancy as the leading measure of survivorship. An alternative aggregate measure of period mortality which has been seen as less sensitive to period changes, the cross-sectional average length of life (CAL) has been proposed as an alternative, but has received only limited empirical or analytical examination. Here, we introduce a new measure, the average cohort life expectancy (ACLE), to provide a precise measure of the average length of life of cohorts alive at a given time. To compare the performance of ACLE with CAL and with period and cohort life expectancy, we first use population models with changing mortality. Then the four aggregate measures of mortality are calculated for England and Wales, Norway, and Switzerland for the years 1880 to 2000. CAL is found to be sensitive to past and present changes in death rates. ACLE requires the most data, but gives the best representation of the survivorship of cohorts present at a given time.cohort life expectancy, cross-sectional average length of life (CAL), life expectancy, mortality, mortality tempo, period life expectancy

The crossover between life expectancies at birth and at age one: The imbalance in the life table

The single most used demographic measure to describe population health is life expectancy at birth, but life expectancies at ages other than zero are also used in the study of human longevity. Our intuition tells us that the longest life expectancy is that of a newborn. However, historically, the expectation of life at age one (e1) has exceeded the expectation of life at birth (e0). The crossover between e0 and e1 only occurred in the developed world in the second half of the twentieth century. Life tables for populations that have not achieved this crossing between life expectancy at birth and at age one are referred to here as imbalanced. This crossover occurs when infant mortality is equal to the inverse of life expectancy at age one. This simple relation between mortality at age zero and mortality after age one divides the world into countries that have achieved the crossover in life expectancies and those that have not. It is a within-population comparison of mortality at infancy and after age one. However, results of these within-population comparisons can be used for comparison between populations. For countries that have already achieved this crossing in life expectancies, the sex differential in the timing of the crossing is marked: Females attain the crossing before males for every single population and in some cases by up to 18 years earlier. However, for most developing countries, life expectancy at age one is still higher than life expectancy at birth, in some cases by several years. Subpopulation comparisons for the US show how black Americans are near to transitioning out of the imbalanced life table situation while the white population has already done so.cross-over, demographic transition, infant mortality, life expectancy, life tables

Decomposing change in life expectancy: a bouquet of formulas in honour of Nathan Keyfitz´s 90th birthday

-Japan, Sweden, causes of death, life expectancy

Decomposing demographic change into direct vs. compositional components

We present and prove a formula for decomposing change in a population average into two components. One component captures the effect of direct change in the characteristic of interest, and the other captures the effect of compositional change. The decomposition is applied to time derivatives of averages over age and over subpopulations. Examples include decomposition of the change over time in the average age at childbearing and in the general fertility rate for China, Denmark and Mexico. A decomposition of the change over time in the crude death rate in Denmark, Germany and the Netherlands is also presented. Other examples concern global life expectancy and the growth rate of the population of the world.components of change, decomposition, derivatives of averages, formal demography

An integrated approach to cause-of-death analysis: cause-deleted life tables and decompositions of life expectancy

This article integrates two methods that analyze the implications of various causes of death for life expectancy. One of the methods attributes changes in life expectancy to various causes of death; the other method examines the effect of removing deaths from a particular cause on life expectancy. This integration is accomplished by new formulas that make clearer the interactions among causes of death in determining life expectancy. We apply our approach to changes in life expectancy in the United States between 1970 and 2000. We demonstrate, and explain analytically, the paradox that cancer is responsible for more years of life lost in 2000 than in 1970 despite the fact that declines in cancer mortality contributed to advances in life expectancy between 1970 and 2000.causes of death, decomposition method, decomposition technique, demography, life expectancy, life tables, morbidity, mortality

How mortality improvement increases population growth

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Cross-sectional average length of life childless

Increases in the average age at first birth and in the proportion of women remaining childless have extended the total number of years that women spend childless during their reproductive lifetime in several countries. To quantify the number of years that reproductive-age women live without children, we introduce the cross-sectional average length of life childless (CALC). This measure includes all the age-specific first-birth information available for the cohorts present at time t; it is a period measure based on cohort data. Using the Human Fertility Database, CALC is calculated for the year 2015 for all countries with long enough histories of fertility available. Results show that women in the majority of the studied countries spend, on average, more than half of their reproductive lives childless. Furthermore, the difference between CALCs in two countries can be decomposed to give a clear visualization of how each cohort contributes to the difference in the duration of the length of childless life in those populations. Our illustration of the decomposition shows that (1) in recent years, female cohorts in Japan and Spain at increasingly younger ages have been contributing to more years of childless life compared with those in Sweden, (2) the United States continues to represent an exception among the high-income countries with a low expectation for childless life of women, and (3) Hungary experienced a strong period effect of the recent Great Recession. These examples show that CALC and its decomposition can provide insights into first-birth patterns.The contribution of Jessica Nisén was supported by the Academy of Finland (decision numbers 332863 and 320162). We are grateful to Marilia Nepomuceno for her initial contribution