Effect of aggregation on the estimation of trend in mortality

There are three approaches to analyzing and forecasting age‐specific mortality: (1) analyze age‐specific data directly, (2) analyze each cause‐specific mortality series separately and add the results, (3) analyze cause‐specific mortality series jointly and add the results. We show that if linear models are used for cause‐specific mortality, then the three approaches often give close results even when cause‐specific series are correlated. This result holds for cross‐correlations arising from random misclassification of deaths by cause, and also for certain patterns of systematic misclassification. It need not hold, if one or more causes serve as “leading indicators”; for the remaining causes, or if outside information is incorporated into forecasting either through expert judgment or formal statistical modeling. Under highly nonlinear models or in the presence of modeling error the result may also fail. The results are illustrated with U.S. age‐specific mortality data from 1968–1985. In some cases the aggregate forecasts appear to be the more credible ones.     

Effects of targets and aggregation on the propagation of error in mortality forecasts

Official forecasts of mortality depend on assumptions about target values for the future rates of decline in mortality rates. Smooth functions connect the jump‐off (base‐year) mortality to the level implied by the targets. Three alternative sets of targets are assumed, leading to high, middle, and low forecasts. We show that this process can be closely modeled using simple linear statistical models. These explicit models allow us to analyze the error structure of the forecasts. We show that the current assumption of perfect correlation between errors in different ages, at different forecast years, and for different causes of death, is erroneous. An alternative correlation structure is suggested, and we show how its parameters can be estimated from the past data.

The effect of the level of aggregation on the accuracy of mortality forecasts is considered. It is not clear whether or not age‐ and cause‐specific analyses have been more accurate in the past than analyses based on age‐specific mortality alone would have been. The major contribution of forecasting mortality by cause appears to have been in allowing for easier incorporation of expert opinion rather than in making the. data analysis more accurate or the statistical models less biased.     

Comparison of microcomputer programs for making population projections: An update

There are many programs for making population projections now available for use with microcomputers. This article reviews six of approximately 15 microcomputer population projection programs. Each program is compared to a standard set of criteria relating to such items as hardware and software requirements, input data requirements and specification of assumptions, methodology and documentation, and summary output indicators. Numerical results from projections of six test data sets reflecting different assumptions about mortality, fertility, and migration are compared. Qualitative comments are included for describing special features and for making an overall assessment of each program.     

Methods for combining ancillary data in stochastic compartment models of cancer mortality: Generalization of heterogeneity models∗

In analyzing mortality data there may be available information from survey and other sources that describe the marginal distribution of risk factors. We present a mortality model where nationally representative survey data on risk factor distributions are combined with data on cohort mortality rates to increase information, i.e., a fixed marginal risk factor distribution is combined with a cohort model representing unobserved individual risk heterogeneity. The model is applied to lung cancer mortality in nine U.S. white male cohorts aged 30 to 70 in 1950 and followed 38 years. Estimates of the cohort specific proportions of smokers were made from the National Health Interview Survey. Comparisons are made for models with different patterns of changes with age of individual heterogeneity.     

Ever since gompertz

In 1825 British actuary Benjamin Gompertz made a simple but important observation that a law of geometrical progression pervades large portions of different tables of mortality for humans. The simple formula he derived describing the exponential rise in death rates between sexual maturity and old age is commonly referred to as the Gompertz equation—a formula that remains a valuable tool in demography and in other scientific disciplines. Gompertz’s observation of a mathematical regularity in the life table led him to believe in the presence of a law of mortality that explained why common age patterns of death exist. This law of mortality has captured the attention of scientists for the past 170 years because it was the first among what are now several reliable empirical tools for describing the dying-out process of many living organisms during a significant portion of their life spans. In this paper we review the literature on Gompertz’slaw of mortality and discuss the importance of his observations and insights in light of research on aging that has taken place since then.     

Socio-economic Differentials in Infant and Child Mortality during Mortality Decline: England and Wales, 1890–1911

In this paper data from the 1911 Census of the Fertility of Marriage of England and Wales are used to study patterns of mortality decline by socio-economic characteristics, principally the occupation of husband. That census reported data on number of wives, children ever born, and children dead by marriage-duration cohorts for 190 non-overlapping occupations of husband. These results, along with those on number of rooms in the dwelling of the family are used to make indirect estimates of childhood mortality using the techniques described in United Nations, Manual X. These procedures produce values of q(a), the probability of dying before reaching some exact age ‘a’. Estimates for q(2), q(3), q(5), q(10), q(15), and q(20) are derived from data on women married 0–4, 5–9, 10–14, 15–19, 20–24, and 25–29 years, respectively. These estimates can also be dated to a point in the past. These values can also be converted to a corresponding level of a Model West life table, which describes the ‘average’ mortality regime which the children of those women experienced. This furnishes a basis to look at mortality decline for various social classes and occupational groups. Ordinary least squares regressions of the levels of Model West life tables implied by the 1(a) values on time give one measure of mortality decline. Another is the absolute amount of the increase in the level of the Model West life tables from marriage-duration cohort 20–24 years to 0–4 years. The aggregate results indicate that social class in England and Wales during the 1890s and 1900s tended to be related to the speed of mortality decline: childhood mortality declined more rapidly in the higher and more privileged social class groups. But the results were neither nearly as strong nor as regular as those which predicted the level of mortality within any marriage-duration cohort. These outcomes are not particularly sensitive to the three different social-class stratification schemes used: the 1911 English Registrar General's classification; the 1951 English Registrar General's classification; and the 1950 U.S. Census classification. There was also a fairly regular and predictable gradient for the number of rooms in the home: child mortality was higher in families who lived in larger dwellings. Analysis of 190 detailed male occupational groups revealed that considerably more of the variation in mortality levels than of trends could be explained by social-class categories. Between 20 and 40 per cent of variation in mortality trend could be accounted for by social class alone, as opposed to 50 to 80 per cent of mortality levels for different marriage-duration cohorts. Results for a more restricted sample of 116 occupations for which income estimates could be made revealed a similar pattern. In addition, income was virtually unrelated to the pattern of mortality decline, and improvement was more rapid in groups who were more urban. This reflects the role of rapidly improving urban sanitation in the late nineteenth and early twentieth centuries in England. In contrast, income was significantly related to childhood morality levels for various marriage-duration cohorts (with higher income associated with lower mortality), while urbanization was inversely correlated with mortality levels (more urban groups experienced higher mortality). Overall, social class (or occupation group), income, and urbanization were more successful in explaining mortality levels than time trends across occupations, although social class and the extent of urbanization did reasonably well in accounting for trends. Over a longer period, the transition in child mortality was under way by the 1890s, but its pace and timing varied in different occupations and social class groupings. Although absolute differences in infant mortality were reduced after about 1911, relative inequality persisted even as infant and child survival improved for all groups.     

Researching to Transgress: The Need for Critical Feminism in Gerontology

SUMMARY

This article defines “empowering research and argues the need for a critical gerontology” informed by feminist and postmodern theories which focus on the connections between language, self, and social action. The author calls for feminist gerontology which evokes critical consciousness on the part of the researcher and participants. Feminist gerontologists are encouraged to engage in self-reflection and self-critique in regards to their own attitudes toward aging and to include personal criticism in their scholarly writings. Examples of feminist research on aging which illustrate these characteristics are provided.     

Women,Aging, and Schizophrenia

SUMMARY

Schizophrenia is a psychiatric disorder of unknown etiology that typically has an onset in early adulthood and persists for the remainder of the life span. For most affected individuals, the illness is recurrent with psychotic symptoms that tend to be episodic in nature. The illness has pervasive and disruptive effects on many life domains; for example, women with schizophrenia are less likely to marry, bear children, and raise their own children than are women in the general population. The age of onset of schizophrenia is later on average in women than men, and women are overrepresented among those who develop the illness after the age of 45. Among younger patients with schizophrenia, women tend to have less severe symptoms than men and better outcomes; however, there are fewer gender differences among older patients with schizophrenia. Older women with schizophrenia are vulnerable to problems of both schizophrenia and aging. Schizophrenia symptoms typically continue in later years and include ongoing psychotic symptoms. Problems of aging such as cognitive decline and chronic medical conditions may be exacerbated by schizophrenia and the disorder is associated with premature mortality. Older women with schizophrenia are at risk for neglect of psychiatric and other health needs that are further compounded by limited social support and low socioeconomic status. More research and clinical attention is needed for the problems of older women with schizophrenia.     

On the distribution of completed parities when fertility is heritable

Over the last one hundred years, there has been, in many developed countries, a demographic convergence towards the two child family. The possible implications for population growth of such a tendency are considered in this paper in terms of both family limitation and also the intergenerational transmission of fertility. These two effects interact so that as the proportion of two‐child families increases, the possible influence of mother‐daughter fertility associations on population growth decreases, though even now it could override otherwise significant changes in either or both of the birth and death intensities. In particular, it is shown that according as to how fertility is transmitted through generations, it is still possible to have zero growth rates consistently with a widely dispersed stable distribution of family size as well as a typical mortality regime.     

Older Women's Body Image and Embodied Experience: An Exploration

ABSTRACT

This paper presents and analyzes findings from unstructured interviews with women aged 61 to 92 regarding their perceptions and feelings about their aging bodies. The data are discussed in light of the existing literature on women's body image which has largely ignored the experiences of women in later life and which has tended to focus on adolescent and middle-aged women. Given the fact that beauty is equated with youthfulness and thinness in our society, older women face unique challenges as they strive to construct and maintain positive evaluations of self. The women in the study exhibit the internalization of ageist beauty norms even as they assert that health is more important to them than physical attractiveness and comment on the ‘naturalness’ of the aging process.     

Elderly Women Show Neither a Shortage of Strategies nor an Overreliance on Drugs in Handling Aging and in Dealing with Minor Health Problems

ABSTRACT

Women 65 years old and over make up the fastest growing population segment in North America. They are, particularly among the underprivileged, known to be heavy consumers of prescribed and over-the-counter drugs. The objective of this study was to identify the role of medication in underprivileged elderly women's strategies for aging well and dealing with minor health problems. A qualitative study was conducted among 40 women aged 65 to 75. Results show that elderly women seldom mention resorting to medication to “age well” although they report using this strategy to deal with minor health problems. Overall, the elderly women mentioned a wide range of strategies to cope with aging and minor health problems, which suggests that they are well equipped to face the challenges of aging.     

Separating the Signal From the Noise: Evidence for Deceleration in Old-Age Death Rates

Widespread population aging has made it critical to understand death rates at old ages. However, studying mortality at old ages is challenging because the data are sparse: numbers of survivors and deaths get smaller and smaller with age. I show how to address this challenge by using principled model selection techniques to empirically evaluate theoretical mortality models. I test nine models of old-age death rates by fitting them to 360 high-quality data sets on cohort mortality after age 80. Models that allow for the possibility of decelerating death rates tend to fit better than models that assume exponentially increasing death rates. No single model is capable of universally explaining observed old-age mortality patterns, but the log-quadratic model most consistently predicts well. Patterns of model fit differ by country and sex. I discuss possible mechanisms, including sample size, period effects, and regional or cultural factors that may be important keys to understanding patterns of old-age mortality. I introduce mortfit, a freely available R package that enables researchers to extend the analysis to other models, age ranges, and data sources.     

Enhancing a Randomized Response Model to Estimate Population Means to Sensitive Questions

ABSTRACT

Candidate parametric mortality models are tested graphically. If the model is correct, the transformed data are distributed exponentially. The graphical test is based on scale and space inference. It involves smoothing of the hazard rate and simultaneous confidence intervals. It is applied to a frailty model used to set annuity reserves. Simulation and the comparison with other non-graphical tests shows that the graphical test helps localize discrepancies of empirical data with respect to the tested model.     

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.     

On Growing Old in America: Perceptions of the Okinawan War Bride

ABSTRACT

The unique perceptions of aging of Okinawan war brides are presented through interviews with 15 subjects. They voiced their thoughts about a range of topics, including available support systems, effects of acculturation, and their sense of security as they approach old age. Pride in culture and fears of lost family connections are expressed as these women speculate about the demands of aging in America.     

Estimating the goodman,keyfitz, pullum kinship equations: An alternative procedure∗

As is often the case in demography, Goodman, Keyfitz and Pullum (1974) developed their theory of the interrelationships of fertility, mortality and kinship numbers by means of continuous mathematics [integrals], but resorted to ad hoc finite approximations for calculating results in concrete empirical cases. Their reason: ‘Ordinarily, we cannot evaluate the l(x) and m(x) functions for arbitrary values of x, since the data are usually collected for five‐year age intervals’ [p. 24]. Recent developments in computer software now provide an alternative, two‐step procedure that avoids extensive programming of finite approximation algorithms: 1) using a popular scientific curve‐fitting package, functions are found to represent particular sets of discrete data on fertility and mortality, 2) the resulting functions and parameter estimates are then inserted directly into the kinship equations, and the integrals evaluated numerically using readily available mathematics software. This procedure has potentially wide application in other areas of population mathematics where theory is given by integrals and other continuous expressions, but data are for discrete age groups.     

The Effects of Allostatic Load on Racial/Ethnic Mortality Differences in the United States

This study expands on previous findings of racial/ethnic and allostatic load (AL) associations with mortality by addressing whether differential AL levels by race/ethnicity may explain all-cause mortality differences. This study used data from the third National Health and Nutrition Survey public-use file, gathered between 1988 and 1994, with up to 18 years of mortality follow-up (n = 11,733). AL scores were calculated using a 10-biomarker algorithm based on clinically determined thresholds. Results of discrete-time hazard models suggest that AL is associated with increased mortality risks, independent of other factors, including race/ethnicity and SES. The results also suggest that the AL–mortality association is stronger for non-Hispanic blacks than for non-Hispanic whites, and that at low levels of AL observed mortality differences between non-Hispanic blacks and non-Hispanic whites are non-significant. These findings suggest that mortality differences between non-Hispanic blacks and non-Hispanic whites may be the result of how early life exposure causes premature aging and increased mortality risks. More attention to resource allocation and local environments is needed to understand why non-Hispanic blacks experience premature aging that leads to differential mortality risks compared to non-Hispanic whites.