Estimating adult mortality levels from information on widowhood

Summary A range of indirect techniques has been developed for mortality estimation in societies lacking adequate vital registration records. Information on orphanhood has been widely used as an estimator of adult mortality, with generally plausible results. Doubts have remained, however, about potential biases, and the method is less satisfactory for the estimation of male mortality. Information on widowhood, or more strictly the survival of first spouse, has several possible advantages over information on orphanhood. Model first marriage functions and model life tables are used to calculate proportions widowed of first spouse, for both females and males, by marital duration and by age. These proportions widowed are then related to life table survivorship probabilities to provide weighting factors for the conversion of observed proportions widowed into estimates of survivorship probabilities. The application of the method is illustrated with data collected by the 1974 post-enumeration survey of Bangladesh, with apparently encouraging results.     

Estimating internal migration from incomplete data using model multiregional life tables

A principal feature of current methods of estimating demographic measures from incomplete data is the use of model life tables that approximate the mortality of a region for which reliable mortality data are unavailable. Observed decennial rates of survivorship may be used to identify out of a set of such model life tables one that best matches the observed data. This paper introduces the concept of a modelmultiregional life table and outlines a procedure for selecting an appropriate one using place-of-birth-by-residence data.     

Modeling and Forecasting Health Expectancy: Theoretical Framework and Application

Life expectancy continues to grow in most Western countries; however, a major remaining question is whether longer life expectancy will be associated with more or fewer life years spent with poor health. Therefore, complementing forecasts of life expectancy with forecasts of health expectancies is useful. To forecast health expectancy, an extension of the stochastic extrapolative models developed for forecasting total life expectancy could be applied, but instead of projecting total mortality and using regular life tables, one could project transition probabilities between health states simultaneously and use multistate life table methods. In this article, we present a theoretical framework for a multistate life table model in which the transition probabilities depend on age and calendar time. The goal of our study is to describe a model that projects transition probabilities by the Lee-Carter method, and to illustrate how it can be used to forecast future health expectancy with prediction intervals around the estimates. We applied the method to data on the Dutch population aged 55 and older, and projected transition probabilities until 2030 to obtain forecasts of life expectancy, disability-free life expectancy, and probability of compression of disability.     

Estimation of demographic measures for India, 1881-1961, based on census age distributions

Abstract India is one of the very few developing countries which have a relatively long history of population censuses. The first census was taken in 1872, the second in 1881 and since then there has been a census every ten years, the latest in 1971. Yet the registration of births and deaths in India, even at the present time, is too inadequate to be of much help in estimating fertility and mortality conditions in the country. From time to time Indian census actuaries have indirectly constructed life tables by comparing one census age distribution with the preceding one. Official life tables are available for all the decades from 1872-1881 to 1951-1961, except for 1911-1921 and 1931-1941. Kingsley Davis(1) filled in the gap by constructing life tables for the latter two decades. He also estimated the birth and death rates ofIndia for the decades from 1881-1891 to 1931-1941. Estimates of these rates for the following two decades, 1941-1951 and 1951-1961, were made by Indian census actuaries. The birth rates of Davis and the Indian actuaries were obtained basically by the reverse survival method from the age distribution and the computed life table of the population. Coale and Hoover(2), however, estimated the birth and death rates and the life table of the Indian population in 1951 by applying stable population theory. The most recent estimates of the birth rate and death rate for 1963-1964 are based on the results of the National Sample Survey. All these estimates are presented in summary form in Table 1.     

The four-parameter logit life table system

Summary Brass's model life table system, which is a two parameter system based on the logit transformation of survivorship values, has been widely and successfully used to describe age patterns of mortality in many populations. As more reliable information has become available for populations with mortality patterns which differ in important ways from the assumed standard pattern of mortality, a more flexible model system is needed. This paper shows how Brass's system can be expanded into a four-parameter model, and evaluates the performance of the new system by examining how well it can fit observed life table data.     

Survivorship Of Sons Under Conditions Of Improving Mortality

The strong desire of fathers to be assured that at least one son will outlive them, coupled with the traditional belief in a high probability of sons predeceasing their father, is often a deterrent to restriction of family size. A calculation of the probabilities of survivorship of sons on the basis of the United Nations Model Life Tables, however, shows that the probabilities of a father being outlived by even one son are remarkably high, particularly after that son has survived the first two years of life. When cohort tables are used, reflecting expected mortality improvements, the probabilities are even higher. In general, it is found that the probability that a two-year-old son will outlive his father is 80% or better, subject to the current mortality level and the age of the father.Finally, this paper examines (1) probabilities of a father being outlived by at least one of two or three sons, (2) probabilities of a mother or of both parents being outlived by a son, and (3) the probability that at least one of two sons will outlive a father when allowance is made for the fact that mortality probabilities of the sons are not independent of one another.     

First-marriage decrement tables by color and sex for the United States in 1958–60

A new set of first-marriage tables is compared with earlier tables that were prepared by Grabill and Jacobson. The new tables show, among other things, the number of first marriages, first-marriage probabilities, and death probabilities for single persons in a stationary (life table) population by color and sex, based on 1960 Census data on marital status and age at first marriage and on general mortality rates for 1959-61. A comparison of the earlier tables with the new tables provides evidence of a decrease of one or two years in the average age at first marriage between 1920-40 and 1958-60 and an increasing tendency for first marriages to be concentrated within a narrower span of years. The prospects for eventual marriage have risen to the point where it is estimated that all but 3 to 5 percent of the young adults are expected eventually to marry. This development has gone so far that the main question remaining is not whether young people will ever marry, but at what age they will marry.     

How old is old? Revising the definition based on life table criteria

"Sixty-five has long been thought of as the point of entry into ?old age'. We propose a number of life table criteria for answering the following questions: If 65 was considered appropriate four decades ago, what is the corresponding age today? If 65 was (implicitly) a male-oriented definition four decades ago, as we believe it was, what would have been the appropriate definition for women at that time, and what is it today? We address these questions by applying our criteria to Canada, using 1951 and 1991 life tables, but the criteria could be applied equally well to other countries. For other developed countries we would expect broadly similar results." (EXCERPT)     

How Long Do We Live?

Period life expectancy is calculated from age‐specific death rates using life table methods that are among the oldest and most widely employed tools of demography. These methods are rarely questioned, much less criticized. Yet changing age patterns of adult mortality in countries with high life expectancy provide a basis for questioning the conventional use of life tables. This article argues that when the mean age at death is rising, period life expectancy at birth as conventionally calculated overestimates life expectancy. Estimates of this upward bias, ranging from 1.6 years for the United States and Sweden to 3.3 years for Japan for 1980–95, are presented. A similar bias in the opposite direction occurs when mean age at death is falling. These biases can also distort trends in life expectancy as conventionally calculated and may affect projected future trends in period life expectation, particularly in the short run.     

How old is old? Revising the definition based on life table criteria

Sixty‐five has long been thought of as the point of entry into “old age.”; We propose a number of life table criteria for answering the following questions: If 65 was considered appropriate four decades ago, what is the corresponding age today? If 65 was (implicitly) a male‐oriented definition four decades ago, as we believe it was, what would have been the appropriate definition for women at that time, and what is it today? We address these questions by applying our criteria to Canada, using 1951 and 1991 life tables, but the criteria could be applied equally well to other countries. For other developed countries we would expect broadly similar results.     

Active life expectancy estimates for the U.S. elderly population: A multidimensional continuous-mixture model of functional change applied to completed Cohorts, 1982–1996

An increment-decrement stochastic-process life table model that continuously mixes measures of functional change is developed to represent age transitions among highly refined disability states interacting simultaneously with mortality. The model is applied to data from the National Long Term Care Surveys of elderly persons in the years 1982 to 1996 to produce active life expectancy estimates based on completed-cohort life tables. At ages 65 and 85, comparisons with extant period estimates for 1990 show that our active life expectancy estimates are larger for both males and females than are extant period estimates based on coarse disability states.     

Age structure,growth, attrition and accession: A new synthesis

This paper shows that each equation describing relationships among demographic parameters in a stable population is a special case of a similar and equally simple equation that applies to any closed population and demonstrates some implications of these new equations for demographic theory and practice. Much of formal demography deals with functions that pertain to individuals passing through life, or to a stationary population in which births of individuals are evenly distributed over time. These functions include life expectancy, probabilities of survival, net and gross reproduction rates, expected years spent in various states and the probability that certain events will occur in the course of life. The stable population model permits the translation of population structure or processes in a more general type of population, with constant growth rates, back into equivalent populations for a stationary population. The method for translation developed in this paper, requiring only a set of age-specific growth rates is even more general, applying to any population. Age specific growth rates may also be useful for performing reverse translations, between a population's life table and its birth rate or its age distribution. Tables of numbers of females by single years of age in Sweden are used to illustrate applications. Tables summarize the basic relations among certain functions in a stationary population, a stable population and any population. Applications of new equations, particularly to demographic estimation of mortality, fertility and migration, from incomplete data, are described. Some other applications include; the 2 sex problem, increment decrement tables, convergence of population to its stable form, and cyclical changes in vital rates. Stable population models will continue to demonstrate long term implications of changes in mortality and fertility. However, in demographic estimation and measurement, new procedures will support most of those based on stable assumptions.     

Labor force status life tables for the United States, 1972

As an ordinary life table follows a closed group from birth to the death of its last member, a labor force status life table follows a closed group through life and through the statuses “in the labor force” and “not in the labor force.” Using data from the January 1972 and January 1973 Current Population Surveys, two types of labor force status life tables were calculated for the United States, 1972. One type was a conventional working life table (for males) which started with an ordinary life table and partitioned the life table population into labor force statuses using age-specific proportions in the labor force. The other type was an increment-decrement table, prepared for both males and females, which was calculated so as to be consistent with the rates of labor force accession and separation implied by the data. Increment-decrement labor force status life tables are generally preferable to conventional working life tables. They reflect the implications of a clearly specified set of behavioral rates, provide detailed measures of the flows between labor force statuses, do not introduce seriously biasing approximations into the calculation of summary measures of labor force experience, and can be applied to female data as easily as male data. In practice, incrementdecrement labor force status life tables can be calculated from current and retrospective data generated by a single labor force survey. The increment-decrement labor force status life tables for the United States, 1972 reflected the extent to which the labor force participation of males exceeded that of females, but indicated that, on the average, half a woman’s lifetime between the ages of 16 and 65 was spent in the labor force. There were marked differences in the proportions, by age, of males and females in the labor force, with the male pattern rising to a single, flat peak and the female pattern being bimodal. Nonetheless, the two sexes shared similar age patterns in the proportions changing, or not changing, their labor force status.     

Sex differences in life cycle measures of widowhood

Using formulas which measure life cycle characteristics of widowhood as a function of life table survivorship and age at marriage, we illustrate changes in patterns of widowhood and widowerhood since 1950, as well as differences by race, by age of bride and of groom, and by age differences between spouses. Although the current inequality in the risks of widowhood and widowerhood for the average couple is mostly due to sex differences in mortality, a one year age difference between spouses has about the same impact as does a one year difference in life expectancy. Calculations based on current distributions of age of groom by age of bride indicate that the older the age of groom, the greater the age difference between spouses and the higher the likelihood of a woman outliving her husband: the typical groom who marries in his fifties faces a 4 to 1 chance that he will be outlived by his spouse.     

Variation in life expectancy during the twentieth century in The United States

The National Center for Health Statistics (NCHS) reports life expectancy at birth (LE) for each year in the United States. Censal year estimates of LE use complete life tables. From 1900 through 1947, LEs for intercensal years were interpolated from decennial life tables and annual crude death rates. Since 1948, estimates have been computed from annual life tables. A substantial drop in variation in LE occurred in the 1940s. To evaluate these methods and examine variation without artifacts of different methods, we estimated a consistent series of both annual abridged life tables and LEs from official NCHS age-specific death rates and also LEs using the interpolation method for 1900-1998. Interpolated LEs are several times as variable as life table estimates, about 2 times as variable before 1940 and about 6.5 times as variable after 1950. Estimates of LE from annual life tables are better measures than those based on the mixed methods detailed in NCHS reports. Estimates from life tables show that the impact of the 1918 influenza pandemic on LE was much smaller than indicated by official statistics. We conclude that NCHS should report official estimates of intercensal LE for 1900-1948 computed from life tables in place of the existing LEs that were computed by interpolation.     

Parental survival data: Some results of the application of Ledermann's model life tables

Summary Ledermann's one- and two-parameter model life tables are used in order to summarize and compare adult mortality estimates derived from parental survival data, and also to link parental survival with child survival data. The Ledermann models provide an alternative to the logit model used by Brass and Hill. Examination of life tables derived from actual child and adult mortality estimates reveals that although the two types of models yield similar overall levels of mortality, they show marked differences in the estimated patterns by sex and age. It has not been possible to disentangle completely how much of this divergence is due to the models themselves and how much to inadequacies in the data available. Finally, we question whether it is always wise to establish a full life table from child and adult mortality estimates when these are based on data which refer to different periods of exposure to the risk of dying, without allowance for possible distortions resulting from mortality change.     

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.     

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.     

Constructing increment-decrement life tables

A life table model which can recognize increments (or entrants) as well as decrements has proven to be of considerable value in the analysis of marital status patterns, labor force participation patterns, and other areas of substantive interest. Nonetheless, relatively little work has been done on the methodology of increment-decrement (or combined) life tables. The present paper reviews the general, recursive solution of Schoen and Nelson (1974), develops explicit solutions for three cases of particular interest, and compares alternative approaches to the construction of increment-decrement tables.     

Estimating Increment-Decrement Life Tables with Multiple Covariates from Panel Data: The Case of Active Life Expectancy*

A fundamental limitation of current multistate life table methodology-evident in recent estimates of active life expectancy for the elderly-is the inability to estimate tables from data on small longitudinal panels in the presence of multiple covariates (such as sex, race, and socioeconomic status). This paper presents an approach to such an estimation based on an isomorphism between the structure of the stochastic model underlying a conventional specification of the increment-decrement life table and that of Markov panel regression models for simple state spaces. We argue that Markov panel regression procedures can be used to provide smoothed or graduated group-specific estimates of transition probabilities that are more stable across short age intervals than those computed directly from sample data. We then join these estimates with increment-decrement life table methods to compute group-specific total, active, and dependent life expectancy estimates. To illustrate the methods, we describe an empirical application to the estimation of such life expectancies specific to sex, race, and education (years of school completed) for a longitudinal panel of elderly persons. We find that education extends both total life expectancy and active life expectancy. Education thus may serve as a powerful social protective mechanism delaying the onset of health problems at older ages.