A flexible two-dimensional mortality model for use in indirect estimation

Mortality estimates for many populations are derived using model life tables, which describe typical age patterns of human mortality. We propose a new system of model life tables as a means of improving the quality and transparency of such estimates. A flexible two-dimensional model was fitted to a collection of life tables from the Human Mortality Database. The model can be used to estimate full life tables given one or two pieces of information: child mortality only, or child and adult mortality. Using life tables from a variety of sources, we have compared the performance of new and old methods. The new model outperforms the Coale-Demeny and UN model life tables. Estimation errors are similar to those produced by the modified Brass logit procedure. The proposed model is better suited to the practical needs of mortality estimation, since both input parameters are continuous yet the second one is optional.     

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.     

Comparison of Four Methods for Estimating Complete Life Tables from Abridged Life Tables Using Mortality Data Supplied to EUROCARE-3

ABSTRACT

To estimate mortality due to cancer, it is necessary to have mortality data by year of age in the population of cancer patients. When such data are not available, estimating one-year (complete) life tables from five-year (abridged) life tables is necessary. Four such methods—Elandt–Johnson, Kostaki, Brass logit, and Akima spline methods—are compared with respect to 782 empirical complete life tables pertaining to 19 European regions or countries, from 1954 to 2000. Abridged life tables are first derived from the empirical ones, then used to produce one-year-life tables by each of the four methods. These reconstituted complete life tables are then compared with the empirical complete life tables. Among the four methods, the Elandt–Johnson demographic method produces the best reconstitutions at adult ages, specifically those ages at which observed cancer survival needs to be corrected.     

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.     

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.     

Mortality in Ghana: Evidence from the cape coast project data

Abstract This paper deals with the estimation of mortality for a rural community of about 20,000 persons in the rain-forest area of south-west Ghana. Specifically, infant, child and adult mortality estimates have been obtained by the application of a wide range of direct and indirect methods of measuring mortality from the different statistics collected by a longitudinal mortality and fertility project conducted during 1974-7. It was noted that infant and childhood mortality rates obtained from death registrations were consistent with those rates yielded by pregnancy histories and child survival statistics. However, the adult mortality estimates derived from orphanhood statistics tended to be lower than those suggested by death registrations. The analysis revealed an infant mortality rate of 100 for boys and 84 for girls, equal childhood mortality rates for boys and girls (85-6), a lower expectation of life at birth for men (45.8 years) than for women (52.8), and a much more severe incidence of mortality among men aged over 40 than for women at the corresponding ages.     

Mortality in Ghana: Evidence from the cape coast project data

This paper deals with the estimation of mortality for a rural community of about 20,000 persons in the rain-forest area of south-west Ghana. Specifically, infant, child and adult mortality estimates have been obtained by the application of a wide range of direct and indirect methods of measuring mortality from the different statistics collected by a longitudinal mortality and fertility project conducted during 1974–7. It was noted that infant and childhood mortality rates obtained from death registrations were consistent with those rates yielded by pregnancy histories and child survival statistics. However, the adult mortality estimates derived from orphanhood statistics tended to be lower than those suggested by death registrations. The analysis revealed an infant mortality rate of 100 for boys and 84 for girls, equal childhood mortality rates for boys and girls (85–6), a lower expectation of life at birth for men (45.8 years) than for women (52.8), and a much more severe incidence of mortality among men aged over 40 than for women at the corresponding ages.     

Comparison of household-survey estimates with projections of mortality and orphan numbers in sub-Saharan Africa in the era of HIV/AIDS

The United Nations publishes estimates of HIV prevalence, AIDS mortality, and orphan numbers for all countries of the world. It is important to assess the validity of these model-based estimates since they underpin much policy concerned with care and prevention. Household surveys that ask questions about the survival of children's parents (orphanhood) offer an independent source of data with which these estimates can be compared. Survey estimates of maternal and paternal orphans are significantly lower than model estimates for 40 surveys in 36 countries of sub-Saharan Africa (p < 0.001, p = 0.002). This is probably because adult mortality from causes other than AIDS is lower than assumed in the models, although under-reporting of orphanhood in surveys may also play a role. Reducing adult mortality from causes other than AIDS brings the model estimates into close agreement with the surveys. This suggests that the fraction of orphans attributable to AIDS is greater than estimated previously.     

The Network Survival Method for Estimating Adult Mortality: Evidence From a Survey Experiment in Rwanda

Adult death rates are a critical indicator of population health and well-being. Wealthy countries have high-quality vital registration systems, but poor countries lack this infrastructure and must rely on estimates that are often problematic. In this article, we introduce the network survival method, a new approach for estimating adult death rates. We derive the precise conditions under which it produces consistent and unbiased estimates. Further, we develop an analytical framework for sensitivity analysis. To assess the performance of the network survival method in a realistic setting, we conducted a nationally representative survey experiment in Rwanda (n = 4,669). Network survival estimates were similar to estimates from other methods, even though the network survival estimates were made with substantially smaller samples and are based entirely on data from Rwanda, with no need for model life tables or pooling of data from other countries. Our analytic results demonstrate that the network survival method has attractive properties, and our empirical results show that this method can be used in countries where reliable estimates of adult death rates are sorely needed.     

The Predictive Validity of Subjective Mortality Expectations: Evidence From the Health and Retirement Study

Several recent studies suggest that individual subjective survival forecasts are powerful predictors of both mortality and behavior. Using 15 years of longitudinal data from the Health and Retirement Study, I present an alternative view. Across a wide range of ages, predictions of in-sample mortality rates based on subjective forecasts are substantially less accurate than predictions based on population life tables. Subjective forecasts also fail to capture fundamental properties of senescence, including increases in yearly mortality rates with age. To shed light on the mechanisms underlying these biases, I develop and estimate a latent-factor model of how individuals form subjective forecasts. The estimates of this model’s parameters imply that these forecasts incorporate several important sources of measurement error that arguably swamp the useful information they convey.     

A simplified robust estimate of the birth rate

It is shown that other estimates of the birthrate can be derived from Coale's robust birthrate estimate. Coale's estimate is nearly equal to the birthrate obtainable from reverse survival or reverse projection of the proportion of a population under age 15 (both sexes), or C(15), using a life table corresponding to l5. As a sequel to this, a birth rate estimate was obtained that does not require reference to stable population models and results in computational economy and ease. Taking advantage of the strong linear relation between l5 and 15L0, a simple robust estimate was derived of the birthrate that does not depend upon model stable populations or model life tables. After presenting these methods, their use is illustrated with data from several Asian and African countries. Coale (1981) suggested using the observed C(15) for both sexes and l5 to locate an appropriate stable population from a family of stable models to represent the observed population and to use its birthrate as an estimate of the population under study. The estimate of l5 can be obtained by any of the indirect methods like the Brass method. Coale observed that such methods yield birthrates that are not much affected even when the populations are not stable. He also suggested an adjustment for the stable birthrate for nonstability. To obtain the birthrate, one needs the denominator, namely, the number of persons that lived. This is obtained by using the rate of increase, r, which differs for a stable and a nonstable or observed population. Various methods can be used to obtain the time reference of the mortality estimate, l5, by providing years prior to the survey or census to which the l5 estimate is applicable.     

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.     

The estimation of adult mortality in Africa from data on orphanhood

Summary Until recently, very little information has been available about the levels and patterns of adult mortality in tropical Africa, but during the past decade several countries have included questions in censuses and surveys as to whether a person's father and mother are still alive. From the data so obtained, estimates of adult mortality have been prepared. This paper compares the results of three such exercises with alternative estimates of adult mortality derived from other sources. In the case of Chad, the orphanhood data obtained in the demographic sample survey of 1964 yielded estimates of mortality which agreed reasonably closely with those obtained from questions on deaths of household members occurring during the twelve months preceding the survey. The latter data however were themselves subject to substantial errors and had to be corrected using techniques based on stable population theory. For Kenya, the orphanhood questions were included in the 1969 census and the results were compared with the mortality estimates derived from inter-censal survival from 1962 to 1969. Once again, the data obtained from the latter were subject to error but in general appeared to be consistent with the orphanhood estimates. The third comparison was made from Malawi, where alternative mortality figures were available from the Malawi Population Change survey which was a 'dual record' type of operation, conducted in 1971/2. The agreement in this case was remarkably close, once the number of deaths had been corrected for omissions by both systems with allowance for positive correlation. It is concluded that as a simple and inexpensive technique of estimating adult mortality, the orphanhood approach has much to recommend it.     

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.     

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.     

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.     

Obtaining multistate life table distributions for highly refined subpopulations from cross-sectional data: A bayesian extension of sullivan’s method

Multistate life table methods are often used to estimate the proportion of remaining life that individuals can expect to spend in various states, such as healthy and unhealthy states. Sullivan’s method is commonly used when panels containing data on transitions are unavailable and true multistate tables cannot be generated. Sullivan’s method requires only cross-sectional mortality data and cross-sectional data indicating prevalence in states of interest. Such data often come from sample surveys, which are widely available. Although the data requirements for Sullivan’s method are minimal, the method is limited in its ability to produce estimates for subpopulations because of limited disaggregation of data in cross-sectional mortality files and small cell sizes in aggregated survey data. In this article, we develop, test, and demonstrate a method that adapts Sullivan’s approach to allow the inclusion of covariates in producing interval estimates of state expectancies for any desired subpopulation that can be specified in the cross-sectional prevalence data. The method involves a three-step process: (1) using Gibbs sampling to sample parameters from a bivariate regression model; (2) using ecological inference for producing transition probability matrices from the Gibbs samples; (3) using standard multistate calculations to convert the transition probability matrices into multistate life tables.