Measuring and explaining the change in life expectancies

A set of new indices for interpreting change in life expectancies, as well as a technique for explaining change in life expectancies by change in mortality at each age group are presented in the paper. The indices, as well as the new technique for explaining the differences in life expectancies, have been tested and examples using United States life tables are presented. The technique for explaining life expectancy differentials can be used for analyzing change in mortality or mortality differentials by sex, ethnicity, region, or any other subpopulations. The technique can be applied to life expectancies at birth or temporary life expectancies between any desirable ages.     

Decomposing change in life expectancy: A bouquet of formulas in honor of Nathan Keyfitz’s 90th birthday

We extend Nathan Keyfitz's research on continuous change in life expectancy over time by presenting and proving a new formula for decomposing such change. The formula separates change in life expectancy over time into two terms. The first term captures the general effect of reduction in death rates at all ages, and the second term captures the effect of heterogeneity in the pace of improvement in mortality at different ages. We extend the formula to decompose change in life expectancy into age-specific and cause-specific components, and apply the methods to analyze changes in life expectancy in Sweden and Japan.     

Changing mortality patterns that led life expectancy in Japan to surpass Sweden’s: 1972–1982

Between 1972 and 1982, Japan caught up to and then surpassed Sweden as the country with the longest life expectancy. The contributions of different causes of death and age groups to life expectancy changes in males during this time period are examined in detail for these two countries. Even though cerebrovascular disease mortality rates remained lower in Sweden over the entire interval, the rapid gain made by Japan relative to Sweden for this cause of death was a prime factor in Japan's ending the period with a higher life expectancy. Important contributions to life expectancy improvement in Japan came from declining mortality rates in those aged 55 and older.     

Changes in mortality and life expectancy: Some methodological issues

Measuring and explaining the effects of mortality changes on life expectancy has been discussed for the past three decades. Different approaches have been proposed using discrete or continuous methods. Two basic ideas underlie these approaches. The first compares two different mortality schedules and quantifies the contribution of each age group to the increase in life expectancy. The second analyzes how the progress in the mortality schedule translates into progress in life expectancy. This paper discusses and compares the approaches proposed by the United Nations (1982), Arriaga (1984), Pollard (1982, 1988), and Vaupel (1986), identifying their problems, advantages, and the types of situations where each one can best be applied.     

Change in disability-free life expectancy for Americans 70 years old and older*

In this article, we examine changes in life expectancy free of disability using longitudinal data collected from 1984 through 2000 from two cohorts who composed the Longitudinal Studies of Aging I and II. Life expectancies with and without ADL and/or IADL disability are calculated using a Markov-based multistate life table approach. At age 70, disability-free life expectancy increased over a 10-year period by 0.6 of a year in the later cohort, which was the same as the increase in total life expectancy, both increases marginally statistically significant. The average length of expected life with IADL and ADL disability did not change. Changes in disability-free life expectancy resulted from decreases in disability incidence and increases in the incidence of recovery from disability across the two survey cohorts. Age-specific mortality among the ADL disabled declined significantly in the later cohort after age 80. Mortality for the IADL disabled and the nondisabled did not change significantly. Those with ADL disability at age 70 experienced substantial increases in both total life expectancy and disability-free life expectancy. These results indicate the importance of efforts both to prevent and delay disability and to promote recovery from disability for increasing life expectancy without disability. Results also indicate that while reductions in incidence and increases in recovery work to decrease population prevalence of disability, declining mortality among the disabled has been a force toward increasing disability prevalence.     

Causes of death contributing to changes in life expectancy in New York City between 1983 and 1992

Recent changes in life expectancy among race and sex groups in New York City were evaluated by analyzing the relative effects of different causes of death in 1983 and 1992, a period in which life expectancy at birth declined by 1.1 years among white males, remained unchanged among black males, and increased 1.2 years among white and black females. Heart disease was found to be the leading cause of death making positive contributions to changes in life expectancy regardless of race or sex, and HIV/AIDS was the leading negative contributor. Overall, deaths from infectious diseases and external causes are becoming more important compared to degenerative conditions in explaining trends in life expectancy in New York City. Past improvements in survival due to reductions in infant deaths are being reversed due to an increase in deaths from preventable causes such as violence and AIDS. Future gains in longevity may require a greater emphasis on policies and programs emphasizing conflict resolution and HIV prevention.     

Steep increase in best-practice cohort life expectancy

We analyze trends in best-practice life expectancy among female cohorts born from 1870 to 1950. Cohorts experience declining rather than constant death rates, and cohort life expectancy usually exceeds period life expectancy. Unobserved mortality rates in non-extinct cohorts are estimated using the Lee-Carter model for mortality in 1960–2008. Best-practice cohort and period life expectancies increased nearly linearly. Across cohorts born from 1870 to 1920 the annual increase in cohort length of life was 0.43 years. Across calendar years from 1870 to 2008, the annual increase was 0.28 years. Cohort life expectancy increased from 53.7 years in the 1870 cohort to 83.8 years in the 1950 cohort. The corresponding cohort/period longevity gap increased from 1.2 to 10.3 years. Among younger cohorts, survival to advanced ages is substantially higher than could have been anticipated by period mortality regimes when these cohorts were young or middle-aged. A large proportion of the additional expected years of life are being lived at ages 65 and older. This substantially changes the balance between the stages of the life cycle.     

Trends in senescent life expectancy

The distinction between senescent and non-senescent mortality proves to be very valuable for describing and analysing age patterns of death rates. Unfortunately, standard methods for estimating these mortality components are lacking. The first part of this paper discusses alternative methods for estimating background and senescent mortality among adults and proposes a simple approach based on death rates by causes of death. The second part examines trends in senescent life expectancy (i.e., the life expectancy implied by senescent mortality) and compares them with trends in conventional longevity indicators between 1960 and 2000 in a group of 17 developed countries with low mortality. Senescent life expectancy for females rises at an average rate of 1.54 years per decade between 1960 and 2000 in these countries. The shape of the distribution of senescent deaths by age remains relatively invariant while the entire distribution shifts over time to higher ages as longevity rises.     

Three measures of longevity: Time trends and record values

This article examines the trend over time in the measures of “typical” longevity experienced by members of a population: life expectancy at birth, and the median and modal ages at death. The article also analyzes trends in record values observed for all three measures. The record life expectancy at birth increased from a level of 44 years in Sweden in 1840 to 82 years in Japan in 2005. The record median age at death shows increasing patterns similar to those observed in life expectancy at birth. However, the record modal age at death changes very little until the second half of the twentieth century: it moved from a plateau level, around age 80, to having a similar pace of increase as that observed for the mean and the median in most recent years. These findings explain the previously observed uninterrupted increase in the record life expectancy. The cause of this increase has changed over time from a dominance of child mortality reductions to a dominance of adult mortality reductions, which became evident by studying trends in the record modal age at death.     

Recent trends in mortality in Australia—an analysis of the causes of death through the application of life table techniques

The paper examines the post-1971 reduction in Australian mortality in light of data on causes of death. Multiple-decrement life tables for eleven leading causes of death by sex are calculated and the incidence of each cause of death is presented in terms of the values of the life table functions. The study found that in the overall decline in mortality over the last 20 years significant changes occurred in the contribution of the various causes to total mortality. Among the three leading causes of death, heart disease, malignant neoplasms (cancer), and cerebrovascular disease (stroke), mortality rates due to neoplasms increased and those of the other two causes decreased. The sex-age-cause-specific incidence of mortality changed and the median age at death increased for all causes except for deaths due to motor-vehicle accidents for both sexes and suicide for males. The paper also deciphers the gains in the expectation of life at birth over various time periods and the sex-differentials in the expectation of life at birth at a point in time in terms of the contributions made by the various sex-age-cause-specific mortality rates.     

我国人口预期寿命分析与预测

本文通过对我国人口年龄和性别构成现状的分析,运用蒋庆琅法利用2003年我国人口抽样和死亡率资料编制当年的简略寿命表,估算我国现阶段人口的预期寿命。接着,对我国自解放至今人口预期寿命的变化及其原因进行分析,并最终利用我国自第四次人口普查至第五次人口普查阶段人口预期寿命增长率等相关资料,对我国人口2001-2020年的预期寿命作出预测,得出今后我国人口预期寿命将继续增长,但增长率依年度的推移而递减。     

[Age-specific mortality and life expectancy].]

The author attempts to assess the degree of influence of infant mortality on average life expectancy and to develop a method to directly revise average life expectancy given a change in mortality.     

The key phases of the European health transition

"This paper will attempt to analyse the health transition [in Europe] from 1910.... The different steps in mortality trends, both in quantitative terms and with regard to structural changes by age and cause, will also be analysed and compared where possible to the far reaching changes which marked the history of mortality in Europe. An attempt at synthesis will be performed, using the data on life expectancy at birth in 1910 onwards until recent times. Particular focus will be placed on the more significant stages of the decline in mortality by age and the cause of death...."     

Divergence in Age Patterns of Mortality Change Drives International Divergence in Lifespan Inequality

In the past six decades, lifespan inequality has varied greatly within and among countries even while life expectancy has continued to increase. How and why does mortality change generate this diversity? We derive a precise link between changes in age-specific mortality and lifespan inequality, measured as the variance of age at death. Key to this relationship is a young–old threshold age, below and above which mortality decline respectively decreases and increases lifespan inequality. First, we show for Sweden that shifts in the threshold’s location have modified the correlation between changes in life expectancy and lifespan inequality over the last two centuries. Second, we analyze the post–World War II (WWII) trajectories of lifespan inequality in a set of developed countries—Japan, Canada, and the United States—where thresholds centered on retirement age. Our method reveals how divergence in the age pattern of mortality change drives international divergence in lifespan inequality. Most strikingly, early in the 1980s, mortality increases in young U.S. males led to a continuation of high lifespan inequality in the United States; in Canada, however, the decline of inequality continued. In general, our wider international comparisons show that mortality change varied most at young working ages after WWII, particularly for males. We conclude that if mortality continues to stagnate at young ages yet declines steadily at old ages, increases in lifespan inequality will become a common feature of future demographic change.     

How Change in Age-specific Mortality Affects Life Expectancy

At current mortality rates, life expectancy is most responsive to change in mortality rates at older ages. Mathematical formulae that describe the linkage between change in age-specific mortality rates and change in life expectancy reveal why. These formulae also shed light on how past progress against mortality has been translated into increases in life expectancy – and on the impact that future progress may have. Furthermore, the mathematics can be adapted to study the effect of mortality change in heterogeneous populations in which those who did at some age would, if saved, enjoy a different life expectancy than those who live.     

A statistical analysis of the life expectancy of the residents of our country, 1973-75]

Statistical analysis of life expectancy is important in assessing population health and its characteristics and in studying human diseases and natural population changes. Life tables are constructed and statistical analysis is performed retrospectively on data accumulated over a 3-year (1973-1975) period. The data were supplied by the Office of Cancer Prevention and Treatment of the Ministry of Health, which originated from 24 provinces, representing an accumulated population of 2.04 billion, with a total mortality of 15.29 million. Results show that life expectancy in China has greatly improved since Liberation. Thus, in 1935, the average life expectancy for Nanjing residents was under 35 years. In 1951, the average life expectancy for male and female residents of Shanghai were 42.74 and 46.76 years respectively. But for the 1973-1975 period, the average Chinese life expectancy was 63.62 years for males and 66.31 years for females, with higher life expectancy for coastal provinces than for inland provinces. Cardiovascular diseases (excluding arteriosclerotic heart diseases), malignant tumors, and cerebrovascular diseases were the major causes of death in regions with higher life expectancy, while respiratory diseases, infectious diseases, and diseases of the newborn were the major causes of death in regions with lower life expectancy.     

A new look at entropy and the life table

The mathematical derivations described in this paper offer a new look at the entropy of the life table, denoted by H. Contrary to previous claims, it is theoretically possible, and has been observed empirically, for life tables to have entropy values greater than unity. A re-expression of H as a weighted average of life expectancy at different ages relative to life expectancy at birth demonstrates clearly the conditions under which reductions in mortality by a fixed amount at all ages can result in even greater gains in life expectancy.     

Trends in Education-Specific Life Expectancy,Data Quality,and Shifting Education Distributions: A Note on Recent Research

Several recent articles have reported conflicting conclusions about educational differences in life expectancy, and this is partly due to the use of unreliable data subject to a numerator-denominator bias previously reported as ranging from 20 % to 40 %. This article presents estimates of life expectancy and lifespan variation by education in the United States using more reliable data from the National Health Interview Survey. Contrary to prior conclusions in the literature, I find that life expectancy increased or stagnated since 1990 among all education-race-sex groups except for non-Hispanic white women with less than a high school education; there has been a robust increase in life expectancy among white high school graduates and a smaller increase among black female high school graduates; lifespan variation did not increase appreciably among high school graduates; and lifespan variation plays a very limited role in explaining educational gradients in mortality. I also discuss the key role that educational expansion may play in driving future changes in mortality gradients. Because of shifting education distributions, within an education-specific synthetic cohort, older age groups are less negatively selected than younger age groups. We could thus expect a greater concentration of mortality at younger ages among people with a high school education or less, which would be reflected in increasing lifespan variability for this group. Future studies of educational gradients in mortality should use more reliable data and should be mindful of the effects of shifting education distributions.     

Changing causes of death and the sex differential in the USA

This paper examines the sex differential in US life expectancy, the changes in this differential over the past 25 years and into the near future, and the apportionment of these differences among the leading causes of death. Movements in the sex differential over the years 1960–1985 were largely determined by changes in the accidents and violence and heart disease causes of death. The use of the life expectancy measure emphasizes the importance of those causes of death that impact most severely at younger ages. The historical analysis is extended through projections of life expectancies by sex. In the projections increased cancer mortality among males contributes to a widening differential, tempered by greater progress against heart disease for males.This is a revised version of a paper presented at the meetings of the Population Association of America, 30 April-2 June 1992, in Denver, Colorado.     

Changes in the age dependence of mortality and disability: Cohort and other determinants

Though the general trend in the United States has been toward increasing life expectancy both at birth and at age 65, the temporal rate of change in life expectancy since 1900 has been variable and often restricted to specific population groups. There have been periods during which the age- and gender-specific risks of particular causes of death have either increased or decreased. These periods partly reflect the persistent effects of population health factors on specific birth cohorts. It is important to understand the ebbs and flows of cause-specific mortality rates because general life expectancy trends are the product of interactions of multiple dynamic period and cohort factors. Consequently, we first review factors potentially affecting cohort health back to 1880 and explore how that history might affect the current and future cohort mortality risks of major chronic diseases. We then examine how those factors affect the age-specific linkage of disability and mortality in three sets of birth cohorts assessed using the 1982, 1984, and 1989 National Long Term Care Surveys and Medicare mortality data collected from 1982 to 1991. We find large changes in both mortality and disability in those cohorts. providing insights into what changes might have occurred and into what future changes might be expected.