Models for the estimation of the probability of dying between birth and exact ages of early childhood

Abstract This paper develops two models, each of which is designed to estimate the probability of surviving from birth to selected exact ages of early childhood: namely ages two, three and five. The models are designed for use in areas with deficient registration systems. They require, as input, statistics which can be derived from retrospective data supplied by census or survey respondents. The first model, the age model, converts statistics on the proportion dead of children ever born to women in age groups 20-24, 25-29 and 30-34 into estimates of q2, q3 and q5. The second model, the marriage model, converts statistics on the proportion dead of children ever born to women of five-year marriage duration intervals into these estimates. The models can be used independently or simultaneously. These models were developed from data generated by a large number of empirical fertility and mortality schedules. Regression analysis was used to determine the parameter values of the relationships specified, and several sets of equations for estimating values of qa, for a = 2, 3 and 5 comprise the final product of the paper. It should be noted that the conceptual basis for the models was first derived by William Brass. The data generated for the regression analysis provided an opportunity to test the original Brass estimated model. We are able to report that the model performed well over the wide range of fertility and mortality conditions included in the test.     

Optimizing the Lee-Carter Approach in the Presence of Structural Changes in Time and Age Patterns of Mortality Improvements

Researchers using the Lee-Carter approach have often assumed that the time-varying index evolves linearly and that the parameters describing the age pattern of mortality decline are time-invariant. However, as several empirical studies suggest, the two assumptions do not seem to hold when the calibration window begins too early. This problem gives rise to the question of identifying the longest calibration window for which the two assumptions hold true. To address this question, we contribute a likelihood ratio–based sequential test to jointly test whether the two assumptions are satisfied. Consistent with the mortality structural changes observed in previous studies, our testing procedure indicates that the starting points of the optimal calibration windows for most populations fall between 1960 and 1990. Using an out-of-sample analysis, we demonstrate that in most cases, models that are estimated to the optimized calibration windows result in more accurate forecasts than models that are fitted to all available data or data beyond 1950. We further apply the proposed testing procedure to data over different age ranges. We find that the optimal calibration windows for age group 0–49 are generally shorter than those for age group 50–89, indicating that mortality at younger ages might have undergone (another) structural change in recent years.     

Weather,nutrition, and the economy: Short-run fluctuations in births,deaths, and marriages,France 1740–1909

This paper analyzes short-run fluctuations in national time series of vital events for France in the period 1740 to 1909. Fertility, mortality, and nuptiality form a simultaneous system which interacts with economic and meteorological conditions. In the short run, the demographic variables are endogenous. Economic and meteorological conditions are exogenous. Our indicator of economic conditions is the price of wheat, the principal food crop. Biometric models of fertility and empirical research on the biologically-based interrelations of fertility and mortality provide insight into the expected timing of events. We combine these results with empirical research on the effects of nutrition on fertility and mortality, research in medical biometeorology, and French historical demographic and economic research to formulate our model. The resultant distributed lag system is estimated. We find that the economic/nutritional effects are more likely to be statistically significant in predicting the time path of vital events than are the demographic variables or the effects of meteorological conditions.     

The development and use of demographic models

In this review, we first examine two classical demographic models - conventional life tables and stable populations - and a modern generalization of stable population theory; we then discuss mathematical models of conception and birth. These models involve purely mathematical relations in formal demography as opposed to empirical regularities. Next we consider model age schedules of mortality, nuptialitiy, marital fertility, fertility, and migration that are explicitly based on such empirical patterns. We close this empirical section with a discussion of model stable populations, which are based on model life tables. We next examine the use of demographic models in forecasting future mortality, nuptiality, and fertility and in population projection. Following a discussion of microsimulation models, which gives us the opportunity to mention model age schedules of post partum amenorrhoea and of sterility, we close with observations about the purposes and uses of demographic models.     

Degrouping mortality data for the elderly

Proposed in this paper is a technique for estimating, from coarsly grouped empirical death data, the age‐specific numbers of deaths for the elderly population. This question is primarily of interest in countries where the empirical data are available only in a grouped form, given usually in quinquennial age groups and in a large open‐ended interval for the ages 85 and over. The main reason that the official data are given in such a form in some countries of Southern Europe and in the Third World is the existence of heaping in the empirical data, i.e. misstatements in age recording, usually rounding to the nearest integer divisible with five. Our evaluation of the method on Swedish mortality data shows that the technique proposed can be efficiently applied to period mortality data.     

Age,period, and cohort effects in demography: a review

This paper considers only the vital events of demographic measurement, the factors influencing the rate at which those events occur and then investigates the consequences of patterns of these events. It reviews the state of the art of age, period and cohort analysis for demographic dependent variables. Major examples of such analyses are given in both mortality and fertility studies. In the area of mortality the conventional approach to such analysis apears to be well suited to a wide range of applications yielding useful results. The reasons for this suitability are: early childhood experience is important in many major disease and death processes, so that cohorts are legitimately viewed as acquiring early on a certain fixed susceptibility; data sometimes stretch back far enough that stationary standards of age patterns can be developed empirically, and applied to later experience; and, logarithmic or logistic transformations linearize comparisons of age schedules or mortality so that standard statistical procedures are suitable. Applications of age, period, and cohort analysis are not always routine; external constraints are required, in the form of theoretically based and mathematically expressed age patterns of mortality, in order to distinguish effectively between period and cohort effects. A set of models of age patterns of mortality that are based on cohort as well as period experience could be constructed with useful applications. With fertility analysis the conventional approach is much less suitable. Once goal directed behavior is introduced, empirical examinations must be based on theories or assumptions about how such goals are formulated and pursued. Conventional analysis might suffice only if one is prepared to accept the assumption that all pertinent goals and strategies are formulated before the initiation of childbearing and remain unaffected by subsequent events. This assumption is untenable for modern developed populations and the forms of analysis appropriate to age period cohort investigations of fertility will have to develop along with theories of reproductive behavior.     

城镇不同社会医疗保险待遇人群死亡率交叉现象研究

本文使用中国老人健康长寿影响因素研究(Chinese Longitudinal Healthy Lon-gevity Survey,CLHLS),2002～2005年调查数据对我国不同社会医疗保险待遇的老年人口的死亡率交叉现象进行了研究。运用离散时间的死亡风险分析,文章的发现支持选择性死亡的理论,即无社会医疗保险的人群,60岁时死亡率一直高于享受医保人群,使得无医保人群中强健的个体幸存下来;随着年龄的增长,这种选择机制的作用逐渐表现为死亡率逆转,即无医保人群的平均死亡率在大约96岁以后开始低于享受医保人群。研究显示,我国享受社会医疗保险的老年的生存优势一直存在至96岁高龄,医疗保险对于老年人口的健康有着显著而长远的积极影响。     

Uncertainty about children's survival and fertility: A test using indian microdata

In this paper we present a non altruistic model of demand for children in the presence of uncertainty about children's survival. Children are seen as assets, as they provide help during old age. Theoretical predictions relating to the change in the mean and variance of the survival rate are derived. The empirical analysis is based on data from the Human Development of India (HDI) survey. Different models for count data variables, such as Poisson and hurdle models have been employed in the empirical analysis. The results highlight the importance of the uncertainty about children's survival in determining parental choices. This shows that realized or expected children's death is not the only link between fertility decision and children's mortality. The policy implications of such findings are briefly discussed. Received: 20 August 1998/Accepted: 19 July 1999     

Discrete Barker Frailty and Warped Mortality Dynamics at Older Ages

We develop a discrete variant of a general model for adult mortality influenced by the delayed impact of early conditions on adult health and mortality. The discrete variant of the model builds on an intuitively appealing interpretation of conditions that induce delayed effects and is an extension of the discrete form of the standard frailty model with distinct implications. We show that introducing delayed effects is equivalent to perturbing adult mortality patterns with a particular class of time-/age-varying frailty. We emphasize two main results. First, populations with delayed effects could experience unchanging or increasing adult mortality even when background mortality has been declining for long periods of time. Although this phenomenon also occurs in a regime with standard frailty, the distortions can be more severe under a regime with Barker frailty. As a consequence, conventional interpretations of the observed rates of adult mortality decline in societies that experience Barker frailty may be inappropriate. Second, the observed rate of senescence (slope of adult mortality rates) in populations with delayed effects could increase, decrease, or remain steady over time and across adult ages even though the rate of senescence of the background age pattern of mortality is time- and age-invariant. This second result implies that standard interpretations of empirical estimates of the slope of adult mortality rates in populations with delayed effects may be misleading because they can reflect mechanisms other than those inducing senescence as conventionally understood in the literature.     

Age composition in the absence of mortality and in other odd circumstances

The age composition of populations experiencing no mortality and various kinds of fertility is derived. It is then shown that, if successive mortality schedules can be expressed as the sum of a component that varies with age and a component that varies with time, only the former has any effect on the age structure of the population. One implication is that a population in which mortality varies with time but not with age has the same composition as a population with no mortality at all.     

Mobile Internet Use and Multidimensional Poverty: Evidence from A Household Survey in Rural China

The impact of specific living conditions on the population of geographically and socially segregated Roma settlements in Eastern Slovakia is considerable. They are characterized by high unemployment, lower education, poor housing and sanitary conditions, a poor quality of life, which all affects significantly their higher mortality rates and worse health status. In this paper we try to approach the problem of adverse mortality conditions and health with a deeper demographic insight. The fundamental goal of the paper is to analyse mortality in the population from Roma settlements over the past two decades using complex demographic methods such as life tables, direct standardization with the objective of eliminating differences in the age structure, single and multi-dimensional decomposition of age, sex and causes of death. We also analyse mortality using the concept of avoidable mortality. The results obtained from Roma settlements confirmed significantly worse mortality rates for both sexes. In addition, it appears that the disparities between them and the majority population are growing over time. The primary reason is the higher mortality of the youngest children and persons at post-reproductive age. Basically, all main chapters of the causes of death shorten the life expectancy of persons from Roma settlements, but cardiovascular diseases have the greatest negative impact. Conclusions obtained from the avoidable mortality analysis point to problems related to the accessibility and quality of health care, as well as the lack of interest of population from Roma settlements in their own health, along with the need for more targeted prevention and screening campaigns in this environment. Although the answers of respondents from Roma settlements to their own health confirm the deteriorating quality of health, increasing morbidity and the degree of restriction of normal daily activities with increasing age, they also point to some problems associated with the use of this approach.

     

Mixed estimation of old‐age mortality

The estimation of the mortality of the “oldest old”; is subject to considerable random error, but important prior information exists that can be used to make the estimates more robust. Mixed estimation is a method of incorporating auxiliary information into the statistical estimation of linear models. We extend the method to cover general maximum likelihood estimation, and show that the mixed estimator can be represented approximately as a weighted average of the purely data based estimator and the auxiliary estimator. The methods can be applied to the analysis of the old‐age mortality via logistic and Poisson regression. A major advantage of the mixed estimator is the simplicity with which it can incorporate partial prior information. Moreover, no special software is needed in the fitting. We show how the targeting methods of Coale and Kisker can be represented as mixed estimation in a natural way that is more flexible than the original proposal. We also derive empirical estimates of the target information based on pooled data from several countries with high quality data. We consider the mortality of Finland at ages 80 +, study the reliability of the evidence of mortality crossover, and derive estimates of life expectancy at age 100.     

Reconsidering mortality compression and deceleration: an alternative model of mortality rates

In this research we develop a model of mortality rates that parameterizes mortality deceleration and compression, permits hypothesis tests for change in these parameters over time, and allows for formal gender comparisons. Our model fits mortality data well across all adult ages 20-105 for 1968-1992 U.S. white data, and the results offer some confirmation of findings of mortality research using conventional methods. We find that the age at which mortality deceleration begins is increasing over time, that decompression of mortality is occurring, and that these trends vary substantially across genders, although male and female mortality patterns appear to be converging to some extent.     

Age patterns of mortality for older women: an analysis using the age-specific rate of mortality change with age

"In this paper we propose a mortality measure that seems useful in analyzing age patterns of death rates. The measure, which will be denoted by k(x), indicates the proportional increase or decrease with age in the risk of death at a given age x, and is called the age-specific rate of mortality change with age." Estimations are presented for women in 10 countries. "Eight of the selected sets of data are for developed nations in the 1960s and 1970s, and the other two sets of data, for Taiwan, 1931-35, and for Germany, 1910-11, represent relatively high mortality. For France and West Germany, three different periods are included for an investigation of cohort effects on the observed age patterns." Other mathematical models of age-specific mortality rates are discussed and compared. (SUMMARY IN FRE)     

Which factors explain the decline in infant and child mortality in Matlab,Bangladesh?

Infant and child mortality rates have decreased substantially in Matlab, Bangladesh, as they have in many developing areas. We use data from the Matlab Demographic Surveillance System on nearly 94,000 singleton live births that occurred between 1987 and 2002 to investigate the extent to which the change in mortality over this period can be explained by changes in reproductive patterns and socio-economic characteristics. We estimate Cox proportional hazards models for four subperiods of infancy and childhood. Changes over time in reproductive patterns (maternal age, parity, and pregnancy spacing) and in the socio-economic characteristics we consider (e.g. maternal education, SES) explain between 10 and 40% of the decline in mortality rates. Changes in maternal education explain the largest portion of the reduction in infant and child mortality over time that we are able to explain, followed by reductions in the incidence of short interpregnancy intervals. In the other direction, decreases in fertility over time led to increases in the proportion of births that were first births, putting upward pressure on mortality.

Changes in cohort wealth over a generation

Empirical computation of expected wealth is hampered by two problems: mortality risks vary in the population and over time; and observation of net estates for most cohorts is truncated, as some individuals in a cohort survive the calendar date on which observation is terminated. These two problems are solved in estimating cohort wealth for a sample of Wisconsin taxpayers. Hazard rate models of differential occupational mortality risks were estimated from the occupational information on the tax records. Values of net estate are simulated for individuals in each birth cohort who survived. Survivors have characteristics that imply greater wealth holdings than the deceased in every birth year covered by the study (1890-1924). Because of this, estimates of wealth-age relationships produced by the estate multiplier method for any given year will have a serious downward bias. Longitudinal data imply that dissaving does not occur after age 65.     

Heterogeneity in the Strehler-Mildvan General Theory of Mortality and Aging

This study examines and further develops the classic Strehler-Mildvan (SM) general theory of mortality and aging. Three predictions from the SM theory are tested by examining the age dependence of mortality patterns for 42 countries (including developed and developing countries) over the period 1955–2003. By applying finite mixture regression models, principal component analysis, and random-effects panel regression models, we find that (1) the negative correlation between the initial adulthood mortality rate and the rate of increase in mortality with age derived in the SM theory exists but is not constant; (2) within the SM framework, the implied age of expected zero vitality (expected maximum survival age) also is variable over time; (3) longevity trajectories are not homogeneous among the countries; (4) Central American and Southeast Asian countries have higher expected age of zero vitality than other countries in spite of relatively disadvantageous national ecological systems; (5) within the group of Central American and Southeast Asian countries, a more disadvantageous national ecological system is associated with a higher expected age of zero vitality; and (6) larger agricultural and food productivities, higher labor participation rates, higher percentages of population living in urban areas, and larger GDP per capita and GDP per unit of energy use are important beneficial national ecological system factors that can promote survival. These findings indicate that the SM theory needs to be generalized to incorporate heterogeneity among human populations.     

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.     

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.     

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.