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.     

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.     

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.     

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 calculation of mortality-rates in the construction of life tables. A mathematical statistical study

Official life tables are frequently calculated for a period of years, rather than for an individual year, and the question arises, how annual rates are to be combined, in order to give an indication of the average mortality of the period. The author examines this problem, and uses methods based on the binomial probability distribution to suggest a solution of the ‘weighting’ problem. Taking as his starting-point the work of the Dutch statistician Van Pesch, he modifies the latter's theory so as to make it applicable to the case, where mortality rates have a secular downward trend, and reaches the conclusion that the ‘most probable values for the mortality rates are not obtained by applying the weighted mean, but by the application of a weighted mean and a correction term. The inclusion of the correction term means that, practically speaking, the results do not differ from those obtained by the application of the unweighted mean. The unweighted mean, which has the advantage of requiring less computational work, may therefore be given preference over the theoretically more accurate method.’     

Estimates Of U.S. Multiple Cause Life Tables

Cause elimination life tables estimated from multiple cause of death data for four race/sex groups are presented for the U.S. population in 1969. These “multiple cause” life tables are then compared to cause elimination life tables where the mortality risk eliminated is that of the cause of death only in its occurrence as the underlying cause of death. An evaluation is made of the possible effects of the multiple cause data on our perception of the relative importance of the major causes of death. The reconceptualization of mortality risks made possible by the multiple cause of death data is also assessed in terms of its providing further insight into the “Taeuber paradox.”     

Bayesian population reconstruction of female populations for less developed and more developed countries

We show that Bayesian population reconstruction, a recent method for estimating past populations by age, works for data of widely varying quality. Bayesian reconstruction simultaneously estimates age-specific population counts, fertility rates, mortality rates, and net international migration flows from fragmentary data, while formally accounting for measurement error. As inputs, Bayesian reconstruction uses initial bias-reduced estimates of standard demographic variables. We reconstruct the female populations of three countries: Laos, a country with little vital registration data where population estimation depends largely on surveys; Sri Lanka, a country with some vital registration data; and New Zealand, a country with a highly developed statistical system and good quality vital registration data. In addition, we extend the method to countries without censuses at regular intervals. We also use it to assess the consistency of results between model life tables and available census data, and hence to compare different model life table systems.     

The Timing and Pace of Health Transitions around the World

Estimates from some 700 mostly national studies of survival in the past are assembled to create a broad picture of regional and global life expectancy gains across space and time and to examine implications of that picture. At the initiation of their health transitions, most countries had a life expectancy between 25 and 35 years. Countries that began later made gains at a faster pace. Those faster gains are usually associated with the dissemination of Western medicine. But rapid gains occurred in the period 1920–50, largely before the availability of antibiotics or modern vaccines. Especially rapid gains came in the years immediately after World War II in countries where the leading causes of death were communicable diseases that could be managed with antibiotics but also in countries where the leading causes of death were degenerative organ diseases. Both periods of rapid gain await satisfactory explanation. The bibliography of more than 700 sources is published separately on the web at « http://www.lifetable.de.RileyBib.htm ».     

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.     

The pattern of mortality change in Latin America

Using 69 new life tables recently made by Arriaga for Latin American countries by stable-population methods, the authors examine the mortality trends for more countries and more periods of history than have previously been available for analysis. For the late nineteenth and early twentieth centuries, the new tables yield a substantially lower life-expectancy than that shown by previously published life tables; for recent decades the difference is smaller, though in the same direction. As a consequence, the new tables show a speed of mortality decline in Latin America greater than the speed hitherto assumed. When the trend is analyzed in terms of economic development, it appears that the decline was extremely slow in the more backward Latin American countries until around 1930, whereas in the more advanced countries of the region, a more rapid decline had set in before that. After 1930, however, in both groups of countries the pace of decline was faster than ever, and it was virtually the same for both groups, suggesting that after that date public health measures were exerting a strong influence independently of local economic development. This result is confirmed by comparison with the past history of now developed countries; the mortality decline in Latin America after 1930 was much faster than it was historically at the same level in the industrial countries. As compared with other underdeveloped countries today, the unprecedented decline of mortality in Latin America is typical. In most underdeveloped countries, whether in Latin America or elsewhere, mortality change seems increasingly independent of economic improvement and more dependent on the importation of preventive medicine and public health from the industrial countries.     

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.     

Potential support ratios: Cohort versus period perspectives

The ‘prospective potential support ratio’ has been proposed by researchers as a measure that accurately quantifies the burden of ageing, by identifying the fraction of a population that has passed a certain measure of longevity, for example, 17?years of life expectancy. Nevertheless, the prospective potential support ratio usually focuses on the current mortality schedule, or period life expectancy. Instead, in this paper we look at the actual mortality experienced by cohorts in a population, using cohort life tables. We analyse differences between the two perspectives using mortality models, historical data, and forecasted data. Cohort life expectancy takes future mortality improvements into account, unlike period life expectancy, leading to a higher prospective potential support ratio. Our results indicate that using cohort instead of period life expectancy returns around 0.5 extra younger people per older person among the analysed countries. We discuss the policy implications implied by our cohort measures.     

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.     

A simple model for linking life tables by survival mortality ratios

Patterns of variation in mortality can be studied by measuring changes in selected life table functions. A model is proposed in which the rate of change over time in the life table survivorship probability at any age has been assumed as proportional to the product of its own value and its complementary probability or the probability of dying by that age, where the proportion is the same for all ages and depends only on the time duration between successive life tables. The end result is that the logit functions of the survivorship probabilities at two points in time are linearly related with a slope of one. The projecting power of the model has been tested by using U.S. life tables for the years 1950 and 1970 as well as Coale and Demeny's regional model life tables. In the latter case, the model produced surprisingly close matches even when the expectations of life differed by as much as 20 years.     

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.     

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.     

The Impact of Exposure to Other Countries on Life Satisfaction: An International Application of the Relative Income Hypothesis

The cause of international differences in life satisfaction is usually ascribed to differences in living standards. Yet, despite improving living standards in a lot of middle-income countries, significant differences in life satisfaction between middle- and high-income countries remain. This paper examines if there is an international comparison effect and assesses to what extent the relative income hypothesis can be applied to explain international differences in life satisfaction. We test this by analyzing how exposure to other countries impacts life satisfaction. It is hypothesized that higher exposure to other countries in low- and middle-income countries has a negative effect due to increased aspirations and relative deprivation, while the opposite holds true for rich countries. We draw on data from the World Value Survey, the World Bank and the KOF Globalization index to perform a multilevel analysis. The results suggest that an international comparison effect indeed exists and is capable of partially explaining international differences in life satisfaction. Additional analyses reveal that people in lower income classes, in all countries, are affected more by exposure to other countries, indicating that individual characteristics are important when assessing the impact of exposure on life satisfaction. We demonstrate the robustness of these findings by showing that both sub-indicators of exposure, informational flow and international contact, have an impact on life satisfaction that is similar to that of our overall exposure-index.     

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.     

Using Subjective Expectations to Forecast Longevity: Do Survey Respondents Know Something We Don’t Know?

Old-age mortality is notoriously difficult to predict because it requires not only an understanding of the process of senescence-which is influenced by genetic, environmental, and behavioral factors-but also a prediction of how these factors will evolve. In this paper I argue that individuals are uniquely qualified to predict their own mortality based on their own genetic background, as well as environmental and behavioral risk factors that are often known only to the individual. Given this private information, individuals form expectations about survival probabilities that may provide additional information to demographers and policymakers in their challenge to predict mortality. From expectations data from the 1992 Health and Retirement Study (HRS), I construct subjective, cohort life tables that are shown to predict the unusual direction of revisions to U.S. life expectancy by gender between 1992 and 2004: that is, for these cohorts, the Social Security Actuary (SSA) raised male life expectancy in 2004 and at the same lowered female life expectancy, narrowing the gender gap in longevity by 25% over this period. Further, although the subjective life expectancies for men appear to be roughly in line with the 2004 life tables, the subjective expectations of women suggest that female life expectancies estimated by the SSA might still be on the high side.     

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.