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.     

The Level and Age Pattern of Mortality in Bandafassi (Eastern Senegal): Results From a Small-Scale and Intensive Multi-Round Survey

The data collected in the Bandafassi demographic study in Eastern Senegal, a small-scale intensive and experimental follow-up survey of a population of about 7,000 in 1983, were analysed to derive an estimated life table. The use of multi-round surveys, combined with anthropological methods to estimate ages and collect genealogies, has resulted in unusually reliable data. Taking into account the uncertainty of the estimates due to the small size of the population, mortality was high, with life-expectancy at birth close to 31 years; a pattern of infant and child mortality close to that observed in other rural areas of Senegal, with a very high level or mortality between ages six months and three years; a seasonal pattern in child mortality with two high-risk periods, the rainy season and the end of the dry season; an adult mortality pattern similar to that described in model life tables for developed countries; no significant difference by sex or ethnic group. The Bandafassi population study and a few similar studies suggest that one possible way to improve demographic estimates in countries where vital registration systems are defective would be to set up a sample of population laboratories where intensive methods of data collection would continue for extended periods.     

Contribution of mortality decline to longer working life: The case of indonesian males 1980–1995

The length of working life of Indonesian males has been estimated for 1980 and 1995. Data on age specific labour force participation rates are obtained from the 1980 census and the 1995 intercensal population survey. Data on agespecific mortality have been adopted from appropriate model life tables based on indirect estimates of child mortality in the absence of any direct information about mortality. The contribution of declining mortality to the lengthening of working life has been greater than the contribution of higher labour force participation rates. Reductions in mortality at ages before entry into the labour force have increased the potential for added and improved education and training needed for the work force, which is also a contribution of reduced mortality to human capital development. The findings have implications for policy and future employment plans.     

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.     

The Courbage-Fargues method of indirect measurement of mortality: adequacy and inadequacy of the case of Togo in 1971

This study tests the validity of an indirect method of estimating mortality from inaccurate data from demographic investigations conducted in Togo in 1971. The method yields good results for Togo where life expectancy at birth is estimated at 40.51 years for males and 43.12 years for females. The article responds to the request of participants of the Colloquim of Abidjan and then corrects the mortality level of Togo in 1971 derived from the biased demographic investigation in Togo in 1971. OCDE tables were used to support estimates of mortality. A hypothesis of the method was that the deaths of the last 12 months are underreported in a constant proportion. A 2nd hypothesis was that the mortality of the country is related to a mortality pattern according to age. This method of Courbage-Fargues has produced satisfactory results. Certain demographers believe that the undercount rates are probably differentials according to age, particularly among those who die in the 1st few years of life. Others believe that knowledge of deaths that occur in the later years lacks certainty. Mortality data in Africa are not adequate enough to utilize as bases for estimates. For Togo, in particular, the application of other indirect measures of mortality is hoped for to allow comparisons.     

The sources of error in Brass's method for estimating child survival: the case of Bangladesh

Abstract Brass's method for estimating child mortality is based on an ingeniously simplified model. However, it frequently leads to values of q(x) that are not consistent with each other. This is most obvious for estimates of q(1). This paper examines the extent to which such inconsistencies are caused by simplifications in the model. Three assumptions are relaxed by adjusting for differences in infant mortality by birth order, taking account of annual fluctuations in mortality, and using a different age pattern of fertility for each cohort. These adjustments are applied to data from the 1974 Bangladesh Retrospective Survey of Fertility and Mortality and the 1975 Bangladesh Fertility Survey in which additional data from the Cholera Research Laboratory are used. The resulting estimates are more consistent both internally and with estimates from other surveys and by other procedures.     

A reconsideration of negro-white mortality differentials in the united states

This paper summarizes the results of an investigation of the validity of Negro-white mortality differentials as reflected in the series of official United States life tables since the turn of the century. Pertinent excerpts from these often-quoted tables are reproduced in Appendix Table A-1 for convenient reference. The paper divides into two main parts.First, mortality levels and differentials beyond early childhood are derived, without use of the existing vital records, by interpreting the series of ten-year cumulative survival rates implicit in the census records for native whites and for Negroes. The results are in general agreement with the official figures, particularly for males.Second, mortality levels and differentials in early childhood are estimated by extrapolating the official 1)5 values via model life tables; that is, by the analytical procedure that would be followed in the absence of direct information on early childhood mortality. Unless it is assumed that age patterns of death for United States Negroes were extremely deviant from those found in populations with reliable census and vital statistics, one must conclude that the official figures grossly underestimate early childhood mortality for Negroes, at least for the period, 1910-40. It follows that, during those decades, Negro-white mortality differentials in terms of expectation of life at birth were also substantially higher than is suggested by the official estimates.     

New african American life tables from 1935–1940 to 1985–1990*

New life tables for African Americans are presented from 1935 through 1990. They are based on a historical series of vital statistics data on deaths that have been corrected for age misreporting, on reconstructed population counts that have been adjusted for census underenumeration, and on births that have been corrected for underregistration. The new life tables show rapid mortality declines for both African American males and females from 1935 to 1950, and relatively steady reductions thereafter for females. The smaller declines in male mortality in young adulthood and middle age since the 1950s have led to exceptionally high ratios of male to female mortality at these ages. Corrections for census undercounts lead to higher values of life expectancy than in official life tables, but to less improvement over time. Official estimates of life expectancy at age 65 appear to be about 10% too high around 1940 but only about 1.5% too high in the late 1980s.     

Far eastern patterns of Mortality

Summary In this paper a mortality pattern is identified which has not previously been described by model mortality schedules and seems to have occurred only in populations in the Far East. Mortality schedules in Taiwan, Hong Kong, Singapore, and Korea during the past several decades have been characterized by excessively high death rates of men at the older ages. This excess mortality has progressively diminished and most recent death rates for men show only slight deviations from West model life tables. An examination of statistics on causes of death suggests that tuberculosis is at least partly responsible for the excess mortality of men.     

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.     

New estimates of the vital rates of the United States black population during the nineteenth century

The difficulties of obtaining credible estimates of vital rates for the black population throughout the entire nineteenth century are overcome in this study. The methodology employed the notion of deviating networks of mortality rates for each general mortality level, which was taken from the United Nations studyThe Concept of a Stable Population. Period life tables and vital rates for intercensal periods were generated from the new estimates of the black population at each census date. The results of this study are highly compatible both with the life tables for the death-registration states in the twentieth century and the recent Coale and Rives reconstruction for the period from 1880 to 1970 and with several estimates of vital rates previously made for the mid-nineteenth century. This study places the mean life expectancy at birth for the black population during the nineteenth century at about 33.7 years for both sexes. The infant death rate (1000m (0)) is shown to have varied between 222 and 237 for females and between 266 and 278 for males. The intrinsic crude death rate centered on 30.4 per thousand during the century, while the birth rate declined from 53.2 early in the century to about 43.8 at the end.     

Model life tables: An empirical test of their applicability to less developed countries

Model life tables are commonly used for estimating various parameters of mortality of populations in developing countries with limited data. The application of the models is based on the assumption that the agemortality pattern of the population under consideration resembles one of the life tables in the models. The analysis in this paper tests the validity of this assumption for developing countries with data usable for the purpose. The major conclusion is that infant mortality in the populations analyzed is higher than predicted by the models corresponding to the levels of adult mortality of these populations. The observed discrepancy is ascribed to the selectivity involved in the construction of model life tables, which are primarily derived from the historical experience of Western countries. Populations in the currently developing countries apparently differ in the process of mortality change from those used in the models. Though the analysis is limited to a few countries and may not necessarily be true for all the less developed countries, it suggests the need for caution in the use of conventional model life tables.     

On the theory and measurement of the determinants of mortality

This article develops a model of mortality that shows how biological, demographic, and environmental factors interact to affect an individual's probability of dying. To illustrate the usefulness of the model, we derive from it (as special cases) the Brass system of model life tables and the proportional-hazard mortality model and apply a logit version of the model to analyze the determinants of child mortality in Sri Lanka.     

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.     

A reducible four-parameter system of model life tables

Abstract In this paper a four-parameter extension of Brass's relational system of model life tables is suggested that (1) matches a wide range of empirical age patterns of mortality, (2) is easy to apply, especially to partial life tables, and (3) contains demographically meaningful parameters. A test of the model on a set of 62 empirical life tables indicates that four parameters are necessary and sufficient for fitting a wide range of mortality patterns. A further test on an historical series of Swedish life tables reveals a consistent pattern of mortality change. Examination of the parameters for a set of geographicallyrelated life tables suggests a way to define families of life tables. Identification of such temporal and spatial relationships allows the model to be reduced to a form with twoor three-parameters for application to incomplete or inaccurate data.     

Evaluation of estimates of underenumeration in the census and the age pattern of mortality,philadelphia, 1880

The schedule of mortality by age for Philadelphia's 1880 population classified by sex and race showed aberrations from Coale and Demeny West, South, and North model life tables. Deviations from standard age patterns of mortality were especially pronounced for the black population. The question addressed in this paper is whether the alternative age patterns of mortality are produced by underenumeration in the 1880 census or by actual variations in the age-specific mortality experience. The conclusion was reached that the underenumeration of the urban population, especially the blacks, exceeds estimates for the national population. In addition, the results indicated that the black population faced risks of dying that genuinely differed from standard age patterns. An attempt to use a Brass logit model to generalize the black mortality experience met with success for females but not for males.     

Mortality in Quebec during the nineteenth century: from the state to the cities

The aim of this paper is to explore mortality in Quebec during the nineteenth century from a demographic perspective. During the nineteenth century, there was excess urban mortality in various countries; in order to identify such mortality differentials, we compared mortality indicators for the province of Quebec and then for the urban areas of Montreal and Quebec City. Using data from various studies, we produced life tables and compared life expectancies. We show that at different times during the nineteenth century, spatial variations in mortality levels across the province of Quebec and its urban areas were significant. According to the data we analyzed, mortality is undoubtedly higher in urban areas even though a convergence in trends took place towards the end of the century, resulting in an overall reduction in mortality. Also, exploring life expectancies within a cohort approach at times of fast-changing mortality patterns has proved to be instructive. Life expectancy estimates based on a cross-sectional approach were systematically lower than those resulting from a cohort-specific one. Trends diverged to a greater extent beginning with the 1870 cohort, reflecting the improvements made from that point on to World War II. Since current mortality levels are substantially determined by the cumulative effects of past behaviour specific to each generation, it is quite obvious that mortality analysis will reveal its true meaning only with the help of cohort life tables.     

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.