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Demography of Aging (1994)

Chapter: 7 Medical Demography: Interaction of Disability Dynamics and Mortality

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Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
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7
Medical Demography: Interaction of Disability Dynamics and Mortality

Kenneth G. Manton and Eric Stallard

As the elderly have become an ever-growing proportion of the American population, and as society has assumed some responsibility for their health, understanding the relationships among the factors that affect health has become crucial to policy makers. In this chapter we seek to build a framework for examining the interactions among the health-related behavior of individuals, genetic predispositions, the incidence of disease and fatality, the aging of the population, and levels of mortality and morbidity. Particularly crucial to policy makers is the relation between disability and mortality: When the incidence of disease or injury falls, so does the incidence of disability; and when death rates for people with a particular disability fall, that condition becomes more prevalent and thus demands on the health care system intensify.

To focus on the elderly demands a special approach because the mortality and health of the elderly and of younger people differ dramatically. The likelihood that someone suffers from multiple diseases, and from functional limitations, increases with age. Moreover, death in the old is due mostly to chronic diseases, with long histories. The models that apply to younger people, therefore, are not suitable for the analysis of the old.

Mortality is often studied with life tables estimated from vital statistics and census data. Life tables are useful for analysis of health policy and for social, epidemiological, and biomedical research. But they are deficient for refined analysis because they often lack information on the risks an individual faces. Everyone in a cohort—consisting, say, of all women, or of all

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

people aged 45 to 64—is assumed to face the same risks as everyone else; thus, such studies cannot be used to analyze such things as the change in the health of given individuals, nor are they useful for assessing the efficacy and cost of interventions.

Medical demography, the study of chronic disease, disability, and mortality in mature and aging populations, has roots in actuarial and biometric models of mortality and insurance of health-contingent events (Spiegelman, 1968). The tradition includes Graunt's ''bills of mortality" (1662), Bernoulli's life-table models of smallpox vaccination (1760), and the models of adult mortality devised by Gompertz (1825), Makeham (1867), Perks (1932), and Beard (1963a,b). Other well known examples include Clarke's use of "bioactuarial" models to isolate mortality associated with old age from mortality from exogenous causes (1950), and Bourgeois-Pichat's (1952, 1978) and others attempts to estimate the biological "limits" to life expectancy.

But medical demography lost impetus as research into the epidemiology of chronic disease specialized. That work, however, had its limitations in its reliance on case-control studies or studies of occupational cohorts and on longitudinal studies of selected populations from which it was difficult to estimate national rates of health events.

Recently, medical demography regained impetus for several reasons. First, concern has arisen because federal forecasts of mortality and population growth show biases with important implications for Social Security, Medicare, and other federal programs. The Social Security "crisis" of 1982-1983 showed that the population aged 65 and older was consistently underestimated, a bias that may still exist (Myers et al., 1987; Preston, 1993). Second, forecasts of the effects of disease on populations and of the health- and cost-effectiveness of interventions were often inaccurate (Walker, 1982; Frank et al., 1992). Third, the need to assess health trends and to characterize the natural history of chronic disease in the very old—those 85 or older— has intensified as life expectancy has lengthened and as that group has grown. Finally, longitudinal surveys of changes in the health of elderly Americans became available that were linked to Medicare data whose age reporting was better than that in decennial censuses (for example, the 1982, 1984, and 1989 National Long-Term Care Surveys, NLTCS).

Medical demography requires biomedically detailed models of the relation of age to health, to change in the ability to function, and to mortality in individuals. Biologically naive models do not accurately anticipate change in health or in the population health burden or the effects of intervention (Evens et al., 1992; Frank et al., 1992; Selikoff 1981; Tsevat et al., 1991). This is especially the case for the very old because of the special nature of the health processes of this group: they experience comorbidity—combinations of problems—impairment of function, a decrease in the ability to maintain biological stability with emergent nonlinearities in the change of

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

population health parameters. Such complex processes are often modeled using parameters estimated from multiple data sets, each with specific sets of biological measures.

Medical demography is crucial in research about aging populations and in analyses of policies affecting them because mortality and health are dramatically different among the elderly than they are among younger people. Thus, demographic models, developed initially for younger populations, must be modified to describe and forecast health changes at late ages. For example, mortality in the old is due mostly to chronic diseases with long natural histories. Furthermore, the likelihood that a person has multiple concurrent diseases, and functional limitations, increases with age. Standard life tables are not designed to model such processes; for one thing, cause-elimination life tables assume that diseases operate independently—an assumption that may better approximate the effects infectious diseases have on the mortality of younger people. To model processes that become more complex with age also requires data that are not available from the usual demographic sources—for example, combinations of data on mortality from vital statistics with data on health from longitudinal health surveys.

The need for medical-demographic analyses to describe health changes in the old has two aspects. First, to describe the effects of preventative and other public health interventions we need models that can both identify relevant inputs—say, risk factors for chronic diseases and the provision of health services—and accurately predict the influence of those inputs on health. Second, anticipating health and functional changes calls both for measures to describe the special health problems of the elderly noted above and for models to anticipate how observed health factors translate into future changes. For chronic diseases in the elderly these requirements entail a long time horizon because the latency of chronic disease ranges, for example, from 7 years for premenopausal breast cancer to 50 years for asbestos-determined lung cancer. Thus, one must recognize that the health of the elderly is subject both to biological inertia and to changes brought about by ongoing interventions, such as the National Cholesterol Education Program (Johnson et al., 1993; Sempos et al., 1993). Recognition of these factors will affect both models of health changes in elderly populations and models of their needs for services.

We explore these issues in the four sections of this chapter. First, we review methodological issues in modeling chronic disease processes such as the nature of hazard functions for chronic disease, the effects of time-varying covariates on health processes, cohort effects, and the mathematical relation of health changes in individuals and in aggregate populations. Second, we examine processes for individuals, relating the interactions of the natural history of a chronic disease with life stage. Doing so is necessary to make the models biologically realistic so that they can accurately predict

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

the effects of interventions. Third, we discuss the relation of disability and mortality; the measurement of disability in elderly persons; and the effects on measurement of using duration-based indicators of disability such as "active life expectancy." This discussion highlights the complexity of the health and functional status of elderly persons which requires assessments of multiple dimensions of function and the effects of comorbidity. Finally, we examine the role of genetics in shaping health in old age, which is different from its role at earlier ages because most lethal genetic defects are expressed by middle age. In elderly populations, health effects are polygenically determined and interact with environmental factors. Throughout, we discuss the use of primary data in estimation and of secondary data in determining model structure, because seldom will a single data set have the information necessary to estimate all relevant parameters for models of chronic disease and functional loss. This presentation assumes the reader has been exposed to the use of life tables, survival functions, hazard models, and common matrix and vector notation used in regression analysis.

Cohort Analysis and Time-Varying Covariates

The concepts of age, period, and cohort are basic in assessing the effect chronic disease has on the population. But they need careful definition to avoid the confounding that arises because cohorts are the interaction of age and period. We present, therefore, two definitions of a cohort. One is a "set" of persons who were all born in a particular year and thus are all the same age at any given point in time. Here the dynamics are demographic turnover—for example, passing age 65 or death. This is the standard concept of a cohort and is often used in gerontological and demographic research, though this work is hampered by the methodological problem of identifying age, period, and cohort parameters from aggregate data (see Schaie, 1983; Mason et al., 1981; and Hastings and Berry, 1979).

The second concept groups individuals, whatever their age, according to their exposure to a common experience at a specific time or place. A cohort might consist of the group of individuals who received a polio vaccination. This concept uses longitudinal microdata to estimate the parameters of a multidimensional, stochastic process that describes developments in the health of individuals. Mechanisms that are functions of the time lived represent aging. Period effects are exogenously generated perturbations, localized in time. Exogenous factors that permanently alter individual parameters are cohort effects. Thus, age, period, and cohort are identified with the temporal dependence of the parameters of processes of change in individual health. The designation of parameters to decompose the temporally changing correlations of multiple health variables permits the identification of the effects of age, period, and cohort (Feskens et al., 1991, 1992).

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

One cannot identify aggregate parameters for these factors using the variation of a single dependent measure—I.Q., for example—because within-cell variation is assumed to be "error." By relating age, period, and cohort parameters to individual health changes, one can construct a state-space model in which "state" is the individual's state of health measured by certain variables at a point in time and "error" is uncertainty about an individual's state. The variation in one individual's state from another's, or in his own over time, identifies the effects of cohort, age, and period.

These issues are illustrated by the individual failure process implicit in hazard models and explicit in state-space models. In a hazard model, the dependent variable is time to death for individual i (t i). In Figure 7-1, A, B, C, and D are hazards describing changes in the distribution of ti as fixed covariates are added. One could stratify the hazard on age, then period, and then cohort. As more covariates are added, the hazard approaches that for an individual—the "ultimate" stratification, described by curve D, that is, a "spike," or infinite hazard, at ti. As a consequence of adding covariates, the shape parameter, which controls the hazard's curvature with time, increases. When ti is known, the hazard is zero up to ti, and then it is infinite. The distribution function of ti, identical for everyone, is a distribution of the effects of unobserved variables over time. The individual's failure process is uninformative in these models (that is, mortality rates go from 0.0 to 8 instantaneously). The probability that, prospectively, ti can be determined exactly is vanishingly small; such models are not valid for predicting change.

Conditions for curve D occur frequently, as in aggregate data when the model is "saturated"—that is the number of data cells showing age by period effects and the number of parameters are the same—or when a hazard, estimated by maximum likelihood from ti's, degenerates into spikes when too many parameters are estimated. This situation can develop unexpectedly if ti is reported, not as a truly continuous variable, but grouped in temporal categories. Such "clumping" was found in data on unemployment duration when labor force reentry clustered at 13, 26, 39, 52 weeks, and so on, when unemployment benefits ran out (Heckman and Singer, 1984a,b). If not "adjusted" by, say, using dummy variables to filter out quarterly effects, the estimation of additional parameters caused the likelihood value to go to infinity. Problems also appear if the hazard rates change too rapidly, for example, declines in infant mortality in the first week, or month, of life may be so rapid that the actual information, and thus the degrees of freedom, is more limited than the sample size suggests (Potthoff et al., 1992). Both problems involve misspecification of the hazard function (Manton et al., 1992).

If continuous hazard functions with specific parameters are to be used to analyze health events, they must be substantively rationalized. The Weibull hazard function assumes that an event emerges after an individual takes m

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Figure 7-1 Illustrative hazard function for aggregate data. The hazard function µ(t) is the mortality rate for the infinitesimal interval ( t,t+Δt). Hence, µ(t)At is the probability of death between t and t+Δt for persons alive at t. The survival function S(t) is obtained from

The distribution function F(t), obtained from F(t) = 1-S(t), is the probability that death occurs at or before age t.

"hits."1 In carcinogenesis, hits are mutations in the genes in a cell controlling its growth and function. If, as for colon cancer, the number of mutations is known, then the shape parameter value, or possibly its range is known (Ashley, 1969; Fearon and Vogelstein, 1990). Using biological data to establish the shape parameter prevents hazard from going to infinity. Without ancillary data to fix the value (or range) of the shape parameter,

1  

The Weibull distribution can be described by the formula µ(t) = btm-1; where µ(t) is the age-specific mortality rate; b is a scale parameter; t is age; and m is the shape parameter.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

the hazard may become infinite. Thus, using a hazard model without a theoretical rationale relies on chance to avoid parametric saturation and a degenerate likelihood (Trussell et al., 1992).

To biologically justify a hazard function requires specification of a mathematical relation between the failure process for an individual and the distribution of times to death in a population. Using a Weibull, the times to tumor onset in a population have the same distribution as the time for the first cell, in an organ's population of cells, to acquire m errors. Functions with these special mathematical properties generate extreme-value distributions (for example, the Weibull and Gompertz; see Mann et al., 1974).

A hazard can be generalized by assuming that each person has his own scale parameter, (see, for example, the work of Vaupel et al. (1979) on modelling frailty). Then, no matter how a population is stratified, tihas irreducible variance. "Mixed" hazards use the marginal distribution of risk factors estimated from national surveys to identify fixed, and random, heterogeneity effects on mortality (Manton et al., 1993a). Slower age increases of the population hazard, assuming the individual hazard is a Weibull (cancer) or a Gompertz (total mortality), are produced both by the scale parameter being distributed over individuals (Manton et al., 1986), and by relating individual risks to a distribution of marginal risk factors. If the hazard is a convex function of risk factors, then the age trajectories of population and individual hazards are related by Jensen's inequality—E(µ()) = µ(E())—the average risk in a heterogeneous population (risk factors are represented by the vector ) is greater than (or equal to) the risk at the means of the risk factors E (). Because survivors have more favorable values of s, heterogeneity, regardless of its distribution, acts to decrease population risk with time.

A hazard function implicitly has a parameter space with two dimensions, persons and time. In the extreme, there is either a time-dependent hazard with no individual heterogeneity, or a time-constant hazard with individual heterogeneity. To identify parameters, information on either individual failure, or risk differences, is needed. The correlation of parameters provides information on the relation of scale and shape parameters of the Gompertz (or other hazard) across populations or over species (Finch, 1990). In a stochastic process, risk-factors are time varying.

Macrolevel Models

Long time series of mortality—for, say, cancer deaths in the United States from 1950 on—can be used to model how vulnerable to specific diseases given cohorts have been. Trends in the causes of death must be distinguished from changes in the causes noted on death certificates; one example of the latter changes is the shift during the 1980s from listing

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

emphysema, bronchitis, and asthma to listing "chronic obstructive pulmonary disease." If conclusions made from these data are to be meaningful, the hazards must be carefully defined.

Mortality data are often used to complement biologically detailed models of health events in select, longitudinally followed populations because few longitudinal data sets are large enough to precisely estimate cohort trends for specific diseases to late ages. Carey et al. (1992) showed that distinguishing between mortality patterns at late ages requires a sample of 100,000 or more. Few longitudinal studies meet this requirement. Conversely, mortality data are insufficient to study survival at late ages when age reporting error may significantly affect the distribution of times of age at death (Kestenbaum, 1992).

The failure process for "mixed" hazards can be described by a "compartment model," that is, a discrete-state, continuous-time, stochastic process in which transitions to unobserved health states are estimated using biologically plausible functions to infer prior health changes from the age distribution of mortality. Compartment models were developed to assess multistate drug metabolism (Jacquez, 1972) and biological experiments (Matis and Wehrly, 1979). They can also be applied to cohort data to study a population's health "metabolism"—the rate at which persons move through specific, but unobserved, health states. For example, to evaluate the utility of mammography, cohort mortality from breast cancer for American women from 1950 to 1988 was modeled as a mix of early, premenopausal, disease and late, postmenopausal, disease: The characteristics of the former are that it is histologically aggressive, that it involves a strong family history, that it is estrogen receptor negative, and that is has a short latency, of 7 years. The characteristics of the latter are that it is fertility sensitive, that it involves a weak family history of the disease, that it is less histologically aggressive, that it is estrogen receptor positive, and that is has a longer latency, 14 years. Data on cohort mortality were combined with data from the National Cancer Institute's Surveillance of Epidemiological and End Results (SEER) program to estimate stage-specific survival rates in order to simulate the efficacy of different age and time schedules for mammographic screening; the measure of efficacy was changes in the proportion of females identified with Stage I disease. By distinguishing early and late disease, with different latencies and age-incidence patterns, different screening schedules were evaluated (Manton and Stallard, 1992a). Second, data on the mortality from lung cancer of cohorts of American men from 1950 to 1988 were linked to data from the National Health Interview Survey (NHIS) on smoking (Harris, 1983). Using the marginal cohort distribution of cigarette consumption, cohort-specific relative risks for smokers and the rate at which persons quit smoking were estimated (Manton et al., 1993a). Third, cohort mortality rates for lung cancer, and for all other causes, were estimated

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

simultaneously (Manton et al., 1993b). Fourth, U.S. mortality data organized by cohort were combined with (1) Weibull functions estimated from the incidence of mesothelioma (a type of lung cancer; Peto et al., 1982); (2), SEER-recorded incidence rates for mesothelioma (1975 to 1989); and (3) reported starts of asbestos exposure arranged in age by date matrices. The lack of detailed data on asbestos exposure necessitated the use of multiple data sources. Early exposures, in "insulation work equivalents" (assuming a linear dose response) were estimated using Weibull functions for specific cohorts to relate 15 years of mesothelioma incidence to reported "age by date" first responses. This assumes the validity of the multihit (Weibull) model of carcinogenesis for mesothelioma (Armitage and Doll, 1961). The use of time since first exposure, rather than age, in the Weibull, assumes that mesothelioma is due only to asbestos, and that other causes of death are elevated for persons with asbestos exposure (due to nonasbestos toxic work exposures). A table of estimated age by date of first exposure is used to forecast other asbestos-related diseases.

Thus, in these examples, combining data sources permitted analyses of specific diseases—though with limitations. Maximum likelihood procedures may not be optimal here because large samples may require smoothing parameter estimates for young and old cohorts with truncated mortality distributions (Manton and Stallard, 1992b). This is because sampling error is small relative to measurement error, and biases, such as right censoring of mortality and age changes in disease mechanisms, may dominate the variation of parameter estimates across cohorts. Second, a model's validity is based on its biological rationale. If there is no biological rationale to constrain model choice, a model fitting the data can always be found because of the inability to identify hazard functions in mortality data (Manton et al., 1994a).

Using clinical and experimental information to specify a model, and assessing it with cohort mortality data, depends on Bayesian principles because parameters are estimated conditionally on ancillary data. This approach differs from meta-analysis, which assesses the consistency of parameters across studies (Thompson and Pocock, 1991). A compartment model is tested against external data, say, cohort mortality rates from specific causes. Compartment models are exclusive: only the "best" studies are used in model development. Meta-analyses use all studies meeting specific criteria, which must be carefully examined to ensure that the selection is not biased. For example, "successful trials" are more likely to be published, and thus overrepresented in the literature, than are trials with negative results. Thus, the studies available in the literature may disproportionately represent certain outcomes. Second, the criteria used to select published studies influence the outcomes of meta-analysis. For example, meta-analysis was used to examine the relation of cholesterol to adverse health effects.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

No study has yet shown a significant decline in total mortality produced by reducing serum cholesterol using drug therapy, though positive outcomes are shown for circulatory disease. Ravnskov (1992) argued that meta-analyses of cholesterol health effects are biased "samples" of studies.

Microlevel Models

Complementing mortality models are analyses of longitudinal microdata, in which the individual is modeled as a complex system whose evolution is governed by time-dependent processes operating at different levels of biological organization. In this view, aging is the loss of system integration—that is, increased entropy—and of homeostatic control of multiple linked processes (Firth, 1991; Goldberg et al., 1992). This type of model contains two types of jointly dependent processes. First, systems of autoregressive equations describe linked changes in J state variables, that is, xijt, (or the vector ), where j = 1, 2, ..., J and i indexes individuals,

Ageit denotes the age of person i at t, are stochastic shocks, are exogenous variables, and is a matrix formed from the . The J trajectories described by (1) represent both fixed and stochastic effects. Fixed effects due either to genetics or to exposures to a risk prior to the study are represented by constants, (for example, ) or age changes (that is, ) of . The expression · Ageit may describe genetic age changes; for example, the age rate of loss of hepatic low-density lipoprotein receptors. These changes can be sex specific (Hazzard, 1990). Estimating an individual constant, , (or parameters of its distribution) requires multiple measures on each i, or assumptions about the distribution of (or ) over persons. Parameters might be estimated from longitudinal data on identical twins. Genetic disease may manifest itself early in a person's life; that is, the stronger the effect of a gene on disease, the higher the rate of early death (Beregi et al., 1991; Marriotti et al., 1992; Takata et al., 1987; Thieszen et al., 1990). For example, the risk of genetic dyslipidemic hypertension is manifest by age 40 and declines with age (Reed et al., 1991). Strong selection can generate a rapid rise in mortality in "mid" age (e.g., age 30-80), with mortality approaching a constant at late ages (Perks, 1932; Thatcher, 1992). Such age patterns, found by Carey et al. (1992) and Curtsinger et al. (1992) in insect models, are manifest in human populations for specific diseases, such as breast and lung cancer, and possibly for total mortality (Lew and Garfinkel, 1990).

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

The term [Ageit × ] represents the alteration by risk factors of the age expression of genotype. For example, testosterone reduces hepatic LDL receptors and stimulates abdominal fat cells, which are more insulin resistant than are other fat cells (McKeigue et al., 1991). Insulin resistance may raise cholesterol and stimulate hyperinsulemia (Modan et al., 1991). The increase may be mitigated by the value (and age trajectory) of other variables, the body mass index (BMI) or the hematocrit.2 Differences in age trajectories of hematocrit may maintain sex differences in mortality at late ages (Heikinheimo et al., 1985; Sullivan, 1991).

The term represents sets of K exogenous factors, , k = 1,...,K. If K= 1, is a scalar: = . If K > 1, is a vertical "stack" of K, JxJ diagonal matrices, where the J diagonal elements of the kth matrix are . To conform with , a5 and a6 have J rows and JxK columns so the products a5 × and × are JxJ. The term a5 × × is the interaction of exogenous factors with state variables; a6 × [Ageit × ] is the interaction of exogenous factors with age changes in state variables. If there is a "normal" trajectory of cholesterol metabolism, and it is affected by other characteristics, then might reflect pharmaceutical control, that is, a drug's effect may be modulated by, say, BMI and age changes in lipid metabolism (Knapp et al., 1992). These interactions determine whether interventions affect mortality at late ages. Clinical studies suggest that some risk factors are significant to late ages; (in one example, treatment of isolated systolic hypertension reduced the risk of stroke; SHEP Cooperative Research Group, 1991).

The terms in equation (1) involving reflect the effect of prior states on future states, , that is, state dynamics. Diffusion (, where d is an age-dependent scale parameter) prevents ti from being "known." Unobserved stochastic processes, ,also influence . Inversely, temporal changes in covariances may be used to infer the characteristics of , especially if are measured often. The variables may be manifest as high-order lags in equation (1) (Manton et al., 1993c). Lags may be described by integrating exposures to risk factors over time, for example, the number of years smoked multiplied by the average number of packs of cigarettes smoked— the "pack years"—reflects cumulative "damage."

The second type of process is described by a mortality function,

2  

The body mass index (BMI) is the ratio of weight in kilograms to height in meters; hematocrit levels may affect atherogenesis by promoting LDL oxidation (McCord, 1991).

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Figure 7-2 Univariate quadratic hazard function for a single risk factor ( x), for a fixed value θ = 0.0805, but at different ages. The quadratic hazard is drawn with the following parameter settings: µ(x) = (0.01+[(x-x*)/100]2)exp[0.0805(Age-65)], and x* = 100.

Equation (2) is a ''Gompertz" with the scale parameter replaced by a quadratic function of the realizations, , of the stochastic process in equation (1). In other words, equation (2) is dependent on time-varying covariates. The quadratic can be decomposed into terms for each of M diseases to allow risk factors to relate differently to different diseases (i.e., the can be different). If θ represents the effects of unobserved age-related variables () on mortality, senescence can be explicated by improving the measurements of the state variables . Alternatively, a cause may have its own θm due to unobserved variable effects specific to m. θ declines in value as more of the age dependence due to senescence measured by θ is assignable to state variables ( become more informative).

A quadratic function is used for several reasons. A U- or J-shaped function describes the relation of mortality to many risk factors (Jacobs et al., 1992; Neaton et al., 1992). The curvature of the quadratic is a function of θ, so the rate of change of risk factor effects on mortality that is related to age reflects interactions with unobserved variables, . The function with θ = 0.0805 is shown for select ages in Figure 7-2. The horizontal axis

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

represents x; x°is a value producing the lowest mortality; for example, µ(x°) = .01 at age 65. The vertical axis is the mortality level. As age increases from 65-95, with θ and fixed, mortality increases.

Changes in θ are illustrated in Table 7-1 for the 34-year follow-up of 10 risk factors from the Framingham Study: 7 dimensions identified from 27 functional and physical performance items for the 1982-1984 NLTCS and mortality for 1982-1986; and 7 dimensions from the 1982-1984-1989 NLTCS and mortality for 1982-1991. For Framingham, risk factors reduce the male θ form 9.4 percent to 8.1 percent, a relative decline of 14 percent. For females, the relative decline in θ is 19 percent, from 10.0 to 8.1 percent. The relative decline of θ using 1982-1984 NLTCS functional scores is 51 to 61 percent. Thus, functional scores described the age dependence of death better than risk factors (Campbell et al., 1985; Dontas et al., 1991; Grand et al., 1990). This finding is consistent with decreased physical activity being a major risk factor at late ages: 56 percent of deaths in a population whose mean age was 84.5 years were due to pulmonary embolism, congestive heart failure, or pneumonia—all diseases associated with reduced activity (Gross et al., 1988). Conditioning θ on functional status, suggests that mortality rises 3.6 to 4.0 percent per year of age (thus it doubles in 17-19 years) compared with a doubling of mortality in 6.9 years for a θ of 10 percent. Controlling income and education, as well as function, reduced θ to 2.6 percent. For the 1982-1984-1989 NLTCS, the relative decline in θ is smaller (35 to 48 percent) because, over the longer period 1984-1989, intermediate transitions cause information in the 1984 scores to decay.

A second measure of information is the proportion of χ2 explained by (that is, test 2, with θ = 0.0). In the Framingham study, risk factors explain 70 percent of the χ2 due to age in the mortality model. In the 1982-1984 NLTCS, 92-95 percent of the χ2due to age is explained. In the 1982-1989 NLTCS, function accounts for 79 percent and 87 percent (for males and females, respectively) of the χ2 explained by age. The decline in the age variation of mortality explained by function for 1982-1989 data is smaller (14 and 7 percent for males and females) than the relative changes in θ, 24.1 and 23.3 percent. Thus, loss of the ability to explain the age dependence of mortality between 2- to 5-year intervals is moderate and similar to that for other types of survey error. θ adjusts for differences in the quantity and type of to better embed the estimated discrete-time process in the underlying continuous-time process, and thus reduces bias.

Other reasons for using a quadratic is that it describes homeostasis in an organism (that is, negative feedback keeps an individual's state within viable regions of ). The quadratic defines a point at which mortality is minimized:

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

TABLE 7-1 Chi-Squared Values Associated with the State Variables, , and with the Senescence Process θ in Cause-Specific and Total Mortality Functions

Data Source, Test

Males

Females

Number (n), and Descriptiona

χ2n

χ2n21(%)

χ2n

χ2n21(%)

Framingham: 10 risk factors

1. Full process

2,174.8

100.0

2,047.8

100.0

2. alone, θ = 0

1,518.8

69.8

1,445.5

70.6

3. Effect of θ

656.0

30.2

602.3

29.4

 

(θ = 0.0805)

 

(θ = 0.0812)

 

4. θ alone, no

1,350.4

62.1

1,406.1

68.7

 

(θ = 0.0939)

 

(θ = 0.1002)

 

1982-1984 NLTCS: 7 functional scores (based on 27 attributes)

1. Full process

3,206.5

100.0

4,728.1

100.0

2. alone, θ = 0

2,945.9

91.8

4,467.5

94.5

3. Effect of θ

260.6

8.2

260.6

5.5

 

(θ = 0.0401)

 

(θ = 0.0364)

 

4. θ alone, no

1,163.6

36.3

2,210.6

46.8

 

(θ = 0.0811)

 

(θ = 0.0937)

 

1982-1984-1989 NLTCS: 7 functional scores (based on 27 attributes)

1. Full process

4,837.9

100.0

7,493.8

100.0

2. alone, θ = 0

3,821.5

78.9

6,550.5

87.4

3. Effect of θ

1,016.4

21.1

943.3

12.6

 

(θ = 0.0528)

 

(θ = 0.0475)

 

4. θ alone, no

2,662.2

55.0

4,466.0

59.6

 

(θ = 0.0815)

 

(θ = 0.0910)

 

a For tests 1, 2, and 4, the baseline model for comparison assumes constant mortality for all ages and risk factor values.

Test 3 compares the models in tests 1 and 2.

SOURCE: Data are from the Framingham Heart Study and the 1982, 1984, and 1989 National Long-Term Care Surveys.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

The second expression arises if Ageit is not in , (for example, if age's effects are represented by θ), with the implication that is constant. If age is in , is a linear function of age. It is also unlikely that a hazard with greater than second-order terms can be estimated in most data sets. The multivariate normal distribution of , implied by a quadratic hazard, is the statistically most conservative estimator of a multivariate distribution with higher-order moments (>2) because it has the maximum entropy of any distribution with a fixed covariance matrix.

The interaction of a quadratic hazard and linear dynamics preserves properties of the distribution that other hazard functions do not. The quadratic mortality matrix = + ... + reduces the variance-covariance matrix of in each measurement interval for each of M causes: it naturally parameterizes cause-specific mortality changes. The logistic only approximates a hazard (the dependent variable is the log of the odds ratio, p/(1-p), where p is the event probability). If one decomposes data by time, or cause of death, a logistic estimated for each interval, or cause, cannot be recomposed to generate a logistic for total time, or mortality, because the product of logistics is not logistic (Woodbury et al., 1981). Estimates from the Cox model (1972) are not consistent if cause-specific rates are not proportional over age; if, for example, exponential hazards are estimated for three causes, (say, cardiovascular disease (CVD), cancer, and other), the three functions produce a sum of exponentials so coefficients for total mortality cannot be compared with coefficients in cause-specific functions. The Cox model also assumes that the population is risk homogeneous and that competing risks are independent (Gill, 1992). Furthermore, in the quadratic the matrix of second-order partial derivatives of µ(·) is independent of , that is,

Thus, interactions of risk factors are constant within age strata. Since the inverse of equation (4) appears in equation (3), all these interactions are represented in . Introducing quadratic terms in a Cox model does not preserve these properties, for one thing, quadratic effects are scale dependent.

Estimation of equations (1) and (2) assumed that the likelihood for a longitudinal study can be factored conditionally on . To integrate parameter estimates from (1) and (2) in life tables, difference equations are needed. Three describe mortality dynamics. Survival is

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

where = , = , and = are from (2), are risk-factor means, and is the risk-factor covariance matrix at t. The vector of mortality-adjusted risk factor means is

Mortality-adjusted variances are

After adjusting for mortality, the of survivors changes:

where and are coefficients in (1). The covariance matrix adjusted for dynamics is

where is the error covariance matrix at age t + 1. For functional scores, which sum to 1.0 and are nonnegative, diagonals of are bounded by Bernoulli variance requiring constraints in equation (9) and on in equation (1) (Manton et al., 1993c). Equations (5) through (9) are used in health forecasts and simulations.

To test the model, first, standard errors of coefficients in equations (1) and (2) are calculated. Second, trajectories of the and are compared with external data. Examining these trajectories requires more data, and is more stringent, than evaluating a hazard's prediction of ti. In Table 7-2, we illustrate the effects of state dynamics. The life tables used parameters estimated from the 25-year follow-up of the Finnish East-West study in equations (5)-(9) (Pekkanen et al., 1992). If life tables are calculated with both fixed and =0.0, (assumption 1) there is a 32-33 percent upward bias in life expectancy. With only = 0.0 (assumption 2) the bias is 10-15 percent. The addition of time-varying covariates (assumption 3) reduces error to 0.4-0.6 percent.

The importance of time-varying covariates, and the effects of specific hazard functions on results, is now realized by epidemiologists. In Gordon et al. (1989), identification of the importance of HDL cholesterol in U.S., but not British, studies was traced to the use of different hazard models. Regression dilution is believed to have caused the effects of cholesterol on mortality to be underestimated (Cooper et al., 1992; Davis et al., 1990;

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

TABLE 7-2 Life Expectancy at Age 40 Under Alternative Assumptions About Risk Factor Dynamics in 25-Year Follow-up of Finnish East-West Study

 

Life Expectancy, e40 (years)

Assumption

East Finland

West Finland

Description

 

29.5

31.8

Life table

1

39.0

42.2

Risk estimated for baseline

 

(+32.2%)

(+32.7%)

risk factor measurements

2

32.5

36.6

Risk estimated from risk

 

(+10.1%)

(+14.9%)

factor means and variances/ covariances

3

29.6

32.0

Risk factor distribution

 

(+0.4%)

(+0.6%)

changes according to regression estimates

 

SOURCE: Data from Pekkanen et al. (1992).

Jacobs et al., 1992), emphasizing the need for multiple measurements to better identify their true level.

θ can be used to adjust for unobserved health differences between populations so that national mortality data that are unbiased, but uninformative about disease mechanisms, can be integrated with longitudinal select population data that may be biased for the national population being studied. Thus, the state-space model can reduce bias in integrating multiple survey and demographic data sources in cross-national studies (Dowd and Manton, 1990). Initial age- and sex-specific risk-factor conditions ( and ) can be estimated from cross-sectional survey data. From national vital statistics, the proportion of mortality for each of M causes can be determined. Because θ represents the average age-related effects of , it reflects unmeasured differences between sources of population data just as it adjusts for unobserved variable effects when different risk factors, or measurement intervals, are used.

Dependent risks can be identified using time-varying state variables measured before death (Tsiatis, 1975). Assessment of dependence suggests that prevention can, by changing xijt, affect other risk factors and several causes of death and thus affect health more than would a treatment that reduces mortality from a specific cause. The dependence of diseases does not have a large effect until mortality risks are high enough to deplete the

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

high-risk groups. Thus, dependence is important at late ages, when most deaths occur and the trajectory of mortality is uncertain. The existence of cause dependency and risk-factor interactions suggests that traditional cohort methods need strong assumptions to reconstruct mortality at late ages. Counts of deaths at late ages, by definition, are small and uncertain, and they reflect nonlinear state dynamics.

Although equation (1) is linear, its use in equations (5) through (9) can produce nonlinear effects, like sex-specific age changes of the means of hematocrit and the vital capacity index (VCI). In Figure 7-3a, the VCI means decline, as expected, until age 105. This pattern is due to the exponential increase of mortality with age which, by 95, is so large that risk-factor means for survivors () must approach . In Figure 7-3b, the hematocrit means for females remain lower, even postmenopausally, than male hematocrit means, which decline after reaching a peak (Sullivan, 1991).

Failure to understand risk-factor interactions and dynamics may be why prevention trials do not reduce mortality by the amount suggested in population studies. A logistic coefficient does not show how intervention changes other risk factors over time. In a state-space model, the dynamic equations describe how changes in risk factors interact over time. Indirect risk-factor effects may be positive or negative. Diuretic use in diabetics decreases blood pressure, but elevates cholesterol and blood glucose: one risk factor is reduced, but several increase. In postmenopausal women with osteoporosis and reduced estrogen, atherogenesis accelerates because increased cholesterol and calcium release into the blood, raises the calcification rate of arterial plaques (Moon et al., 1992). Treatment of osteoporosis with estrogens has beneficial effects on multiple risk factors and outcomes and may produce improvements larger than those measured in population studies (Stampfer et al., 1992).

Because of diffusion, the uncertainly of forecasts from state-space models is higher than is the uncertainty of forecasts from aggregate models. This difference can be represented in aggregate forecasts using empirical Bayes methods (see, for example, Manton et al., 1989). Uncertainty may be dealt with by imposing a utility function on the outcome distribution, discounting the costs of some and increasing costs of others. Confidence in a decision may increase when outcomes are weighted. For example, the answer to the question of whether shortfalls in Social Security trust funds are as important as, or more important than, excesses could reduce uncertainty about decisions on marginal tax rates.

Thus, to deal with cohort effects in medical demography, one needs both macrolevel compartment models represented by differential equations with parameters specified from biomedical data, or microlevel state-space models estimated from longitudinal data in which measurements of multiple risk factors are made. The procedures are complementary. Estimates from

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Figure 7-3 Variation in vital capacity index and hematocrit by age and sex.

SOURCE: Data are from the Framingham Heart Study.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

the one may be used to help specify and estimate the parameters of the other.

DISEASE STAGES, NATURAL HISTORY, AND THE LIFE-CYCLE

Because chronic diseases take a long time to develop, they cannot be treated as events. They must be modeled as processes, with characteristic (and lengthy) natural histories whose evolution interacts with the characteristics of the person suffering from the disease. Representing these effects by the age dependence of mortality presents problems because changes in the age dependence may not be recognized for several reasons: reliance on standard hazards like the Gompertz, analyses of the logarithm of rates—a transformation that hides significant deviations, and the use of statistically inefficient estimators (like ordinary least squares). Despite improvements in the quality of data for late ages, reliance on assumptions about the age trajectory of mortality is common. (See, for example, National Center for Health Statistics, 1987; Lee and Carter, 1992). Human mortality at advanced ages often deviates from the Gompertz (Bayo and Faber, 1985; Kestenbaum, 1992; Thatcher, 1992).3 Although human data are subject to age misreporting 4, that alone does not explain all deviations from a Gompertz. Making assumptions about the tail of the distribution of human ages at death is similar to designing experiments assuming that the Gompertz is valid, and making studies large enough to estimate Gompertz parameters but not large enough to test alternative models. Even if a Gompertz fits cohort data, it is not clear what to expect in cross-sectional data representing a changing mix of cohorts with different parameters (Manton et al., 1986).

Not all risks of chronic disease increase monotonically with age. Osteo-arthritis, for example, decreases after age 75 (Bagge et al., 1992); and if they survive to middle age, persons with familial high cholesterol appear to have normal survival. Furthermore, persons predisposed to a disease are selected out of the population or, if not selected out, have the disease controlled. As diseases are controlled, the age trajectory of mortality changes shape.

Medical demography is concerned not only with the lifetime distribution of health events, but also with their distribution within life stages, in

3  

Carey et al. (1992) and Curtsinger et al. (1992) show that the Gompertz did not describe mortality in large, controlled insect studies.

4  

In 1979, of 850 alleged centenarians traced in Great Britain, age was reported incorrectly for 2.5 percent (Thatcher, 1992).

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

which health is dominated by specific diseases. Disease models with differing time scales, and with more detail about the effects of age on mortality and risk-factor processes, are required to design interventions. Prevention or treatment may have larger effects if introduced before significant organ damage occurs (as they do in the case of osteoporosis, Overgaard et al., 1992), and renal function loss in diabetics (Chan et al., 1992). Diseases once limited to a certain life stage may become lifelong, with multiple recurrences, and require medical surveillance and intermittent treatment. Early-stage, premenopausal breast cancer, treated successfully, may recur 30 years later if the disease reflects immunological defects. Below we briefly review the characteristics of several chronic conditions or syndromes important in elderly populations.

Dementia

Diseases that are prevalent at late ages include Alzheimer's and related dementias. Alzheimer's has a long natural history, with death often due to comorbidity; in one study, 70 percent of deaths were due to pneumonia (Burns et al., 1990). Data from the Baltimore study of aging suggests that dementia cases, with good care, may live nearly normal life spans. Two difficulties in studying Alzheimer's disease are that its progression is indicated by slow changes on multiple cognitive dimensions and that it often coexists with other types of dementia.

Heart Disease

Heart disease progresses over time. Onset of the disease at early ages is often caused by genetic factors. Factors that affect heart disease between ages 30-50 may be quite different to those affecting the older population.5 Treatment is effective early in a heart attack. Besides improving function, coronary bypass surgery in patients over age 80 did much better than medical treatment in increasing 3-year survival: the ratios were 77.4 percent and 55.2 percent, respectively (Ko et al., 1992). As procedures have improved, the benefits of surgery have increased (Muhlbaier et al., 1992). If persons survive early heart disease, they may later develop chronic health failure

5  

For example, disease that affects those from 30-50 years old may be due to cardiac vasospasm resulting from catecholamine stimulation, aggravated by nicotine and carboxyhemoglobin from smoking, and producing cardiac arrhythmias—especially with arterial damage due to hypertension (Golino et al., 1991; Gutstein, 1988; Yeung et al., 1991). Later, atherosclerosis in those aged 50-75 produces myocardial ischemia, causing infarction. Hemostatic factors may lower the age of infarction by accelerating the development of thromboses at the sites of atheromas not yet occluding an artery.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

(CHF) and left ventricular hypertrophy (LVH) because of the interaction of reduced peripheral circulation, reduced cardiovascular efficiency, and hypertension (Kitzman and Edwards, 1990; Lakatta, 1985). The age-standardized U.S. hospitalization rate for CHF from 1973-1986 increased 60 percent (Ghali et al., 1990). Now both CHF and LVH are treatable using ACE-II inhibitors (SOLVD Investigators, 1991; Weber and Brilla, 1991).

The effect of cholesterol on CVD varies with age, especially for women (Jacobsen et al., 1992; Knapp et al., 1992). This variation may be due to a U-shaped relation of cholesterol to total mortality and to the fact that some premenopausal women have cholesterol low enough to raise other disease risks (see, for example, Neaton et al., 1992). Thus, when cholesterol rises postmenopausally for some women, risks could decline.6

Nutritionally Related Disorders: Systemic Factors

A newly appreciated aspect of chronic disease is the effect of nutrition on antenatal development. The data suggest that maternal malnutrition, which produces low birth and placental weight, affects the fetal development of multiple organs and that these effects become manifest above age 65 as chronic diseases (Barker, 1990; Barker and Martyn, 1992; Barker et al., 1989, 1991a,b, 1992a,b,c). Fetal physiology requires the brain to receive nutrition at the expense of other organs. The liver can be damaged, affecting fibrinogen and other hemostatic factors and increasing CVD risk (Barker et al., 1992a; Barker and Martyn, 1992). Lung and pancreatic function can be impaired, so that chronic lung disease and adult-onset diabetes mellitus appear.

The effects of antenatal nutrition on chronic disease may explain long-term changes in the risks of chronic disease. Despite literature suggesting that chronic diseases are consequences of industrialized society (Dubos, 1965; Omran, 1971), declines of some of those diseases started long before major prevention efforts. Antihypertensive therapy was first introduced in the 1950s, and a national program did not begin until 1972-1973. Yet, U.S. mortality from stroke declined after 1900—41.7 percent from 1900-1948, for example. An analysis of diagnostic practices and coding on death certificates suggests that declines were real by 1925 (Lanska and Mi, 1993).

6  

Frank et al. (1992) found that reducing cholesterol below 200 milligrams per deciliter increased mortality for 60 percent of the population—a proportion varying by sex and by age: it was smaller at 30 and higher at 75. The relation of low cholesterol to mortality from several diseases (Frank et al., 1992; Jacobs et al., 1992; Neaton et al., 1992) may explain why cholesterol has little relation to CVD risks for woman at late ages and why their optimal values are higher (220 mg/dl) than those for men (177 mg/dl; Manton et al., 1993c).

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Research by Fogel at the University of Chicago shows that chronic disease rates were higher for Civil War veterans aged 65 in 1910 than for veterans over age 65 in the 1985-1988 NHIS. The decline per decade in chronic disease was 6 percent over the 75 years—a decline that correlated with changes in body mass and stature. Heart disease was 2.9 times more common in the 1910 cohort of veterans than it was for veterans in 1985-1988. This work, for which Fogel won the 1993 Nobel Prize in economics, is consistent with the antenatal nutrition model.

Micronutrients may have long-term effects on disease. Zinc governs birth weight, and males are susceptible to gestational zinc deficiency (Andrews, 1992; Hales et al., 1991). Zinc deficiency affects both adult-onset diabetes mellitus and schizophrenia, diseases whose incidence is correlated. Recently, it was recommended that women of child-bearing age take folic acid supplements because deficiency early in fetal development is responsible for 60 percent of birth defects of the neural tube—spina bifida, for example, Vitamin B and other deficiencies may be related to late-age dementia (Zaman et al., 1992; Martin et al., 1992). Thus, there is a linkage of health in the antenatal and later life stages due to deprivation of both macro- and micro-nutrients at childbearing ages. If maternal nutrition varies over cohorts (and, within cohorts, by socioeconomic status at childbearing ages), then those effects must be distinguished from genetic factors. What look like genetic effects could be the effects of low socioeconomic and cultural status that persist in families from one generation to another.

Immunologically Related Diseases: Interactions of Viral and Nutritional Factors

Nutrition affects the immune system. Some chronic diseases, are due to early viral infections; for example, cytomegalia virus is implicated in CVD (Mozar et al., 1990). Viruses may trigger autoimmune diseases (like rheumatoid arthritis and systemic lupus erthymatosis). Some of these diseases may moderate with age. Other diseases like humoral autoimmunity (i.e., the prevalence of antinuclear antibodies) or multiple myeloma (a form of cancer) may increase with age (Beregi et al., 1991). Nutritional supplements may be important in changing immunological responses with age. For example, age-related loss of gastric immunity is reversed by supplementation with vitamins A, C, and E (Penn et al., 1991a,b).7 Other examples include recent studies showing significant effects, starting after 1 or

7  

In noninstitutionalized healthy persons aged 66-86, those receiving balanced supplements of vitamins and minerals had improved immune function and fewer days with illnesses due to infection than controls (23 versus 48 days; Chandra, 1992).

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

2 years, of antioxidant supplements—beta carotene, vitamin E, and selenium—on total, cancer, and stroke mortality (Blot et al., 1993).

Nutritional and other types of supplementation for the elderly is complex because of the need to maintain homeostasis. CVD is reduced by estrogen replacement, a result correlated with improvement in status on multiple risk factors (Nabulsi et al., 1993). However, when that therapy is combined with vitamin D, lean women showed no improvement in cholesterol (Mysrup et al., 1992). Hypercalcemia, produced by vitamin D, raised CVD risk without an increase in cholesterol (Moon et al., 1992). Thus, though nutritional and hormonal supplementation are important at late ages, its parameters, and their linkage, are not yet clear. Furthermore, the most biologically active form of many micronutrients is not known.8 Consequently, trials of nutritional interventions must rely heavily on laboratory data (Prasad and Edwards-Prasad, 1992).

Multiple Diseases, Host Factors, and Their Interactions at Late Ages

Analysis of age differences in disease and risk-factor processes requires biologically detailed models in which failure is multidimensional, each dimension potentially having its own time scale. A state-space model has this capability if a θ is assumed for each disease. For breast cancer and Alzheimer's disease, one must identify early and late disease with different etiologies, genetic determinants, and rates of progression. In Manton et al. (1993c) the quadratic estimated from all deaths behaved differently from a quadratic that was the sum of three disease-specific functions (with a single θ). Time functions can differ by disease: the quadratic for cancer could be estimated with a Weibull—not a Gompertz. M causes, with different θs, can be summed if the causes are disjoint (Manton and Stallard, 1988).

Some life-cycle effects, if explains much of the variation associated with θ, can be represented in equation (1). For example, adult-onset DM lowers the age at death for multiple conditions (Goldstein et al., 1978; Jones, 1956). So, DM could be expressed as a rapid increase of blood glucose (and its variance) with age in (1), which increases mortality by raising risk-factor levels in (2). For persons treated for DM, a person's variability of blood glucose is an important measure of risk—even, possibly, for dementia (Sachon et al., 1992).

Exogenous factors, whose effects vary with age, may be used to link health and socioeconomic factors. The adverse effect of low income on health may be represented by the effect of on risk factors. If health

8  

An isomer of vitamin E, α tocopherol succinate, is active as an anti-oxidant and a redifferentiating agent (Prasad and Edwards-Prasad, 1992); other isomers of vitamin E are not.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

affects retirement, then retirement could be both an outcome and a cause of a change in health. Thus, a state-space model can represent exogenous inputs influencing health and nonlinear risk-factor processes.

Life-cycle effects differ by sex and race. Fertility may affect mortality from chronic diseases, like CVD and breast cancer (Beral, 1985; MacMahon, 1973). Postmenopausally, lower estrogen levels lead to female osteoporosis and atherosclerosis. African-Americans have elevated risks of hypertension and of renal failure, which peak in late mid-life (Walker et al., 1992; Brancati et al., 1992).9

DISABILITY AND MORTALITY

Disability is a complex phenomenon that manifests itself in many ways and that evolves over a long time. Thus, the definition of disability is subject to measurement and conceptual difficulties. But the attempt to measure disability is important because, given its relation to Medicare use and costs, and to morbidity and mortality, disability has strong predictive validity (Manton et al., 1993c). Moreover, functional impairment is important because of its prevalence at late ages and its association with decreased autonomy and increased demand for long-term care (LTC). One measure of functioning is the number of years one can expect to live free of disability, that is Active Life Expectancy (ALE) (Katz et al., 1983). ALE can be calculated from single- or multiple-decrement life tables and from cross-sectional or longitudinal surveys (Sullivan, 1971; Crimmins et al., 1989; Rogers et al., 1989; Manton and Stallard, 1991).

The assessment of the population impact of disability needs refinement. In most studies, a discrete threshold for disability, constant across age, is used to define the ''impaired" population as those who require help in the activities of daily living (ADLs)—dressing, bathing, eating, and so on; or instrumental activities of daily living (IADLs) (Lawton and Brody, 1969). A "threshold" model of disability has two limitations. First, there will be people who are close to the threshold, but above or below it. They will

9  

End-stage renal disease (ESRD) may be reduced in African-Americans (and in whites as well) by better control of hypertension, blood glucose, and use of ACE-II inhibitors. Treatments changed between 1977 and 1987, when the peak incidence of ESRD changed from the fourth to fifth decade of life (Qualheim et al., 1991). African-American women have elevated DM risks, so that mortality increases in middle and late middle age. The age trajectory of cholesterol differs for African-American and white females (Knapp et al., 1992). The CVD risk of African-Americans, and possibly Hispanics, may be reduced by lowering sun-induced production of calciferol (Moon et al., 1992), or by lowering serum Lp(a) in Hispanics (this is a lipoprotein stabilizing thromboses; Haffner et al., 1992). Hispanics have lower CHD risk despite having more obesity, and DM, higher waist-hip ratios, and greater insulin resistance.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

have higher misclassification rates than do persons with no disability or with severe disability. Depending on where the threshold is set, large proportions of persons may be misclassified if the time derivative of the age distribution of disability is large. Second, the oldest-old will have a high prevalence of partial disability, though only a small proportion may be severely disabled: some disability, after all, is due to treatable or preventable conditions (Marx et al., 1992; Taylor, 1993).10

To deal with measurement error, and with different types and intensities of disability, multivariate procedures can be used to estimate scores for disability dimensions affecting persons at different ages due to different diseases. When multiple discrete measures of disability are projected onto a multidimensional "fuzzy" state space (Manton and Stallard, 1991), if, say, one of 27 disability items is miscoded, an individual's score changes incrementally: he does not jump from a disabled to a nondisabled state. Scores more precisely assess the type and intensity of disability (see Maddox and Clark, 1992). And, they better describe covariate effects; for example, disability for a fixed level of physical disease may be negatively correlated with education as in the case of osteoarthritis (Hannan et al., 1992). Scores may better describe short episodes of disability and improvements in functional status for individuals. With scores, changes in the intensity of disability can be described in autoregressive functions like equation (1).

Scores (properly scaled) can be used to partition life expectancy into components specific to disability type. By representing within-class heterogeneity they behave better stochastically because diffusion, though bounded, is continuous. In the NLTCS, scores were calculated from 10 ADL, 8 IADL, and 9 physical performance items (like difficulty in climbing stairs and in holding a 10-pound package). We estimated male and female life tables (for the 1982-1989 NLTCS and mortality for 1982-1991) for seven dimensions identified from the 27 items for models in which a person is a member of one class (a discrete-state model) or has partial membership in multiple classes (a fuzzy-state model). A discrete-state model was implemented by fixing the covariance matrix in equations (6) and (8) at 0.0. Doing so yields a homogeneous population process comparable to the heterogeneous population process modeled in equations (5) through (9) except for the effects of altering the covariances. Alternatively, a Markov transition model could be constructed by classifying individuals into the state in which they had the highest disability score. Since that model does not use equations (5) through (9), differences in outcomes are confounded with differences in model structure.

In Table 7-3 we combined the seven dimensions, into four groups.

10  

One example is impairment due to cataracts, which costs Medicare $3.2 billion per year.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Although life expectancy at 65 is similar if not identical for the two models, survival declines less rapidly for the discrete-state model for both sexes to age 75. The prevalence of disability increases faster in the discrete-state model because, with only between-class heterogeneity, mortality increases only when a person "jumps" to a more disabled state. In the fuzzy-state model there is within-class heterogeneity that mortality selects against; that is, as a person's scores on severely disabled dimensions increase with age, interactions for the pair wise (but partial) occupancy of states allows mortality to increase continuously with age. In the discrete-state model, mortality is downwardly biased until sufficient proportions move into states with high mortality. The discrete-state model generated increases in the proportion in severely impaired and institutional groups inconsistent with the 1984-1986 Longitudinal Study of Aging (LSOA).11

The age trajectories for the two models are shown in Figure 7-4 for the least and the most impaired classes. The two discrete-state trajectories for males converge faster than the fuzzy-state trajectories starting at age 75. For females, convergence is also faster in the discrete-state model, though it occurs later. The slower covergence for males is consistent with their shorter survival time at any disability level and age. For both sexes, the age-specific prevalences of low and high disability cross over in the discrete-state model. Fuzzy-state trajectories do not. The fuzzy-state model illustrates the effects of interactions of nonlinear age increases in mortality and linear disability dynamics produced in equations (5) through (9). With age, the "average" health of the population approaches stable points in a convex state space because of the moving equilibria of prevalence on multiple disability dimensions and increases in states with high mortality. The equilibria models, like extreme-value hazard models, represent isomorphisms between the statistical mechanics of population health and the kinetics of aging for individuals. Thus, the "strange attractor" (nonlinear change) behavior observed at late ages is due to failure mechanisms becoming more complex with age. At early ages, death is often due to the catastrophic failure of one system. At late ages, it reflects the overwhelming of homeostasis by the accumulation of loss of function in multiple organs. This is why the age trajectory of functional loss predicts mortality well.

Analyses of the NLTCS indicate that the prevalence of disability de-

11  

In that study 33 percent of persons aged 80 and older are physically robust, that is, they have no difficulty on five physical tasks; 49 percent have no difficulty walking a quarter of a mile; 57 percent have no difficulty climbing a flight of stairs (Suzman et al., 1992). Branch and Ku (1989) followed persons aged 85+ for 15 months and found that 55 percent were ADL independent as were almost 50 percent of 160 centenarians followed for 8 years in Shanghai (Zheng et al., 1993).

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

TABLE 7-3 Cohort Life Tables and Disability Scores for Males and Females, With and Without Heterogeneity Within Classes Eliminated; Estimates for Persons Reaching Age 65 in Mid-1980s

 

 

 

 

Percent of Life Expectancy at Age t in Class

Age t

Model Typea

Proportion Age t, lt(%) Surviving to

Life Expectancy at Age t, et (years)

Little Impairment; No Physical and Mild or no Cognitive Disability

Moderate Physical Impairment:

Heavy Physical Impairment

Extreme Impairment Moderate ADL, Frail, and Institutionalized

Males

 

 

 

 

 

 

 

65

Fuzzy state

100.0

15.6

96.3

0.7

0.6

2.4

 

Discrete state

100.0

15.4

93.3

0.7

0.6

2.4

75

Fuzzy state

69.2

10.3

94.0

0.8

1.0

4.3

 

Discrete state

69.7

9.8

92.1

1.0

1.3

5.7

85

Fuzzy state

33.0

6.1

84.7

1.3

2.4

11.6

 

Discrete state

32.5

5.3

73.9

2.0

3.7

20.5

95

Fuzzy state

6.3

3.4

70.1

1.6

5.3

23.0

 

Discrete state

4.0

2.3

34.6

2.8

8.6

54.0

105

Fuzzy state

0.3

2.4

72.0

0.2

3.5

24.3

 

Discrete state

0.0

1.1

11.3

0.9

4.9

82.8

Females

 

 

 

 

 

 

 

65

Fuzzy state

100.0

20.9

95.6

1.0

0.7

2.7

 

Discrete state

100.0

20.9

95.6

1.0

0.7

2.7

75

Fuzzy state

82.6

14.1

91.8

1.3

1.2

5.7

 

Discrete state

83.3

14.0

90.1

1.6

1.4

6.8

85

Fuzzy state

55.2

8.5

76.6

2.2

2.8

18.5

 

Discrete state

56.7

8.0

67.9

3.2

3.5

25.4

95

Fuzzy state

19.5

5.0

57.4

1.9

5.0

35.7

 

Discrete state

18.7

4.0

29.4

3.3

6.1

91.3

105

Fuzzy state

2.5

3.8

58.1

1.1

5.0

35.8

 

Discrete state

1.1

2.3

8.8

1.6

3.7

85.9

a In the fuzzy state model, an individual can belong to more than one class.

SOURCE: Data are from the 1982, 1984, and 1989 National Long-Term Care Surveys.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×
Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Figure 7-4 Comparing discrete to fuzzy-state models. SOURCE: Data are from the 1982, 1984, and 1989 National Long-Term Care Surveys.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

TABLE 7-4 The 1982, 1984, and 1989 Prevalence of Chronic Disability in the U.S. Population Age 65 and Over Estimated from the 1982, 1984, and 1989 National Long-Term Care Surveys

 

Population (thousands) with Percentages and SE

Differences (%) with SE and t Test

Disability Level

1982

1984

1989

1984-1989

1982-1989

1982-1989, Age Standardized

Nondisabled

20,548

21,403

23,906

1.1

1.1

1.7

 

76.3(±0.30)

76.3(±0.29)

77.4(±0.30)

(±0.42;t=2.6)

(±0.42;t=2.6)

(±0.42;t=4.1)

IADLs only

1,434

1,590

1,360

-1.3

-0.9

-1.4

 

5.3(±0.16)

5.7(±0.16)

4.4(±0.14)

(±0.21;t=6.2)

(±0.21;t=4.3)

(±0.21;t=6.7)

1-2 ADLs

1,740

1,831

1,993

0.0

0.0

-1.2

 

6.5(±0.17)

6.5(±0.17)

6.5(±0.17)

(±0.24;t=0.0)

(±0.24;t=0.0)

(±0.24;t=-5.0)

3-4 ADLs

732

797

1,079

0.7

0.8

0.7

 

2.7(±0.11)

2.8(±0.11)

3.5(±0.13)

(±0.17;t=4.1)

(±0.17;t=4.2)

(±0. 7;t=4.2)

5-6 ADLs

937

882

848

-0.4

-0.8

-0.9

 

3.5(±0.13)

3.1(±0.12)

2.7(±0.11)

(±0.16;t=2.5)

(±0.17;t=4.7)

(±0.172;t=5.3)

Institutional

1,532

1,538

1,685

0.0

-0.2

-0.4

 

5.7(±0.16)

5.5(±0.16)

5.5(±0.16)

(±0.23;t=0.0)

(±0.23;t=0.9)

(±0.23;t=-1.7)

Total Population

26,924

28,042

30,871

 

NOTE: SE = standard error.

SOURCE: Data are from the 1982, 1984, and 1989 National Long-Term Care Surveys.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

creased from 1982-1989 (Manton et al., 1993a). In Table 7-4 are estimates of prevalence in 1982, 1984, and 1989 for six groups: (1) not disabled; (2) disabled only for IADLs; (3) disabled on 1 or 2 ADLs; (4) disabled on 3 of 4 ADLs; (5) disabled on 5 or 6 ADLs; and (6) institutionalized. The 1.1 percent increase in the proportion of nondisabled from 1982 to 1989 is significant. It represents a 4.7 percent relative decline in the prevalence of disability. Because the U.S. elderly population grew 14.7 percent between 1982 and 1989, and also became older, the age-standardized rate of disability declined 1.7 percent; the age-and sex-standardized rate declined 2.8 percent. Reductions in the incidence of disability were large at late ages—even adjusted for mortality. At age 85 the mortality-adjusted likelihood of becoming disabled in 5 years declined 23.2 percent between 1982-1984 and 1984-1989 (Manton et al., 1993a).

The prevalences in Table 7-4 require no assumptions about between-surveys transitions or calculations of scores. The validity of these declines may be examined by comparing them with covariates with known trends. They are consistent with declines in population-weighted proxy response rates (indicative of severe impairment) from 19.8 percent (1982) to 17.6 percent (1989). Because the use of a proxy is determined before an interview, rates are unlikely to be affected by the reassessment of an individual. The use solely of equipment to cope with disability increased both absolutely and relatively from 1982 to 1989—suggesting a reduction in disability and an increase in social autonomy within the disabled population (Manton et al., 1993b). The use of equipment with personal assistance increased. Only the use of personal assistance by itself declined. Thus, decreases in informal care due to higher participation by women in the labor force and to smaller family size may be compensated for by use of equipment.

The 1982, 1984, and 1989 NLTCS and the 1982-1991 Medicare mortality data were used to construct cohort life tables based on disability scores. Cohort life expectancy at age 65 was 15.6 years for males and 20.9 years for females in 1989—increases from 14.2 years and 18.6 years, respectively, in 1982-1984. These life expectancies are projected to be achieved in 1993 for males and by 2010 for females in Census mid-range projections (Day, 1993), and in the low-mortality variant for females by 2003. Thus, the male values are conservative. The age trajectories of the seven disability dimensions, with mortality effects removed, are shown in Figure 7-5 by sex for 1982-1984 and 1982-1989. Before comparing results, we first note procedural differences. The results are based on changes in disability between 1982 and 1984 surveys and mortality between 1982-1986. The 1982-1989 analysis had to deal with different follow-up intervals (2 versus 5 years). This difference was handled by assuming that scores estimated for a survey are constant over the follow-up interval. While this practice permits estimates to be made on a monthly basis, with equal intervals, a strong

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Figure 7-5 Female distributions of seven disability types produced from state-space models. SOURCE: Data are from the 1982, 1984, and 1989 National Long-Term Care Surveys.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

mortality gradient makes the imputed population appear healthier at late ages. However, estimating mortality coefficients with the imputed monthly data to remove survival bias yields accurate life tables. Bias in health scores is less of a problem if it is recognized that the scores describe a mixture of the current state of the population, and the state at a previous survey date (an average of 1 or 2 1/2 years earlier). Thus, changes in Figure 7-5 reflect the effects of improvements from 1982 to 1989 (Table 7-4) and the use of imputed monthly data. We investigated several methods for imputing monthly disability data using other dynamic assumptions and found that the results were similar (Manton et al., 1994b). Estimates of disability for 1982-1989 increase less rapidly with age than do those for 1982-1984—similar to the slowing of mortality age increases in Carey et al. (1992) and Curtsinger et al. (1992). This finding may reflect diseases associated with different life stages. Disabling conditions have peak effects at different ages; for example, DM peaks before 65 to 70; osteoarthritis before 75; and Alzheimer's disease before 90. For DM, this pattern is related to a lower life expectancy; for osteoarthritis, it may be due to the trajectory of the disease process; for Alzheimer's, the cause may be the exhaustion of susceptible persons.

In analyses of the Longitudinal Study of Aging, education was significantly related to robustness. Persons with 9 or more years of education had 2.1 to 2.4 times the likelihood of remaining robust than persons with 6 or fewer years had. Thus, declines in disability are consistent with cohort changes in education in Table 7-5. Above age 85, life expectancy and active life expectancy increased for the group with low education (8 or fewer years). Life expectancy for males in this group increased a year while active life expectancy increased 1.9 years—nearly twice as fast. Life expectancy for better-educated males increased a year; active life expectancy 0.4 year. Life expectancy and active life expectancy were absolutely higher in high-education groups (4.8 versus 7.3 years) in 1982-1989. Females manifest similar patterns. Overall life expectancy and active life expectancy increased for women more than for men for each education group because of the rapid growth of high-education groups above 85. Between 1980 and 2015 the proportion of persons 85 to 89 with 8 or fewer years of education is projected to decline significantly (Preston, 1992). Consequently, because education and function are associated, active life expectancy is expected to improve (Maddox and Clark, 1992; Suzman et al., 1992).12

12  

The changes in the education of cohorts 85-89 may be compared with projections made by Preston (1992) using 1980 census data and education-specific mortality for 1960 (Kitagawa and Hauser, 1973). For 1980, Preston estimated that 54.7 percent of females aged 85-89 had 8 or fewer years of education compared with our 1982 estimate of 59.3 percent. Our 1989 estimate is 48.6 percent. Preston's 1990 estimate is 44.0 percent. Thus, our estimates for females with low education are 4 percentage points higher than Preston's. Our decline from 1982-1989 (10.7 percent) is identical to his 1980-1990 decline. Thus, agreement is good, given that his projections use education-specific mortality ratios from 1960 (that is, pre-Medicare). Our decline for low-education males 85 and older is 18.9 percent, 1982-1989, compared with Preston's projection of 8.7 percent. His projections for males did not use education-specific survival, possibly explaining the difference.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Our model can be compared with disability data weighted by time of exposure. Figure 7-6 presents observed data (including imputed monthly data) and model-generated age trajectories for the least disabled for 1982-1989. The model fits the data well: there is little trend in the residuals for either sex. For both sexes, there is a flattening, and then a slight increase, for the least disabled at late ages. One source of this pattern is suggested by the trajectories for the most disabled community residents (Figure 7-7). The prevalence of the most disabled class declines above age 95, similar to risk-factor dynamics: the force of mortality is so high for the oldest old in this group that they cannot survive ill for very long.

Figure 7-8 plots sex-specific age trajectories for the least disabled group, as observed and as modeled, for each survey year. To smooth these data we plotted scores averaged over ages t to 105:

At 65, we plot the average score for 65 to 105; then the average for ages 67 to 105, and so on. The trajectory of model-generated scores for the least disabled fits the data well. In Figures 7-9 and 7-10 we plot the trajectories for the least and most disabled using smoothed data for males and females. The data and the model results are similar. In both, severe disability declines at late ages. These results, unlike the prevalences reported in Table 7-4, depend on model assumptions. The scores are more reliable because they are a weighted average of multiple functional items. Figure 7-5 can be compared with the results of a model in which groups are defined by IADL-only disability, 1 to 2 ADLs, 3 to 4 ADLs, 5 to 6 ADLs (physical performance is not represented). The 5-year transition matrix for persons age 65 is given in Table 7-6. The extrapolation of these transitions (by multiplying the four transition matrices for persons age 65, 70, 75, and 80) produces the distribution in Table 7-7. The proportion remaining nondisabled is, adjusting for mortality, 58 percent—close to the value for the least disabled at age 85 depicted in Figure 7-5. Thus, discrete-state changes are similar to score trajectories for times and ages where a comparison is possible.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

TABLE 7-5 Life Expectancy and Active Life Expectancy for Males and Females 1982-1984 and 1982-1989 at Age 85; Total and Stratified by Education

 

Males

Females

Period

Percentage of Life Years Expected to be Lived at a Given Education Level

Life Expectancy (years)

ALE (years)

Proportion of Life Active (%)

Percentage of Life Years Expected to Be Lived at a Given Education Level

Life Expectancy (years)

ALE (years)

Proportion of Life Active (%)

Total

 

 

 

 

 

 

 

 

1982-1984

5.0

3.1

61.8

6.3

3.1

49.6

1982-1989

6.1

4.4

72.5

8.5

5.5

64.3

Change

+1.1

+1.3

 

+2.2

+1.4

 

Low educationa

 

 

 

 

 

 

 

 

1982-1984

64.7

3.8

1.2

30.8

81.7

4.6

0.9

19.6

1982-1989

40.8

4.8

3.5

72.9

62.5

5.6

3.6

64.2

Change

-23.9

+1.0

+1.9

 

-19.2

+1.0

+2.7

 

High educationb

 

 

 

 

 

 

 

 

1982-1984

35.5

6.3

5.0

79.1

18.3

9.3

6.4

68.7

1982-1989

59.2

7.3

5.4

74.0

37.5

10.3

6.7

70.9

Change

+23.9

+1.0

+0.4

 

+19.2

+1.0

+0.3

 

a Eight years or less of education.

b Nine years or more of education.

SOURCE: Data are from the 1982, 1984, and 1989 National Long-Term Care Surveys.

GENETICS

Models and Methods

The effects of genetics on longevity are complex. Models in which a single gene controls biological senescence are obsolete. Genetic influences are polygenic, and the expression of genetically determined traits depends on environment. To estimate the effects of genetics on population health

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

one must posit a model of these effects and compare the actual to the theoretical distribution of events. Such model-based integration of data, and indirect inference, is often used in medical demography. Often, problems involving latent variables must be dealt with in genetic models: some are time-constant effects such as fixed genetic factors, and some are time-variable effects. Though the terminology changes with the topic being addressed, the mathematics and statistics are similar (for example, the assumption of local independence, Suppes and Zanotti, 1981; or the missing-

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Figure 7-6 Comparing observed monthly mean scores to state-space model, predictions for the category ''healthy" using combined survey data. SOURCE: Data are from the 1982, 1984, and 1989 National Long-Term Care Surveys.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Figure 7-7 Comparing observed monthly mean scores to state-space model, predictions for the category "frail" using combined survey data. SOURCE: Data are from the 1982, 1984, and 1989 National Long-Term Care Surveys.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Figure 7-8 Comparisons of the observed smoothed mean monthly scores for the category "healthy," in the three surveys to the predicted smoothed scores in the state-space model. SOURCE: Data are from the 1982, 1984, and 1989 National Long-Term Care Surveys.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Figure 7-9 Comparing the smoothed mean monthly scores for the category "healthy" from the three surveys combined to the values predicted by the state-space model. SOURCE: Data are from the 1982, 1984, and 1989 National Long-Term Care Surveys.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Figure 7-10 Comparing the smoothed mean monthly scores to the state-space model prediction for the category "frail" for all three surveys combined. SOURCE: Data are from the 1982, 1984, and 1989 National Long-Term Care Surveys.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

TABLE 7-6 Five-Year Transition Probabilities from Age 65-70 Estimated from the 1984 to 1989 NLTCS, With and Without Mortality Adjustments

Status at Age

Status Age 70 in 1989

65 in 1984

Nondisabled

IADL Only

1-2 ADLs

3-4 ADLs

5-6 ADLs

Institutional

Dead

Nondisabled +age-ins

.800

.026

.032

.012

.011

.009

.111

(excluding dead)

.900

.029

.036

.014

.012

.010

IADL only

.228

.158

.220

.049

.031

.043

.272

(excluding dead)

.314

.217

.302

.067

.042

.059

1-2 ADLs

.147

.074

.250

.136

.050

.073

.270

(excluding dead)

.202

.101

.343

.187

.069

.100

3-4 ADLs

.015

.042

.200

.199

.154

.050

.339

(excluding dead)

.023

.063

.303

.301

.234

.076

5-6 ADLs

.038

.019

.082

.089

.156

.096

.520

(excluding dead)

.079

.040

.171

.185

.325

.200

Institutional

.000

.019

.011

.012

.012

.553

.393

(excluding dead)

.000

.031

.018

.019

.020

.912

 

SOURCE: Data are from the 1984 and 1989 National Long-Term Care Surveys.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

TABLE 7-7 Twenty-Year Transition Probabilities for Age 65-85 Estimated from the 1984 to 1989 NLTCS, With and Without Mortality Adjustments

 

Status at Age 85

Status at Age 65

Nondisabled

IADL Only

1-2 ADLs

3-4 ADLs

5-6 ADLs

Institutional

Dead

Nondisabled +age-ins

.218

.024

.041

.025

.019

.047

.626

(excluding dead)

.583

.063

.110

.066

.050

.127

IADL only

.088

.012

.026

.018

.013

.035

.808

(excluding dead)

.456

.065

.134

.092

.069

.184

1-2 ADLs

.063

.010

.023

.016

.012

.034

.841

(excluding dead)

.397

.064

.142

.104

.077

.217

3-4 ADLs

.025

.006

.016

.013

.010

.028

.901

(excluding dead)

.253

.063

.166

.134

.100

.285

5-6 ADLs

.021

.004

.011

.008

.006

.020

.930

(excluding dead)

.296

.060

.151

.116

.089

.289

Institutional

.006

.002

.007

.004

.003

.030

.947

(excluding dead)

.114

.038

.125

.081

.066

.577

 

SOURCE: Data are from the 1984 and 1989 National Long-Term Care Surveys. Estimates are the results of multiplying the 5-year transition matrices for ages 65 (see Table 7-6), 70, 75, and 80.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

information principle; Orchard and Woodbury, 1971). A combination of models from the two areas could be beneficial. One possibility would be to combine analyses of the genetic control of aging with stochastic-process models using fuzzy-state mapping of discrete traits to allow evaluation of high-dimensional discrete spaces, and their mapping to nonstationary stochastic processes, without Gaussian assumptions.

Weiss (1990) reviewed standard approaches for analyzing the genetics of chronic diseases. One method assumes that phenotype is controlled by the additive effects of a gene locus (G), a component representing all other genetic determinants (PG), and environment (E). The distribution is

(See, for example, Elston, 1981, 1986). This does not produce a one-to-one mapping of genotype and phenotype. The population is composed of subsets of individuals for each genotype with mean µg and variance (spg2 + se2). The presence of a gene locus produces a nonnormal distribution. This model can be fitted to family disease pedigrees with µ's and s's estimated by maximum likelihood to identify genetic effects. A limitation of the model is the effect of individual differences in exposures. Exposure effects can be assumed to be normally distributed if independently generated. This assumption fails if there are interactions between genotype and environment (G x E). These may be studied in experiments using animal models with well-characterized genetic traits (for example, Curtsinger et al., 1992) or in human studies of identical twins (a natural experiment in which genetic endowment is identical but must be contrasted with same-sex fraternal twins to control for environmental variation). Effects, however, are not identifiable in this case unless the gene loci are identified.

Thus, identifying the genetic effects on health can require multiple data sets, such as laboratory analyses identifying genes, family history, or data on identical twins. The problems are more complex when one gene affects multiple phenotypes, that is, pleiotropy. For example, the genetic control of an enzyme, 5 alpha reductase, which converts testosterone into dihydrotestosterone, affects the risk of both baldness and prostate cancer. The correlation of trait expression can be used to analyze how a gene of interest is related to genes whose location on o chromosome is known (Ott, 1985). Modifications of the Elston-Shinant algorithm can represent covariates in these relations. A model based on the correlation of continuously distributed risk factors between a random pair of relatives and its effect on the probability of being affected by a risk factor, modeled as a logistic, is less

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

computationally burdensome (Hopper and Carlin, 1992). A moderately frequent appearance of a disease in a family over time may imply strong familial risk factors.

Hazard functions are often nuisance parameters in genetic epidemiology. In medical demography the age dependence of health events is often a primary concern, for example, the rectangularization of the survival curve, the compression of morbidity, and the plasticity of aging. Weiss (1990) suggests that, to analyze age effects, one must relate genotype to disease risk by defining a hazard with the distribution of risk factors conditional on genotype modeled as a separate factor, or,

This mixed hazard can be related to multivariate trait selection. A gap exists between population models of multiple quantitative traits and identification of classical Mendelian genes (Hartl and Clark, 1989). Random genetic drift has been represented by differential equations (Kimura, 1955). An approximation (assuming Markovity) uses a diffusion process to obtain φ(x,t), the distribution of x alleles at t. Phenotype and genotype are assumed to be Gaussian distributed with selection of one phenotype over another altering φ's moments. If zn is the phenotypic value of the nth trait, the vector of traits is

where are genetic differences for N traits and are environmental effects. If , , and are covariance matrices for , , and , then the fitness (probability of survival) is,

The mean phenotype after selection (environmental effect mean is assumed 0.0) is,

where g(x) is the distribution of genetic effects and () is the mean fitness of genotype . The change in the mean genotype is

Applying the del(∇) operator to the mean fitness function produces a gradient,

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

where is the vector of selection differentials,

or,

In (20a), are average phenotypic changes, are selection differentials, and is the fraction of phenotypic variation that is additive genetic variance. Changes in for "weak" selection are

where (see equation 18) (Hartl and Clark, 1989). To relate this to the state-space model, we substitute equation (3) into equation (6):

where corresponds to , is a quadratic matrix (as is ); and x0t - is the vector of deviations from optimal values (corresponding to ). Thus, the diffusion model of quantitative traits with selection for fitness is related to the state-space model—except the force of selection in the state-space model has a specific form (quadratic); and deterministic and stochastic age-variable components of change in phenotypic variation are explicit. In equation (1), fixed components represent variation. Time-varying components generalize to where time dependency is multivariate. The state-space model allows to vary with time; that is, the age variation of genotypic risk is a mix of risk-factor-specific hazards, multiplied by the probability of having a given risk-factor value, given a genetic factor (g). In the state-space model, Prob in (13) is replaced by a multivariate process for , with genetic variance represented by fixed effects (for example, ). The interaction of G with E is represented by exogenous processes, and interactions with fixed effects. The identifiability of components of the state-space model depends on the length of follow-up and measurement density. In the hazard model, in addition to risk conditional on , θ represents the average age effects of unobserved factors on with µ0t(=µ0 · eθt) representing senescence. Genetic effects are represented by the dependence of mortality on or in the dynamics, for example, for a one-step forecast, t to t+l,

The interaction of dynamics and mortality leads to multistep forecast equations like (5) through (9).

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
×

Examples of Genetic Analysis in Studying Chronic Disease and Aging

As indicated above, the effects of genetic differences are not directly observed in human populations but must be inferred. Examples of genetic analysis in studying chronic disease and aging are Knudson's (1971) work on the effects of genes on the cancer retinoblastoma; other researchers have shown that the risk of early breast cancer is strongly related to family pedigree: (the relative risk is 50 to 1 for a woman whose mother and a sister have had early breast cancer); but late-onset breast cancer bears no strong relation to family history (Lynch and Watson, 1990; Mettlin et al., 1990; Roseman et al., 1990).

Genetic analyses are often not adjusted for cohort, or heterogeneity, effects. Failure to recognize cohort trends can produce biased estimates— and compromise genetic inferences. For example, U.S. lung cancer mortality has been increasing over birth cohorts, which makes cross-sectional estimates of m too large.

Experimental studies can identify genetic factors. For example, Farrar et al.'s (1990) work on the effect of aluminum on Alzheimer's risk suggests that a genetic defect in the blood-brain barrier allowed, experimentally, gallium (an element chemically similar to aluminum) transfer in both Down's and Alzheimer's patients. Head injuries, another Alzheimer's risk factor, might also damage the blood-brain barrier (Graves et al., 1990).

Genetic heterogeneity at ages 90 or 100 and more is not much different from that for persons, say, age 50 (Thieszen et al., 1990; Beregi et al., 1991; Takata et al., 1987; Marriotti et al., 1992).13 Models in which senescence is controlled by a few genes regulating the number of cell replications such as the Hayflick limit are too simple to explain longevity, though some believe genes controlling growth factors regulating cell death may be significant, (see Hayflick and Moorhead, 1961; Finch, 1990; Cristofalo et al., 1989).

Studies suggest that genetic diseases are important at early ages. For example, Reed (1990) found that the concordance rate for CVD risk factors decreased with age. As discussed above, genetically determined breast cancer is expressed early. And, most genetically determined lung cancer is manifest before age 70 (Sellers et al., 1990).

13  

Only a few human leukocyte antigen markers for autoimmune disorders were depleted in centenarians (Takata et al., 1987), although Glueck et al. (1976) suggest that genetic traits controlling lipid profiles confer longevity. HLA heterogeneity may be a marker of longevity (Gerkins et al., 1974). Mooradian and Wong (1991a,b) suggest that strict genetic control of senescence is unlikely; that is, a polygenic determination of multiple dimensions of survival is more probable because of the different ages at which diseases operate, producing different effects over the life span.

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
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We need new multivariate-process models to detect the stochastic generation of mutations in DNA with age over the life span and to distinguish those from genetic endowment. If free-radical damage to DNA accumulates with age, the fidelity of DNA replication is affected (Cutler, 1991). This could be modeled as a stochastic process with a diffuse effect on genes emerging at late ages, (such as plasma cell abnormalities of unknown significance; Alexanian et al., 1988). Free-radical damage at advanced ages may affect mitochondrial, DNA, rather than nuclear DNA, thus affecting energy production. Thus, DNA changes may be involved in aging—but not necessarily through inheritance; the effects could be similar to neoplasia, in which fidelity of function is lost as DNA errors accumulate.

CONCLUSION

Because of the very high costs of caring for people with health impairments, models that demonstrate the potential impact of various health policies and that accurately project changes in disability rates are extremely valuable tools for policy makers.

In this chapter we have discussed the tools of medical demography and the areas of research to which they may be applied. Many of these tools require the development of biologically detailed models of changes in the health of populations. We have discussed the factors affecting the use of such models to describe changes in health between two elderly populations at a given point in time and changes in the health of a given population as they age through time. We need to understand better the processes related to age that affect health, and we need to learn how to exploit longitudinal and demographic data to describe those effects. Because biomedical science is advancing so rapidly, so must the evolution of models. We can accomplish this evolution by using a general state-space model that can be elaborated as more refined data become available.

Medical demography is conceptually and procedurally distinct from the epidemiology of chronic disease. The epidemiologist attempts to discern causal relations between risk factors and disease endpoints, often using general statistical models to test the significance of relations. To investigate causality requires experimental designs and randomized trials. The medical demographer uses estimates of epidemiological and clinical relations in population models to asses their implications, with and without interventions, for both current and future populations. However, in performing those tasks, the validity of the basic epidemiological relations are tested at the population level, and the result may be estimates of population effects with implications for the interpretation of epidemiological data. In addition, it may be necessary to estimate different types of models of complex health processes whose parameters may require evaluation in multiple

Suggested Citation:"7 Medical Demography: Interaction of Disability Dynamics and Mortality." National Research Council. 1994. Demography of Aging. Washington, DC: The National Academies Press. doi: 10.17226/4553.
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data sets. Finally, the biostatistician is often interested in assessing the effects of clinical interventions—usually for relatively short periods of time. Thus, many biostatistical methods do not deal with the long-term age changes that are the focus of medical demography.

Of greater importance to the medical demographer than to epidemiologists or biostatisticians is the effect of functional change in the population. Analysis of such changes involves endpoints that are difficult to measure and that evolve over long periods of time. The medical demographer is also more concerned with cohort and life-cycle effects and with the use of longitudinal survey data to assess changes in health over time without significant population bias. Designs of longitudinal surveys appropriate for assessing complex changes in the health of the elderly will require methodological research. A state-space model such as we have detailed here may aid this development. The effects of length of time between measurements, and the effects of the detail of measurement, can be examined by considering changes in θ over design parameters.

Thus, medical demography is an endeavor to synthesize scientific insights from multiple disciplines to explain and forecast change in the health outcomes of populations that are attributable to age. It thus relies on multivariate, stochastic models to represent the interactions of disease, disability, and mortality as they change over time, and as they affect people as people age. Recent evidence indicates that these dynamics are more complex than once supposed and that simple hazards do not describe them. This finding is not surprising. These dynamics are the consequences of changes in the health of individuals as they age, related to declines in mortality and to increases in life expectancy, which permit manifestation of nonlinear behavior. Clearly, what is called for is much more research on these processes before interventions can be carefully coordinated with simultaneous changes in health.

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As the United States and the rest of the world face the unprecedented challenge of aging populations, this volume draws together for the first time state-of-the-art work from the emerging field of the demography of aging. The nine chapters, written by experts from a variety of disciplines, highlight data sources and research approaches, results, and proposed strategies on a topic with major policy implications for labor forces, economic well-being, health care, and the need for social and family supports.

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