A hazards-Model analysis of the covariates of infant and child mortality in Sri Lanka

The purpose of this paper is twofold: (a) to provide a complete self-contained exposition of estimating life tables with covariates through the use of hazards models, and (b) to illustrate this technique with a substan-tive analysis of child mortality in Sri Lanka, thereby demonstrating that World Fertility Survey data are a valuable source for the study of child mortality. We show that life tables with covariates can be easily estimated with standard computer packages designed for analysis of contingency tables. The substantive analysis confirms and supplements an earlier study of infant and child mortality in Sri Lanka by Meegama. Those factors found to be strongly associated with mortality are mother’s and father’s education, time period of birth, urban/rural/estate residence, ethnicity, sex, birth order, age of the mother at the birth, and type of toilet facility.     

The Association Between Individual Income and Remaining Life Expectancy at the Age of 65 in the Netherlands

This article quantifies the association between individual income and remaining life expectancy at the statutory retirement age (65) in the Netherlands. For this purpose, we estimate a mortality risk model using a large administrative data set that covers the 1996–2007 period. Besides age and marital status, the model includes as covariates individual and spouse’s income as well as a random individual specific effect. It thus allows for dynamic selection based on both observed and unobserved characteristics. We find that conditional on marital status, individual income is about equally strong and negatively associated with mortality risk for men and women and that spouse’s income is only weakly associated with mortality risk for women. For both men and women, we quantify remaining life expectancy at age 65 for low-income individuals as approximately 2.5 years less than that for high-income individuals.     

The longevity of Jews in Canada, 1940–1942

A life table for the Jewish population of Canada, based upon their mortality experience during 1940–2, yielded an average length of life (expectation of life at birth) of 67–53 years for males and 69·89 years for females. These figures are greater than those for the general population of Canada by 4·58 years for males and 3·60 years for females. These margins decrease with advance in age; the expectations of life for Jews and for the total Canadian population are equal at age 25 in the case of females, and at age 35 in the case of males.

Jewish infants in Canada start life with a mortality rate, in the first year, only two-fifths of that for the general population. This advantage for Jews is observed through childhood, adolescence, and early maturity. However, the margin between the Jewish and total populations decreased with advance in age until, shortly after age 50, the Jews begin to show the higher mortality rates.

The Jewish populations of the United States and of Canada have great similarities in their social and economic structures. They also share, very largely, in their European origins, and they have come to North America during the same period. It is, therefore, a fair assumption that the longevity and mortality characteristics of the relatively small Jewish population of Canada may be indicative of what might be found for the millions of Jews in the United States, for whom such information is not available.     

Revised regional model life tables at very low levels of mortality

This paper presents and discusses new model life tables at very low mortality, which make use of age-specific death rates from the 1960s, 1970s, and 1980s. These life tables fit recorded death rates in very low mortality populations better than do the existing ones at expectations of life of 77.5 and 80 years. The old tables incorporate too-high mortality at the higher ages and in infancy and they incorporate regional differences that no longer exist. The new tables "close out" the mortality schedules above age 80 more realistically. The convergence of age patterns of mortality at very high life expectancies in populations that used to conform to different families is in itself of demographic interest. Some convergence may perhaps be expected. Sullivan (1973) found that, in Taiwan, the comparison of mortality at ages 1-5 to mortality at 5-35 in the late 1950s showed higher mortality at the younger ages relative to the ensuing 30-year age interval than was found in any of the models, including the South model, which has the highest relative mortality from ages 1-5 among the 4 regional patterns. Then, in the late 1960s, the relation of mortality at 1-5 to mortality at 5-35 in Taiwan fell to a position intermediate between the West and South tables. Sullivan found in data on mortality by cause of death a large reduction in mortality from diarrhea and enteritis, no doubt as a result of environmental sanitation. Mortality from these causes is concentrated among young children, and reduction in deaths from these causes would naturally diminish the excess mortality in this age interval. The East pattern, characterized by very high mortality in infancy (but not from 1-5), may be the result of the prevalence of early weaning or avoidance of breast feeding altogether in the populations characterized by this pattern. As health conditions have improved, evidenced by the overall design of mortality, these special factors are diminished or erased. Model life tables at these very low mortality levels have different uses from most applications of model life tables at higher mortality. The use of model tables to estimate accurate schedules of mortality when the basic data are incomplete or inaccurate is less relevant in this range of mortality levels.     

Starting age and subsequent birth intervals in cohabitational unions in current danish cohorts, 1975

This paper presents some main results of an investigation by life table methods of birth interval data in cohabitational unions (marriages as well as consensual unions) in current Danish cohorts. Our results confirm previous findings that an early age at the start of recorded exposure to childbearing risk is indicative of a rapid pace and high level of subsequent fertility. The analysis modifies previous results and adds several new details regarding cohort trends and the effect of parity at the start of reported cohabitation. For each parity within a period of cohabitation, fertility differentials by reported starting age seem to have diminished from our older cohorts (of age up to 49 years in 1975) to our younger ones (of age less than 30 years in 1975). There are indications of a dramatic change in childbearing behaviour following the arrival of novel attitudes to non-marital cohabitation and childbearing in Denmark about 1967.     

Age,Period, Cohort and Early Mortality: An Analysis of Adult Mortality in Italy

Changes in adult mortality in Italy for cohorts born between 1882 and 1953 are analysed and interpreted by means of two different statistical models. The first, an Age–Period–Early Mortality (APEM) model, is employed to analyse the possible relationships between adverse conditions during the first 15 years of life and subsequent mortality. It is shown that higher mortality early in life is associated with higher mortality up to age 45 and lower mortality at latter ages. Finally, possible links between the observed decline in early mortality and the evolution of adult mortality are analysed and discussed.     

Extending the Lee-Carter Method to Model the Rotation of Age Patterns of Mortality Decline for Long-Term Projections

In developed countries, mortality decline is decelerating at younger ages and accelerating at old ages, a phenomenon we call “rotation.” We expect that this rotation will also occur in developing countries as they attain high life expectancies. But the rotation is subtle and has proved difficult to handle in mortality models that include all age groups. Without taking it into account, however, long-term mortality projections will produce questionable results. We simplify the problem by focusing on the relative magnitude of death rates at two ages (0 and 15–19) while making assumptions about changes in rates of decline at other ages. We extend the Lee-Carter method to incorporate this subtle rotation in projection. We suggest that the extended Lee-Carter method could provide plausible projections of the age pattern of mortality for populations, including those that currently have very high life expectancies. Detailed examples are given using data from Japan and the United States.     

US mortality in an international context: age variations

Compared to other developed countries, the United States ranks poorly in terms of life expectancy at age 50. We seek to shed light on the US's low life expectancy ranking by comparing the age-specific death rates of 18 developed countries at older ages. A striking pattern emerges: between ages 40 and 75, US all-cause mortality rates are among the poorest in the set of comparison countries. The US position improves dramatically after age 75 for both males and females. We consider four possible explanations of the age patterns revealed by this analysis: (1) access to health insurance; (2) international differences in patterns of smoking; (3) age patterns of health care system performance; and (4) selection processes. We find that health insurance and smoking are not plausible sources of this age pattern. While we cannot rule out selection, we present suggestive evidence that an unusually vigorous deployment of life-saving technologies by the US health care system at very old ages is contributing to the age-pattern of US mortality rankings. Differences in obesity distributions are likely to be making a moderate contribution to the pattern but uncertainty about the risks associated with obesity prevents a precise assessment.     

Increment–Decrement Life Table Estimates of Happy Life Expectancy for the U.S. Population

Using large nationally representative longitudinal data on changes in happiness and mortality and multivariate increment–decrement life tables, we assess length of quality life through cohort estimates of happy life expectancies. We examine population-based and status-based life expectancies in absolute term of years and relative term of proportions. We find that happy life expectancies exceed unhappy life expectancies in both absolute and relative terms for the overall population and population in each state of happiness at any given age. Being happy (as opposed to unhappy) at any age brings a longer life and more of the future life spent in happiness. We also examine social differentials in the estimates of happy life expectancy at each age by sex, race, and education. The educational gap in happy life expectancies is larger than the sex and race gaps. For the better educated, longer life consists of a longer happy life and shorter unhappy life in both years and proportions and regardless of happy or unhappy status at any given age.     

Losses of Expected Lifetime in the United States and Other Developed Countries: Methods and Empirical Analyses

Patterns of diversity in age at death are examined using e ^†, a dispersion measure that equals the average expected lifetime lost at death. We apply two methods for decomposing differences in e ^†. The first method estimates the contributions of average levels of mortality and mortality age structures. The second (and newly developed) method returns components produced by differences between age- and cause-specific mortality rates. The United States is close to England and Wales in mean life expectancy but has higher life expectancy losses and lacks mortality compression. The difference is determined by mortality age structures, whereas the role of mortality levels is minor. This is related to excess mortality at ages under 65 from various causes in the United States. Regression on 17 country-series suggests that e ^† correlates with income inequality across countries but not across time. This result can be attributed to dissimilarity between the age- and cause-of-death structures of temporal mortality reduction and intercountry mortality variation. It also suggests that factors affecting overall mortality decrease differ from those responsible for excess lifetime losses in the United States compared with other countries. The latter can be related to weaknesses of health system and other factors resulting in premature death from heart diseases, amenable causes, accidents and violence.     

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.     

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.     

Continued Reductions in Mortality at Advanced Ages

Mortality data for 30 mostly developed countries available in the Kannisto–Thatcher Database on Old‐Age Mortality (KTDB) are drawn on to assess the pace of decline in death rates at ages 80 years and above. As of 2004 this database recorded 37 million persons at these ages, including 130,000 centenarians (more than double the number in 1990). For men, the probability of surviving from age 80 to age 90 has risen from 12 percent in 1950 to 26 percent in 2002; for women, the increase has been from 16 percent to 38 percent. In the lowest‐mortality country, Japan, life expectancy at age 80 in 2006 is estimated to be 6.5 years for men and 11.3 years for women. For selected countries, average annual percent declines in age‐specific death rates over the preceding ten years are calculated for single‐year age groups 80 to 99 and the years 1970 to 2004. The results are presented in Lexis maps showing the patterns of change in old‐age mortality by cohort and period, and separately for men and women. The trends are not favorable in all countries: for example, old‐age mortality in the United States has stagnated since 1980. But countries with exceptionally low mortality, like Japan and France, do not show a deceleration in death rate declines. It is argued that life expectancy at advanced ages may continue to increase at the same pace as in the past.     

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.     

Diverging Trends in Female Old‐Age Mortality: The United States and the Netherlands versus France and Japan

In the most advanced countries, child mortality and adult mortality under age 65 years have fallen so low that further improvement in life expectancy relies almost completely on the decline of mortality at older ages. This phenomenon is particularly pronounced among women, who are far ahead of men in survival rates. Thus, to project the future of life expectancy, this study focuses on trends in female life expectancy at ages 65 and older. Four countries are selected for this analysis: the United States, Netherlands, France, and Japan. It is particularly interesting to understand why American and Dutch trends in female old‐age mortality have been diverging from those in France and Japan for two decades. It is shown here that most of the divergence derives from the fact that decline in cardiovascular mortality is more and more offset by increases in other causes of death in the United States and the Netherlands, while the other two countries are more successful in reducing mortality from all causes at increasingly older ages. This latter phenomenon could represent a new stage of the health transition.     

Mortality Attributable to Cigarette Smoking in the United States

Cigarette smoking is an especially pernicious behavior because of its high prevalence and mortality risk. We use the powerful methodology of life tables with covariates and employ the National Health Interview Survey‐Multiple Cause of Death file to illuminate the interrelationships of smoking with other risk factors and the combined influences of smoking prevalence and population size on mortality attributable to smoking. We find that the relationship between smoking and mortality is only modestly affected by controlling for other risk factors. Excess deaths attributable to smoking among adults in the United States in the year 2000 were as high as 340,000. Better knowledge of the prevalence and mortality risk associated with different cigarette smoking statuses can enhance the future health and longevity prospects of the population.     

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.     

A reply to Kim's comment

This reply criticizes Kim's note as incorrectly characterizing the essential feature of the method proposed for life table construction. The method suggested for estimating N(a), the number attaining age 2 during the intercensal period, is to make a separate estimate of the contribution to N (a) made by each single-year cohort that attains 'a' during the period between censuses. Each cohort estimate is constructed by interpolation, utilizing as data the recorded number in the relevant single-year cohorts in the 2 censuses. 2 methods of interpolation were proposed. 1 is an iterative procedure that constructs a preliminary life table by linear interpolation for each cohort and then derives more refined interpolation factors from this preliminary life table. The other procedure derives interpolation factors on the assumption that the proportionate distribution of deaths by age as each cohort moves from the earlier to the later census date is the same as the proportionate distribution of deaths by age over the same age range in a model life table. The advantage of the proposed procedure is that it supplies better estimates of N (a) than do alternative methods. The author concedes that a life table calculated from accurately recorded deaths and an accurately enumerated population would ordinarily be superior. However, he also notes that in the absence of registered deaths data, there is no precise enough conventional method to yield accurate values of average intercensal single-year age-specific mortality rates from nothing more than 2 accurate censuses 11 years apart. A common procedure for calculating life expectation at a very advanced age is to calculate the reciprocal of the death rate among persons over the age in question.     

Life Potential as a Basic Demographic Indicator

This paper proposes an indicator that integrates life expectancy with the demographic structure of the population for a given society. By doing this, we have a simple indicator of mortality and aging combined, which could be very useful for developed societies. As is widely known, life expectancy at birth is independent of the demographic structure of the population, and therefore is adequate for measuring overall mortality. However, it neglects to take into account the fact that as life expectancy increases society ages, and so looking at life expectancy alone can produce an overly optimistic view of the development process, especially if we pay attention to future sustainability. Aging can in fact affect quality of life and sustainability in the long run. The indicators for aging are usually very crude, such as providing information on the share of the population who are 65 and over. We propose a simple indicator that integrates life expectancy at different ages, not only at birth, with the demographic structure of the population at a given point in time. The indicator has an intuitive interpretation in terms of the life potential, or biological capital, of society; and given that it is a weighted average, its changes can be easily decomposed into reductions in mortality (gains in life expectancy) and aging for different age intervals.     

The influence of cause-specific mortality conditions on the age pattern of mortality with special reference to Taiwan

Abstract This paper discusses the relationship between the level of mortality at ages one to four, on one hand, and five to 34 on the other. This relationship has been observed to vary considerably among mortality schedules at different levels of mortality and even among schedules at the same general level of mortality. This variation is shown among the modem life table systems of the Regional Model Life Tables and the United Nations Model Life Tables. Controlling for the leyel ofmortality from age five to age 34, the West Tables and the United Nations Tables embody approximately the same 'average' relationship between early childhood and adult mortality. Relatively to this average relationship, the South and East Tables consistently display higher childhood mortality rates for a given level of adult mortality. Indeed, the childhood rates of the South Table are twice those of the West Tables over a range of life expectancy at birth from 40 to 70 years. The relationship between childhood and adult mortality from 1957 to 1968, a period of rapid mortality decline, was investigated in Taiwan. In 1957, the Taiwanese data reflected the severe childhood mortality of the South Model Tables. However, by 1968, due to an especially large decline in childhood mortality, this relationship was more moderate and resembled the mortality pattern of the West or East Model Tables. An analysis of the decline in cause-specific mortality during the period revealed that a dramatic decline in childhood mortality from gastro-enteritis was primarily responsible for the shift in the relationship between childhood and adult mortality in Taiwan. It is asserted that, while any of several diseases which result in fatalities primarily among children of pre-school ages, could cause relatively severe childhood mortality, gastro-enteritis is likely to be a primary contributor to such an age pattern. This assertion is based on the fact that, especially in the developing areas of the world, malnutrition and gastro-enteritis are usually precipitating and complicating factors of other childhood diseases. A limited test of this hypothesis was provided by considering the causal components of childhood mortality rates in two populations known, for certain periods, to have exhibited relatively severe childhood mortality conditions; Spain and Portugal. For the years in which those populations were characterized by the South mortality pattern, gastro-enteritis was a principal cause of mortality in childhood. Moreover, with the decline in mortality from gastro-enteritis, the mortality pattern in Spain and Portugal no longer exhibited childhood mortality rates which were severe relative to those of adult life. The implications of these findings for the analysis of mortality conditions in many areas of the developing world, where the gastro-enteritis malnutrition syndrome annually claims a heavy toll of life in early childhood, are not clear. In those areas, the effect of this syndrome on the age pattern of mortality could be offset by special conditions inflating adult mortality rates. Nevertheless, in circumstances where there is evidence indicating substantial childhood mortality from this syndrome and no evidence indicating compensating severe adult mortality, there is reason to suspect that the existing mortality pattern reflects the relatively severe childhood mortality conditions of the South Model Tables. Additionally, where mortality from the gastro-enteritis malnutrition syndrome has been severe in past years, but has been reduced to low levels in recent years, it is probable that the relationship between childhood and adult mortality will shift in favour of the former - quite possibly, in the manner of Taiwan, from a South to an East or West age pattern.