Bayesian Estimation of Age-Specific Mortality and Life Expectancy for Small Areas With Defective Vital Records

High sampling variability complicates estimation of demographic rates in small areas. In addition, many countries have imperfect vital registration systems, with coverage quality that varies significantly between regions. We develop a Bayesian regression model for small-area mortality schedules that simultaneously addresses the problems of small local samples and underreporting of deaths. We combine a relational model for mortality schedules with probabilistic prior information on death registration coverage derived from demographic estimation techniques, such as Death Distribution Methods, and from field audits by public health experts. We test the model on small-area data from Brazil. Incorporating external estimates of vital registration coverage though priors improves small-area mortality estimates by accounting for underregistration and automatically producing measures of uncertainty. Bayesian estimates show that when mortality levels in small areas are compared, noise often dominates signal. Differences in local point estimates of life expectancy are often small relative to uncertainty, even for relatively large areas in a populous country like Brazil.     

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.     

Mortality estimation from registered deaths in less developed countries

Age-specific population growth rates were introduced to demographic analysis in earlier work by Bennett and Horiuchi (1981) and Preston and Coale (1982). In this paper, we derive a method which uses these growth rates to transform what may be a set of incompletely recorded deaths by age into a life table that accurately reflects the true mortality experience of the population under study. The method does not rely on the assumption of stability and, for example, in contrast to intercensal cohort survival techniques, is simple to implement when presented with nontraditional intercensal interval lengths. Thus we can obtain mortality estimates for less developed countries with defective data, despite departures from stability. Further, we assess the sensitivity of the method to violations in various assumptions underlying the procedure: error in estimated growth rates, existence of non-zero net intercensal migration, age dependence in the completeness of death registration, and misreporting of age at death and age in the population. We demonstrate the use of the method in an application to data referring to Argentine females during the period 1960 to 1970.     

Demographic data collection in less developed countries 1946-1996

This evolution over the last 50 years of data collection systems in less developed countries is assessed. The progress made by civil registration systems has been extremely disappointing. Except in Central and South America, their role in providing vital rate estimates is still very limited. In contrast, the promulgation of regular population censuses has been a success, particularly in Africa. The relative merits and demerits of different types of demographic surveys are described. To some extent multi-round designs have given way to single-round surveys, such as the Demographic and Health Surveys (DHS). DHS-style enquiries are particularly suitable for evaluation of interventions but are less appropriate if the main aim is to measure vital rates.     

Atechnique for estimating life expectancy with crude vital rates

This paper describes a method of estimating life expectancy at birth on the basis of crude vital rates. The method is derived from stable population theory and it furnishes good estimates insofar as the current crude vital rates of a population are close to its intrinsic rates. This condition is generally met in closed populations which have not experienced sharp movements in fertility. The method is useful for estimating life expectancy in developing nations with good sample registration systems but for which information on age is of poor quality. It is also useful for estimating the movement of life expectancy in certain European nations in the period prior to regular census taking. There are a number of nations and regions in Europe for which long series of birth and death rates are available but for which census age counts are widely spaced.     

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.     

Bayesian Probabilistic Projections of Life Expectancy for All Countries

We propose a Bayesian hierarchical model for producing probabilistic forecasts of male period life expectancy at birth for all the countries of the world to 2100. Such forecasts would be an input to the production of probabilistic population projections for all countries, which is currently being considered by the United Nations. To evaluate the method, we conducted an out-of-sample cross-validation experiment, fitting the model to the data from 1950–1995 and using the estimated model to forecast for the subsequent 10 years. The 10-year predictions had a mean absolute error of about 1 year, about 40 % less than the current UN methodology. The probabilistic forecasts were calibrated in the sense that, for example, the 80 % prediction intervals contained the truth about 80 % of the time. We illustrate our method with results from Madagascar (a typical country with steadily improving life expectancy), Latvia (a country that has had a mortality crisis), and Japan (a leading country). We also show aggregated results for South Asia, a region with eight countries. Free, publicly available R software packages called bayesLife and bayesDem are available to implement the method.     

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.     

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.     

Estimation of vital rates for Ghana

Abstract A complete and efficient registration system, of the type which would provide good data on births and deaths, does not exist in Ghana. However, registration of vital events is supposed to be compulsory in 39 towns in the country but the data collected in these areas are too inadequate and defective to provide a sound basis for the analysis of the dynamics of population growth. The results of the censuses conducted by the colonial governments are so defective and unreliable that they do not allow scientific research in the field of population analysis. Before 1960, therefore, when the national census and the post-enumeration survey (based on a 5% sample of the population) were carried out, estimates of fertility and mortality levels were little more than guesses. In this study an attempt has been made to utilize the information on the age-sex composition provided by the 1960 census and post-enumeration survey data on births and deaths to determine, as far as possible, the levels of fertility and mortality and the rates of population growth in Ghana. The fertility estimates-i.e. a crude birth rate of 50, total fertility rate of 6.9 and a gross reproduction rate of 3.4-show that Ghana's fertility is one of the highest in the world. An expectation of life at birth of 40 years, an infant mortality of 160 and a crude death rate of 23 appear to be the most plausible estimates. These estimates yield a rate of natural increase of 2.7% and a growth rate of 3.0% per annum.     

Sample registration in India

India's ad hoc sample registration scheme for obtaining current estimates of rural birth and death rates for the whole country is being implemented quite rapidly. Five states have 140 sample units, and eleven states will have from 20 to 100 units in the study depending upon the stage of implementation by March, 1967.Essential elements of the project for each unit are: (1) continuous registration of vital events by a paid part-time local enumerator, (2) a six-month household survey to detect births and deaths which occurred during the previous six months, and (3) matching events from registration and surveys and field recheck of unmatched events to obtain the "best" count of real number of events. Preliminary results in a non-random sample indicate that the crude birth and death rates are around 37.1 and 15.7 per 1,000, respectively, for India's rural population, but these probably will be found to be on the low side.Most of the problems of implementation are operational or administrative rather than statistical: (1) For various reasons, some states are slow in agreeing to assume financial and other responsibilities for the scheme. (2) In many states, even after the scheme has been accepted, there are delays in recruiting the staff, training, and so forth. (3) The most serious problem in the whole project is maintaining control of field operations well enough at each stage to insure that prescribed instructions and methodology are being followed.Experience in India indicates that staged implementation of such projects is highly desirable when trained staff are limited. There still are a number of methodological problems which must be tested as the sample registration evolves. Sample registration is one of the first steps in the Indian program to. develop an adequate vital statistics system. Exploratory studies to measure completeness of civil registration are being done now in an effort to develop means of using civil registration data alone for measurement of vital rates.     

Maternal mortality in South Africa: lessons from a case study in the use of deaths reported by households in censuses and surveys

South Africa is unique in being a developing country which has asked questions on pregnancy-related deaths in both its 2001 census and 2007 household survey, and monitors maternal and pregnancy-related mortality through vital registration and a confidential enquiry into maternal deaths. These sources of data provide a wide range of estimates of maternal mortality for the country. This paper examines these estimates to assess to what extent the differences between them are due to data deficiencies, methodological deficiencies or definitional differences. The results show that since maternal deaths are relatively rare it is fairly difficult to establish the maternal mortality rate with a great degree of accuracy in a setting where data are less than perfect. They also show that to some extent the differences are due to differences and errors in processing of data but that pregnancy-related mortality should not be treated as synonymous with maternal mortality. However, after adjustment, pregnancy-related mortality from vital registration was comparable with the level that may be expected using several alternative approaches, while the rate reported by households in census and surveys was about double that from vital registration. Nonetheless, all the data indicate an upward trend in maternal mortality that is in keeping with the impact of the HIV/AIDS epidemic, which is likely to have contributed to the discrepancies.     

A reconstruction of the size and composition of Jewish Holocaust survivors in the Netherlands, 1945

Compared to other countries that have suffered from the Nazioccupation, the destructive impact of the Holocaust on theJewish population has been particularly strong in the Netherlands. This paper gives a demographicreconstruction of the Jewish population in the Netherlands by the end of the war (1945),disaggregated by age and sex. The reconstruction is based on two approaches: a forwardprojection 1941–1945, starting from registration data supplemented by information onHolocaust losses; and a backward projection 1966–1945, starting from an enumerationof Halachic Jews carried out in 1966. The two approaches yieldtwo estimates that are comfortingly similar.     

Vital rates in India 1961-71 estimated from 1971 census data

Abstract In the last decade the increase in the population of India, while, of course, very large, was smaller than predicted by official forecasts. With the use of recent census and sample registration data - in the absence of age-specific rates and adequate vital statistics - this paper provides estimates of fertility and mortality through the reverse-survival and forward-projection methods. Birth rates are estimated as 40·5-42, death rates as 18-20, and life expectancy at birth as 45-46 years. Mortality decline had been smaller than forecast but more than during any comparable period in the past, even though current mortality levels, particularly infant mortality, are still high. Males continue to have a longer life expectation than females, with a difference that has widened in the past decade. The decline of between seven and ten per cent in the crude birth rate is largely due to changes in marital fertility and to some extent to changes in age and marital composition. Because of greater decline in death rates than birth rates, the 1961-71 decade shows a higher rate of population growth than previous periods.     

A Flexible Bayesian Model for Estimating Subnational Mortality

Reliable subnational mortality estimates are essential in the study of health inequalities within a country. One of the difficulties in producing such estimates is the presence of small populations among which the stochastic variation in death counts is relatively high, and thus the underlying mortality levels are unclear. We present a Bayesian hierarchical model to estimate mortality at the subnational level. The model builds on characteristic age patterns in mortality curves, which are constructed using principal components from a set of reference mortality curves. Information on mortality rates are pooled across geographic space and are smoothed over time. Testing of the model shows reasonable estimates and uncertainty levels when it is applied both to simulated data that mimic U.S. counties and to real data for French départements. The model estimates have direct applications to the study of subregional health patterns and disparities.     

Probabilistic population projections for countries with generalized HIV/AIDS epidemics

In 2015, the United Nations (UN) issued probabilistic population projections for all countries up to 2100, by simulating future levels of total fertility and life expectancy and combining the results using a standard cohort component projection method. For the 40 countries with generalized HIV/AIDS epidemics, the mortality projections used the Spectrum/Estimation and Projection Package (EPP) model, a complex, multistate model designed for short-term projections of policy-relevant quantities for the epidemic. We propose a simpler approach that is more compatible with existing UN projection methods for other countries. Changes in life expectancy are projected probabilistically using a simple time series regression and then converted to age- and sex-specific mortality rates using model life tables designed for countries with HIV/AIDS epidemics. These are then input to the cohort component method, as for other countries. The method performed well in an out-of-sample cross-validation experiment. It gives similar short-run projections to Spectrum/EPP, while being simpler and avoiding multistate modelling.     

Infant mortality in the Marshall Islands

Levy and Booth present previously unpublished infant mortality rates for the Marshall Islands. They use an indirect method to estimate infant mortality from the 1973 and 1980 censuses, then apply indirect and direct methods of estimation to data from the Marshall Islands Women's Health Survey of 1985. Comparing the results with estimates of infant mortality obtained from vital registration data enables them to estimate the extent of underregistration of infant deaths. The authors conclude that 1973 census appears to be the most valid information source. Direct estimates from the Women's Health Survey data suggest that infant mortality has increased since 1970-1974, whereas the indirect estimates indicate a decreasing trend in infant mortality rates, converging with the direct estimates in more recent years. In view of increased efforts to improve maternal and child health in the mid-1970s, the decreasing trend is plausible. It is impossible to estimate accurately infant mortality in the Marshall Islands during 1980-1984 from the available data. Estimates based on registration data for 1975-1979 are at least 40% too low. The authors speculate that the estimate of 33 deaths per 1000 live births obtained from registration data for 1984 is 40-50% too low. In round figures, a value of 60 deaths per 1000 may be taken as the final estimate for 1980-1984.     

General growth balance method: A reformulation for populations open to migration

This paper proposes a reformulation of the general growth balance method for estimating census and registration completeness so as to make it applicable even to populations that are affected by migration. It also discusses a new procedure of line fitting that could be useful in countries where the input data are severely affected by age misreporting. The method is applicable to countries where data on age distribution of the population are available for two points in time from either censuses or surveys. Following closely the original proposal of Brass, it involves adjusting the ‘partial’ birth rates for age-specific disturbances from growth and migration rates. Beyond correcting the death rates, the method is useful in inferring the relative completeness of the censuses, and in deriving a robust estimate of birth rate under certain conditions. The application of the method is illustrated using the example of the male population of the Indian state of Uttar Pradesh for the period 1981 to 1991.     

Estimates of vital rates for the Canadian Indians, 1960–1970

The present paper is an attempt to evaluate the registered data on Canadian Indians collected by the Department of Indian Affairs and Northern Development and to prepare vital rates for 1960–1970 using the adjusted data. A cursory examination of registered data for the purpose of developing various demographic indices and for making future estimates of population indicates certain anomalies that call for a careful appraisal of the data. The main problem is the inconsistency in the reporting of births, due largely to the late registration of births. One plausible reason for late registration may be the increased outward movement of Indians from their reserves. Indirect methods are used to adjust the number of births and infant deaths reported annually since 1960. On the basis of the adjusted data, vital rates for the Canadian Indians are calculated for the period 1960–1970. The crude death rate decreased from 10.9 in 1960 to 7.5 in 1970. The infant mortality rate registered a drastic decline, from 81.5 deaths per 1,000 births in 1960 to 34.9 in 1970. During this same time period the birth rate also declined, from 46.5 to 37.2.     

Population statistics] as of July 1, 1999

Reported in tabular form are population statistics published by the Institute for Population and Social Research, Mahidol University, in Thailand, as of July 1, 1999. The three objectives of the table were 1) to present the most recent estimates of relevant population numbers and vital rates twice a year, 2) to provide the most accurate demographic estimates possible through the use of standard techniques of demographic analysis, and 3) to disseminate the demographic data to Thailand, and international researchers and planners. The table shows statistics on the following elements: total population; population by sex; population in urban and rural areas; population by region; population by age group; crude birth and death rates; natural growth rate; infant mortality rate; life expectancies at birth and at 60 years and over; total fertility rate; contraceptive prevalence rate; and median age. A new basis for age estimates is also presented.