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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



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Demography of Aging 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

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Demography of Aging 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

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Demography of Aging 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

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Demography of Aging 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).

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Demography of Aging 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

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Demography of Aging 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.

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Demography of Aging 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

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Demography of Aging 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

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Demography of Aging 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.

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Demography of Aging 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).

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Demography of Aging 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).

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