Convergence of body mass with aging: The longitudinal interrelationship of health, weight, and survival

Economics and Human Biology 6 (2008) 469–481

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Economics and Human Biology journal homepage: http://www.elsevier.com/locate/ehb

Convergence of body mass with aging: The longitudinal interrelationship of health, weight, and survival Zhou Yang a,*, David Bishai b,1, Jeffrey Harman c,2 a

Department of Health Policy and Management, Rollins School of Public Health, Emory University, 1518 Clifton Road NE, Atlanta, GA 30322, United States b Population and Family Health Sciences, Johns Hopkins University, Suite 4622 615 N. Wolfe St., Baltimore, MD 21205, United States c Department of Health Services Research, Management, and Policy, University of Florida, 101 S. Newell Dr. Rm 4135, Gainesville, FL 32610-0195, United States

A R T I C L E I N F O

A B S T R A C T

Article history: Received 3 April 2008 Received in revised form 16 June 2008 Accepted 16 June 2008

There has been ongoing debate about the health risks associated with increased body weight among the elderly population. One issue has not been investigated thoroughly is that body weight changes over time, as both the reasons and results of, the development of chronic diseases and functional disabilities. Structural models have the ability to unravel the complicated simultaneous relationship between body weight, disability, and mortality along the aging process. Using longitudinal data from the Medicare Current Beneficiary Survey from 1992 to 2001, we constructed a structural model to estimate the longitudinal dynamic relationship between weight, chronic diseases, functional status, and mortality among the aging population. A simulation of an age cohort from 65 to 100 was conducted to show the changes in weight and health outcomes among the cohorts with different baseline weight based on the parameters estimated by the model. The elderly with normal weight at age 65 experience higher life expectancy and lower disability rates than the same age cohorts in other weight categories. The interesting prediction of our model is that the average body size of an elderly cohort will converge to the normal weight range through a process of survival, senescence, and behavioral adjustment. ß 2008 Elsevier B.V. All rights reserved.

Keywords: BMI Aging Dynamic Structural

1. Introduction The prevalence of overweight and obesity has become a serious public health concern in the United States. Approximately 35% of the adults in the U.S. are overweight and an additional 30% are obese (Flegal et al., 2002; Hedley et al., 2004). By the end of the 20th century, it was widely accepted that very low or high body mass index (BMI)3 is associated with heightened mortality (Calle et al., 1999; Stevens et al., 1998), making the relationship between mortality and BMI U-shaped or J-shaped. The lowest mortality was thought to occur between BMI of 23.5 to 24.9 in men, and between 22.0 and 23.4 in women among adult population of the U.S. (Calle et al., 1999). Although the prevalence of overweight and obesity is increasing, the average life expectancy in the U.S. has been continuously increasing at the same time, despite it is well below that of most industrialized countries. By the year 2003, the average life expectancy at birth of the U.S. population is approximately 77 years old, and the majority of deaths happen after

* Corresponding author. Tel.: +1 4047273416; fax: +1 4047279198. E-mail addresses: [email protected] (Z. Yang), [email protected] (D. Bishai), [email protected]fl.edu, [email protected]fl.edu (J. Harman). 1 Tel.: +1 410 955 7807; fax: +1 410 955 2303. 2 Tel.: +1 352 273 6060; fax: +1 352 273 6075. 3 BMI is measured by an individual’s weight in kilograms divided by the square of their height in meters. 1570-677X/$ – see front matter ß 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.ehb.2008.06.006

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age 65.4 One central issue about the health risks associated with extra body weight is the ongoing debate about the optimal weight among the elderly population. Previous research produced controversial conclusions. Using recent nationally representative data, Flagel et al. found that among the general adult population in the U.S., the relative risk of death only begins to increase above BMI of 30 and that the relative risk of death between BMI of 25 and 30 is no higher than for BMI between 20 and 25. They explained the improvement in mortality among overweight people as due to improvement in general health conditions of people with chronic diseases because of better medical technology (Flegal et al., 2005). Other studies found that conditional on surviving into older age (65 or higher), the overweight or even slightly obese elderly people (BMI close to 30) could experience lower mortality rates than those with lower body weight (Grabowski and Ellis, 2001; Taylor and Østbye, 2001). On the other hand though, existing research also found overweight or obesity could be associated with higher risk of death among the elderly, and suggested the relationship between body weight and mortality among elderly requires further investigation (Adams et al., 2006; Corrada et al., 2006; Freedman et al., 2006). The previous research was limited to survival analysis to either investigate the relationship between baseline BMI and mortality years later (Stevens et al., 1998; Calle et al., 1999; Janssen et al., 2005; Adams et al., 2006), or assessing correlation between concurrent BMI and mortality (Taylor and Østbye, 2001; Grabowski and Ellis, 2001; Flegal et al., 2005). No previous research investigated one unique feature of weight issue among the elderly population—the change of body weight, and its dynamic relationship with chronic diseases, functional status and mortality. Without good longitudinal data that tracks the changes of weight and health status among the elderly population, or appropriate econometric method to model these changes, these previous research failed to resolve the debate concerning the threshold beyond which BMI elevations threaten health among the aging population. Not all of the conditions associated with lower weight are harbingers of death. There are natural changes in body habitus accompanying aging that may or may not affect mortality. As part of senescence, height decreases gradually because of the loss of fluid from intervertebral disks. In addition, natural senescent weight losses also occur due to reductions in lean body mass caused by cachexia and wasting accompanying chronic diseases, such as heart disease and cancer. Aging is thus related to natural changes in both body habitus that may or may not be causally related to survival. Hence, there are four obstacles which make it challenging to estimate the relationship between health and body mass among the elderly population empirically and which motivates the adoption of a longitudinal dynamic perspective. First, weight is correlated with the probability of chronic diseases, such as diabetes or hypertension, and major medical events, such as strokes or heart attacks.5 The incidence of chronic diseases or major medical events are in turn correlated with subsequent body weight and mortality. Second, functional disabilities are common among aging people. Their incidence is imperfectly correlated with body mass, and hence will confound the relationship between weight and mortality. Previous studies found development of functional disability and weight loss happening concurrently before death (Newman et al., 2001). Third, people can make choices to adjust their weight based on perceptions of risks and benefits. For example, people may begin exercising after a heart attack, or may alter their diet after being diagnosed with hypertension or diabetes to lose weight. Fourth, medical care would alter the lethality of the major medical conditions, but may not be uniformly available to all members of the population. For example, people with higher income, more generous health insurance coverage, or more information may have better access to medical care, and hence could perform better in survival by investing more in health care compared with people in similar health status but less financial resources to pay for health care. Therefore, in this study, we use structural equation methods widely accepted and applied by economists, psychologists, and an increasing number of epidemiologists to investigate dynamic personal choices and adaptations to changing environmental and personal threats and opportunities. Specifically, we constructed a system of simultaneous equations (also known as a structural equation models) to quantify the relationship between annual changes in BMI, experience of chronic conditions, changes in functional status, and mortality. We are not aware of any existing research using such method to investigate body weight related health issues among the aging population.

2. Data The analysis uses data from the Cost and Use files of the Medicare Current Beneficiary Survey (MCBS). The MCBS is a longitudinal survey conducted by the Center for Medicare and Medicaid Services to examine the medical care use, and health status of a representative sample of Medicare beneficiaries in the U.S. (Adler, 1994). The Cost and Use files of MCBS provide two important types of data: individual survey and medical claims. Demographic features, height, weight, and health status (including mortality, functional status, and existing chronic diseases) are collected from the survey. The survey is updated every calendar year to record annual changes in these characteristics. The medical claims files include the date, charge, and payment information of each inpatient, outpatient, medical provider (mostly physicians), nursing home, home health, and 4 Three quarters of deaths in the United States occur among persons 65 years of age and over according to Health, United States, 2003, Table 32. Data source comes from Centers for Disease Control and Prevention, National Center for Health Statistics, National Vital Statistics System. 5 The major medical events are also defined as ‘‘health shocks’’ in the economics literature. The difference between chronic disease and ‘‘health shocks’’ is that chronic diseases are usually time-consistent conditions, and the patients are well aware of it. But major medical events, or say ‘‘health shocks’’ are not time consistent, or predictable by patients themselves. For example, diabetes, or high cholesterol level is a chronic condition, but heart attack, or stroke are ‘‘health shocks’’.

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hospice event during the survey time frame. The charge and payment of each outpatient prescription drug refill is also recorded in the claims file. As part of a longitudinal survey, the respondents were followed for between 1 and 5 years. However, not all of the respondents in MCBS were followed for the same number of years. Some of them died or dropped out randomly. Additionally, new individuals were brought into the survey each year allowing the sample size to be relatively similar across time. A more thorough description of the MCBS is provided elsewhere (Adler, 1994). Cost and Use Files of MCBS from 1992 to 2001 are used in the analysis and all disabled beneficiaries under 65 are excluded. All respondents with missing height or weight information are also excluded. Because this study focuses on the dynamic changes of body weight and health status during the aging process, it requires at least 2 years of observation for each individual for the empirical estimation. Therefore, all respondents with only 1 year of observation are excluded. From an initial 45,966 individuals, this resulted in an analytical sample of 85,038 person-year level observations representing 28,906 unique individuals.6 The summary statistics of the study sample are shown in Table 1. 2.1. Body mass index (BMI) BMI is derived from the self-reported height and weight collected from the survey. The average BMI in our study sample is 25.47 (see Table 1), with standard deviation at 4.80. The lowest BMI value observed in the data is 10.71 and the highest is 65.54. About 5% of the sample are underweight with BMI less than 18.5, 45% are in normal weight with BMI between 18.5 and 25, 35% are overweight with BMI between 25 and 30, and 15% are obese with BMI greater than 30. The overweight or obese elderly account for about 50% of the study sample. The BMI of each respondent in the study sample does not remain constant over time. From year to year, about 24% of the observations gained weight, 27% lost weight, and 49% of the observations remained the same weight. The between observation standard deviation of BMI is 4.78, and the within observation standard deviation is 1.69. Hence, the data illustrates the dynamics of body weight among the elderly. 2.2. Mortality and functional status The deaths occurred during the survey period are recorded with the average mortality rate across all ages in our study sample of approximately 5%. Functional status measurement is also derived from the survey, and is grouped into four categories: no functional limitations, moderately disabled with at least one Instrumental Activities of Daily Living (IADL) limitation and/or up to three Activities of Daily Living (ADL) limitations, severely disabled with four or more ADL limitations. Table 1 presents the details of the distribution of functional status in the sample. Whereas 49% do not have functional limitations, 33% are moderately disabled, 14% are severely disabled. 2.3. Chronic conditions and related major medical events Existing chronic conditions are collected from the survey. We include four types of chronic conditions that are the major threats to mortality or functional disability among the elderly population (Ferrucci and Guralnik, 1997): cardio/cerebral vascular diseases (hypertension, heart diseases, stroke et al.), respiratory system diseases (COPD, bronchitis, etc.), cancer except skin cancer, and diabetes (both type I and type II). Major medical events refer to clinical diagnoses of three chronic diseases for respondents who actually sought inpatient, outpatient, or physician care to treat these chronic diseases during the survey period. Unlike the existing chronic conditions that are collected from self-report on the survey, major medical events are derived from medical claims with accurate ICD-9 codes, including: cardiovascular or cerebrovascular disease (ICD-9 390–490), respiratory system diseases(ICD-9 480–496), and cancer (ICD-9 140–209).7 The respondents in our study sample may have zero, one, or multiple claims of one or more types of major medical events in a year. The existing chronic conditions coupled with the major medical events help to measure the dynamic features of the development of chronic diseases among the elderly population. For example, a person without self-reported chronic conditions may experience an acute myocardial infarction and become a chronically ill patient with heart disease. On the other hand, a person with existing chronic conditions, such as diabetes, may or may not necessarily experience any major medical event due to good chronic care. Nevertheless, both the existing chronic conditions, and major medical events relate to body weight. The statistics in Table 1 show that prevalence of chronic diseases among the elderly is high. About 42% of our study sample have had cardio/cerebral vascular diseases, 14% have respiratory system diseases, 18% have cancer and 17% have diabetes. The rates of major medical events per year are lower than the prevalence of chronic diseases. Heart disease or stroke is the major threat with about 22% seeking medical treatment for heart disease or stroke per year in our sample, and about 5% seeking medical treatment for cancer or respiratory diseases separately. 6 Considering the exclusion of these subjects may bias the estimation because of the selection of study sample, we compare the study sample with the observations being excluded. We compared the summary statistics of the demographic features of these two samples and did not find statistically significant differences. Therefore, although height and weight information is missing in some of the objects in the excluded sample, we believe the exclusion is more a random event that is not likely to raise sample selection concern. 7 We did not model diabetes as major medical events for three reasons: First, the onset of new diabetes among the study sample (after the first period of observation) is very small, although the percentage of people with existing diabetes is close to 17%. Second, heart diseases and stroke are the common comorbidities of diabetes that cause worse health outcomes, and we modelled these conditions already. Third, the MCBS allows for up to three ICD-9 codes for classification of medical claims. So that when other more acute conditions, such as heart diseases or stroke, are listed, diabetes is not listed among the three.

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Table 1 Summary statistical of MCBS 1992–2001 Variable

Mean

Body weight BMI Under weight (BMI <18.5) Normal weight (BMI between 18.5 and 25) Overweight (BMI between 25 and 30) Obese (BMI greater than 30)

25.47 (4.80) 5% 45% 35% 15%

Weight change Gained weight Lost weight Remained the same weight

24% 27% 49%

Health status Mortality rate No disability Moderately disabled (IADLs or up to 3 ADLs) Severely disabled (4 or more ADLs)

5% 49% 33% 14%

Self-reported chronic conditions Cardio/cerebro vascular diseases Respiratory diseases Cancer Diabetes

42% 14% 18% 17%

Major medical care events Heart diseases or stroke (ICD-9 390–430) Respiratory system diseases (ICD-9 480–496) Cancer (ICD-9 140–209)

22% 5% 5%

Demographics Age Male (omitted: female)

76.45 (7.52) 41%

Race (omitted: white) Black Other non-white

9% 5%

Marital status (omitted: married) Widowed Divorced, never married or separated

40% 10%

Education (range: 0–18 years) Income (in thousand dollars) Rural resident (omitted: urban) Ever smoked cigarettes

10.06 (4.29) 22.01 (73.26) 28% 56%

Notes: Standard deviations of continuous variables are in parentheses.

3. Econometric model 3.1. Dynamic model The empirical analysis is conducted at a person-year level. We construct a dynamic simultaneous equation system as a proxy of the aging process that help to quantify the relationship between the changes in body weight and the changes in health status. Fig. 1 depicts such dynamic process. In specific, in every year t, the probability of health shocks St is determined by the existing health status Ht1 inherited from previous period, the existing chronic conditions and body weight BMIt1 . Consequently, current health status and the events of health shocks influence the demand for health care Eqt . Next,

Fig. 1. Dynamics of BMI and health transition.

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conditional on the existing health status, the frequency and severity of health shocks, as well as the effectiveness of the medical care, each person’s health status is updated to a new status Ht that will be carried on to the next period t þ 1. At the same time, body weight changes in response to the experience of health shocks, the associated treatment and behavioral change, as well as changes in functional status to BMIt , which is the initial weight for time period t þ 1. Such process will continue until death. Therefore, the simultaneous equation system is characterized by three types of equations: (1) a health transition equation to predict the probability of death or incidence of functional disability conditional on age and body weight; (2) Three medical event equations to predict the probability of the incidence of any one of the three types of major medical events in every year; and (3) A BMI equation to estimate the change of BMI from year to year conditional on survival. In the health transition equation, the dependent variable is the health condition by the end of each year (Ht ). It is categorized according to the respondents’ health outcomes at the end of each year, including: no functional disability, moderately disabled (IADLs, or up to 2 ADLs), severely disabled (3 or more ADLs), and death. The respondent’s BMI at the beginning of the year (BMIt1 ) is one major independent variable. Because of the well-documented U-Shaped ‘‘Waaler Curve’’ relationship between weight and health outcomes (Fogel, 1994), where people with lowest and highest body weight experience highest mortality rate and disability rate, we include the quadratic of BMI as an independent variable (BMI2t1 ). The respondents’ functional status at the beginning of the year (Ht1 ), and the incidence of the three major medical events during the year (Skt , k ¼ 1 if heart diseases or stroke, 2 if respiratory system diseases, 3 if cancer) are included as independent variables because the person who has functional disabilities or experiences major medical events will have a higher probability of worse health outcomes. Other independent variables include health care utilization and expenditures (Eqt , q ¼ 1 if inpatient, 2 if outpatient, 3 if long-term care, 4 if prescription drugs), because the access and use of health care services significantly influence the health outcomes.8 Current smoker, smoking history, and other demographics (Dt ) (age, gender, race, marital status, educational level, income and urban/rural residents) are also included as independent variables. The health transition equation is estimated with a multinomial logit model where9: exp ðah Y t Þ PðHt ¼ hÞ ¼ P4 0 h0 ¼1 exp ðah Y t Þ

(1)

where

ah Y t ¼ ah0 þ ah1 Ht1 þ ah2 BMIt1 þ ah3 BMI2t1 þ ah4 Sk þ ah5 Eqt þ ah6 Dt þ uht ;

h ¼ 1; . . . ; 4

While the incidence of major medical events influences health transition as well as changes in body weight, it also relates to lagged body weight, and lagged functional status. For example, overweight and obese people have higher risk of acute cardiovascular diseases or cancer than normal weight people, and older people with functional disability are more likely toexperience respiratory diseases (e.g. pneumonia). Therefore, we use three logit equations to estimate the probability of any oneof the three major medical events during a year (Skt ; k ¼ 1; 2; 3): any diagnosis of cardiovascular or cerebrovascular diseases (ICD-9 390–490), any diagnoses of respiratory diseases (ICD-9 480–496), and any diagnoses of cancer (ICD-9 140– 209). Estimating three separate equations enables our model to include all possible combinations of multiple major medical events, as a person may have zero, one, or more than one of these medical events during a year. A multinomial logit equation cannot appropriately model all these scenarios. The independent variables include lagged BMI (BMIt1 ), its quadratic (BMI2t1 ), and the interaction of age and BMI (BMI  Age) to control for the different influence of body weight on the probability of the major medical events at different age. Functional status at the beginning of a year is also included (Ht1 ). In addition, because people with existing chronic diseases are more vulnerable to health shocks, we control for each of existing chronic conditions (cardiovascular diseases/stroke, respiratory diseases, cancer, and diabetes, Ctw ; w ¼ 1; 2; 3; 4) in these 8 The health care utilization and expenditures are treated as endogenous in the health transaction function, as they are also related to body weight and health status. We modelled the health care expenditures along with the three major equations in the maximum likelihood estimation. In specific, we estimated 4 two-part models for the 4 types of health care services: inpatient care, outpatient physician services, long-term care, and outpatient prescription drugs. The first part is a logit model to predict the probability of any one type of health care service use, and the second part uses an OLS model to predict the natural log expenditures conditional on positive health care expenditures. The independent variables include supplemental insurance choices, BMIt1 , BMI2t1 , functional status (Ht1 ), existing chronic conditions at the beginning of a year (Ctw ; w ¼ 1; 2; 3; 4), major medical events during a year (Skt ; k ¼ 1; 2; 3), and demographics (Dt ). Because the focus of this paper is not on the cost associated with body weight, we do not discuss the setup, estimation of cost equations, or the simulated health care cost in this paper, the estimation results are available upon request to the authors though. 9 We here use multinomial logit, instead of an ordered logit/probit model, which probably could model the deteriorations of health status more appropriately for two reasons: First, although death is the absolute worst health outcome, based on our observation of the data, the change of functional status from year to year is not necessarily monotonic toward worse health condition. For example about 15% of the observations experienced improvement in functional status from 1 year to the next. Therefore, a multinomial logit provides more flexibility in the estimation. We tested the fit of the model. The comparison of the predicted mortality rate and observed mortality rate is presented in Fig. 3, it shows good fit of the estimation of mortality. We also compared the predicted disability rae with the observed disability rate which are not presented here, the result also shows good fit. Such results indicate that the multinomal logit model captures the dynamic changes in health status with great accuracy. Second, an ordered logit/probit model will increase the computational burden of our dynamic model significantly. Because the good fit of the simulation with original data, we stayed with multinomial logit model. We are aware of the necessity of IIA assumption in application of multinomial logit models. In this specific situation, because the probability of one health outcomes, e.g. death, does not influence the probability of other health outcomes, e.g. moderately disabled, conditional on previous health status, so that we believe the IIA assumption hold.

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three logit equations. Demographics features are also included as independent variables. k

PðSkt ¼ 1Þ ¼

exp ðd Y t Þ

(2)

k

1 þ exp ðd Y t Þ

where

dk Y t ¼ dk0 þ dk1 BMIt1 þ dk2 BMI2t1 þ dk3 BMIt1  Age þ dk4 Ht1 þ dk5 Ctw þ dk6 Dt þ ust ; k

k ¼ 1; 2; 3

The annual change in BMI is estimated with linear regression. The dependent variable is the BMI at the end of a year (BMIt ) . The independent variables include BMI at the beginning of the year (BMIt1 ) and its quadratic(BMI2t1 ) to estimate the nonlinear or non-monotonic natural weight change tendencies for people in different weight categories when they age. Lagged BMI is a strong predictor of current BMI because it is the outcomes of a person’s general life style. Without major medical events or effort to change life style due to health reasons, body weight does not fluctuate significantly from year to year. Lagged functional status (Ht1 ) is included as an independent variable because functional status is closely related to muscle mass, metabolism rate, and body weight. Because major medical events and their treatment may cause weight change (e.g. chemotherapy could cause significant weight loss), we also include the major medical events that happened during a year (Skt ) as independent variables. Demographic features (Dt ) are also controlled. BMIt ¼ b0 þ b1 BMIt1 þ b2 BMI2t1 þ b3 Ht1 þ b4 Skt þ b5 Dt þ ubt

(3)

All of these measures of functional status, BMI, and major medical events affect one another. For example, an overweight senior person may have diabetes already, and hence will have a higher risk of suffering a medical event of heart attack or cancer. The medical events and associated treatment (open heart surgery, or chemotherapy) may in turn save her life and reduce her weight to normal weight, or even underweight. Consequently, she could either recover, or become disabled after the medical event. Conditional on that, she may regain her weight, stay in the same weight, or keep on losing weight conditional on her health conditions, diet, physical activity, and choices in health care and other aspects of her personal life. Such dynamic weight changes in body weight, health status and behavioral adjustment can continue until the person eventually dies. Therefore, we estimated all these equations (Eqs. (1)–(3)) simultaneously using maximum likelihood.10 Considering other unobserved individual factors, such as genetic features, unobserved medical events, health related behaviors, or personnel habit, also influence people’s weight and health conditions, discrete random effects were used to control for the unobserved individual heterogeneity to subsume these unobserved health and weight related conditions (Blau and Gilleskie, 2001; Cutler, 1995; Goldman, 1995; Heckman and Singer, 1983; Khwaja, 2005; Mello et al., 2002; Mroz, 1999; Stern and Checkovish, 2002; Yang et al., 2005).11 Hence, the simultaneous equation system captures more of the complex interrelationship of the aging process which involves the dynamic relationship between body weight, development of major chronic diseases, changes in functional status, and longevity. 3.2. Cohort simulation The interpretation of estimated parameters in a simultaneous system of equations such as this is difficult, as the effects of the coefficients in one single equation spill over to other equations as well. If one were to try to assess the relationship between mortality and a one time change in a single covariate such as BMI, one would have to account for the indirect effects of BMI on major medical events and functional status. So the best way to illustrate the dynamic changes of BMI over time and its influence on the health status among the aging population is to apply all of the coefficients simultaneously to a virtual cohort of population sample and to thereby simulate all of the direct and indirect effects that emerge based on their baseline body weight at age 65. The sample used in the simulation includes all the observations at age 65 in the study sample. We performed 2000 replications of the simulation for each individual using the parameters obtained from our analytical model starting at age 65 with the observed demo-graphic features, BMI, and existing chronic conditions. Each replication draws a random set of error terms for all the equations from age 65 until 100. In the years following age 65, the BMI, functional status, and probability of major medical events are updated based on the simulation. In addition, if a person who never had chronic diseases is simulated having any one of the major medical events in a year, and survived to the next year, her chronic conditions will be updated as having the correspondent chronic conditions at the beginning of the next year. If a person is simulated dead, the program will automatically stop, otherwise the simulation will continue until age 100. 10

The MLE includes the health expenditure equations introduced in footnote 6. The error terms in the equations (utj ; j ¼ h; b; sk ; e) is decomposed into three components: utj ¼ r j m þ v j nt þ etj . m represents the time-consistent unobserved heterogeneities, such as genetic features, and nt represents the time-varying unobserved heterogeneities, such as the unobserved natural deteriorating rate of health, et is and i.i.d error that is assumed to have normal distribution for OLS equations, dichotomous distribution for logit equation, and extreme value distribution for multinomial logit equations. r and v are estimated factor loadings of unobserved heterogeneities on different outcomes. Instead of normal distributions assumption, m and nt are modelled with discrete distributions which are denoted m ¼ ðmm ; m ¼ 1; . . . ; MÞ and (nt ¼ ntl ; l ¼ 1; . . . ; L), respectively, where M and L are the number of mass points in the discrete approximations to the distribution. For details of the estimation method, please refer to Mroz (1999). 11

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3.3. Limitations This study does have some limitations in the estimation. First, the data we used come from a short panel with the longest observation at 5 years. Although we can learn about mortality in the period of the mid-1990s at ages ranging from 65 to 90, it is possible that cohort effects (from being born in the 1930s as opposed to the 1910s) may be confounding the effects of age because no one individual can be followed for more than 5 years. Further studies using longer panels will provide estimates that can better adjust for cohort effects. Second, the weight and height information we used to construct the BMI measurement are self-reported information from survey, and are not as accurate as the objective measures from clinical data. Third, our empirical analysis did not include exercise or diet behaviors due to the limitations of the data, further research focusing on the health behavior or education interventions will help to answer the policy questions related to better control of obesity. Fourth, access and utilization of medical care is important for the elderly population. Although we modelled the effect of health care use in the health transition equation, the disparities in insurance coverage with supplemental services among Medicare beneficiaries (e.g. prescription drugs benefit) may cause differences in health care utilization and subsequent health outcomes. Future applications of structural models can improve the study of other simultaneous processes such as health policy, insurance coverage, health indicators and body size. 4. Results 4.1. Descriptive analysis The results of descriptive analysis are shown in Fig. 2. Note the study sample includes surviving Medicare beneficiaries across all age groups with up to 5 years of follow-up, so that although it is a longitudinal data sample, it is not a cohort data sample. The top panel shows the mortality rate increases from 5% at age 65 to close to 30% at age 100. In the middle panel, the average BMI among survivors decreases from close to 27 at age 65 to approximately 22 at age 100. In addition, in the bottom panel, we present the distributions of survivors in each weight categories by age. It shows that the percentages of obese and overweight survivors are decreasing by age, but the percentages of normal weight and underweight survivors are increasing. Among the survivors at age 65, about 60% are overweight or obese, close to 40% are normal weight, and few are underweight. However among those who survive up to age 100, about 60% are normal weight, 20% are underweight, and only 20% are overweight or obese. There could be two explanations for this phenomena: the heavier people die earlier, and/or natural and behavioral weight loss happened concurrently with the aging process. Although the descriptive results are informative, they cannot provide enough information of dynamic weight change as a cohort goes through the entire aging process. The descriptive data is based on multiple cohorts observed at multiple ages with no individual being observed for more than 5 years. Thus, these descriptive patterns cannot distinguish effects of body size in the present from the effects of body size 10 years ago. Only the results from our cohort simulation could answer such a question. 4.2. Dynamic equation estimates The estimates of the health transition function are presented in Table 2. The coefficients of BMI on worse health outcomes are negative and statistically significant, but the coefficients of its quadratic term are positive and statistically significant. Such results indicate that the relationship between concurrent BMI and worse health outcomes is nonlinear, either high or low BMI is associated with worse health outcomes. BMI between 20 and 25 is associated with the best health outcomes. The coefficients of other right hand side variables are in the expected direction. Those who reported having functional disabilities are more likely to stay in disabled conditions or die, and those who experienced major medical care events are more likely to die or be disabled. Table 3 reports the coefficients of the BMI equation. The coefficient of lagged BMI on current BMI is 1.042, but the coefficient of the square of lagged BMI is –0.307, and both are statistically significant (P < 0:05). Such results indicate that the average body weight among the elderly survivors is changing over time in a nonlinear pattern. Being moderately disabled does not appear to influence the annual BMI change significantly (coefficient ¼ 0:024, S.E. = 0.017), but being severely disabled is associated with lower body weight (coefficient ¼ 0:087, S.E. = 0.024, P < 0:05). Major medical events could influence the weight, experiencing any one of the three types of major medical events is associated with lower body weight. In addition, existing chronic diseases relate to body weight. Having cardio/cerebro vascular diseases or respiratory diseases is associated with lower body weight, but having diabetes is associated with higher body weight. Our results contradict the common expectation that heavier people are more likely to have cardiovascular diseases. The reasons for the negative relationship between chronic cardio/cerebro vascular diseases and body weight could be (1) high collinearity between chronic cardio/cerebro vascular diseases and diabetes as cardiovascular disease is the most common co-morbidity of diabetes; or (2) people could consciously change their behavior to lose weight after being diagnosed with cardiovascular disease. The coefficients of the three logit regressions to predict the probability of major medical events are reported in Table 4. Generally, BMI, the square of BMI, and the interaction of age and BMI all have significant influence on the probability of the incidence of these three types of major medical events. The coefficients of BMI are generally positive, but the coefficients of BMI squared and the interaction term are generally negative. Such results indicate that the relationships between BMI and

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Fig. 2. Descriptive results of average mortality, weight by age from MCBS 1992 to 2001.

major medical events are nonlinear, and vary by age. The coefficients of other right hand side variables are in the expected direction, where having functional disabilities or chronic diseases are associated with higher probability of major medical care events. As we discussed in the method section, the coefficients in each of the equations only represent one aspect of the shortterm health changes or body weight changes during the aging process. Therefore, we could hardly draw meaningful conclusions by discussing the coefficients in these equations separately. The cohort simulation based on the model estimation will present the results in a more meaningful way. 4.3. Cohort simulation As the cohort simulation is based on the estimation from the simultaneous dynamic model, we first test the robustness of our simulation. In specific, instead of applying simulation to one age cohort, we applied the simulation program for all the observations to their first year of observation in our study sample, and let the simulation proceed for up to 5 years, which is

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477

Table 2 Coefficients of health transaction equation

Weight at the beginning of a year BMI BMI square/100 a

Death

Severely disabled

Moderately disabled

0.355 (0 028) ** 0.532 (0.056) **

0.188(0.024) ** 0.365 (0.047) **

0.080 (0.019) 0.183 (0.039)

**

2.231 (0.025) 2.003 (0.052)

Functional status at the beginning of a year Moderately disabled Severely disabled

1.871 (0.056) 3.713 (0.066)

**

Major medical care events during a year Heart/stroke(ICD-9 390–439) Respiratory (ICD-9 480–496) Cancer (ICD-9 140–209)

0.675 (0.058) 0.815 (0.082) 1.429 (0.084)

**

(0.592) (0.064) (0.122) (0.025) (0.173) (0.027) (0.648) (0.071)

**

Health care utilization and expenditures Any inpatient care Inpatient expenditures Any physician care Physician care expenditures Any prescription drugs Prescription drugs expenditures Any nurshing home care Nursing home care expenditures

3.201 0.617 0.857 0.369 0.072 0.016 6.606 0.605

**

** **

** ** **

** **

3.127 (0.058) 5.547 (0.069)

0.497 (0.049) 0.661 (0.077) 0.401 (0.098)

2.852 0.463 1.440 0.425 1.601 0.231 1.431 0.019

(0.792) (0.085) (0.126) (0.033) (0.152) (0.031) (0.929) (0.100)

**

**

** ** ** ** ** **

0.161 (0.037) 0.439 (0.059) 0.248(0.065)

0.894 0.157 0.682 0.131 0.747 0.226 4.519 0.491

(0.355) (0.039) (0.088) (0.012) (0.076) (0.012) (0.609) (0.067)

** **

** **

** **

** ** ** ** ** ** ** **

Note: Additional independent variables include demographic features. Standard errors are in parentheses. a Square of BMI is scaled down to 1/100 of its original value for the convenience of estimation. ** Joint significance at the 5% level.

Table 3 Coefficients of BMI equation Variable

Coefficients

Weight at the beginning of a year BMI BMI square/100 a

1.042 **(0.010) 0.307 **(0.022)

Functional status at the beginning of a year Moderately disabled Severely disabled

0.024 (0.017) 0.087 **(0.024)

Major medical care events during a year Heart/stroke Respiratory Cancer

0.357 **(0.020) 0.270 **(0.036) 0.484 **(0.041)

Existing chronic conditions Heart/stroke Respiratory Cancer Diabetes

0.039 **(0.016) 0.075 **(0.022) 0.009(0.019) 0.109 **(0.019)

Note: Additional independent variables include demographic features. Standard errors are in parentheses. a Square of BMI is scaled down to 1/100 of its original value for the convenience of estimation. ** Joint significance at the 5% level.

the longest time a single individual was followed in MCBS. Then, we compared the simulated outcomes with the observed outcomes in the original MCBS data. We picked the two most important outcome measures for the test of robustness: mortality rate and BMI. The results are depicted in Fig. 3, where the average simulated mortality rate and average simulated BMI in all ages is very close to the average observed mortality rate and observed BMI from MCBS, which is evident that the empirical model is robust.12 The cohort simulations of longevity of people in one age cohort in different weight categories at age 65 are shown in Table 5. The male cohort in normal weight range at 65 has an average life expectancy of 81.91 conditional on surviving up to 65. The male overweight cohort has the second longest life expectancy of 81.15. The male underweight and obese cohorts have shorter life expectancy of 79.80 and 80.15. In addition to life expectancy, we simulated healthy life expectancy, which is the length of life without functional disabilities (ADLs or IADLs). The male normal weight cohort experience the longest average healthy life expectancy of 75.44. Although the male underweight cohort may die earlier, their healthy life expectancy is the 12

Both the cohort simulation and robustness test were conducted by STATA version 9.0.

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Table 4 Coefficients from equations predicting probability of medical events Heart disease/stroke ICD-9 390–439 Weight at the beginning of a year BMI BMI square/100 a Age  BMI=100 a

0.333 (0.022) 0.791 (0.040) 0.488 (0.033)

Functional status at the beginning of a year Moderately disabled Severely disabled

0.033 (0.031) 0.023 (0.043)

Existing chronic conditions Heart/stroke Respiratory Cancer Diabetes

1.062 0.065 0.137 0.503

(0.033) (0.040) (0.037) (0.032)

** ** **

Respiratory ICD-9 480–496

Cancer ICD-9 140–209

0.016 (0.032) 0.238 (0.056) 0.244 (0.055)

0.415 (0.050) 1.027 (0.095) 0.502 (0.072)

0.393 (0.051) 0.386 (0.067) **

** **

0.081 1.934 0.013 0.103

(0.047) (0.049) (0.056) (0.056)

** **

** **

* **

*

0.058 (0.054) 0.605 (0.086)

0.213 0.322 1.987 0.129

(0.054) (0.072) (0.050) (0.063)

** ** **

**

** ** ** **

Note: Additional independent variables include demographic features. Standard errors are in parentheses. a Square of BMI and Age  BMI are scaled down to 1/100 of their original values for the convenience of estimation. * Joint significance at the 10% level. ** Joint significance at the 5% level.

second longest of 75.32. The male overweight cohort’s average healthy life expectancy is lower than both the normal weight and underweight cohorts of 74.10, and the male obese cohort has the lowest healthy life expectancy of 73.81. Hence, mmong older men, the normal weight cohort appears to have the longest life expectancy and healthy life expectancy compared with other weight cohorts.

Fig. 3. Robustness of simulation: actual vs. simulated average mortality and BMI by age.

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Table 5 Simulated life expectancy at age 65 by baseline weight Men

Women

Baseline normal weight Life expectancy Healthy life expectancy

81.91 75.44

85.24 73.52

Baseline underweight Life expectancy Healthy life expectancy

79.80 75.32

83.98 73.67

Baseline overweight Life expectancy Healthy life expectancy

81.15 74.10

84.72 72.38

Baseline obese Life expectancy Healthy life expectancy

80.15 73.81

83.82 71.86

Fig. 4. Average BMI among survivors of different weight cohorts by age.

The simulated results of older women are also depicted in Table 2. The patterns of longevity and healthy life expectancy among different female weight cohorts are similar to the male weight cohorts, except women in all weight categories have longer life expectancy, but shorter healthy life expectancy than men. Specifically, the normal weight women have both the longest life expectancy (85.24) and healthy life expectancy (73.52). Underweight and obese female cohorts have the shortest life expectancy (83.98 and 83.82), and the obese female cohorts have the shortest healthy life expectancy (71.86). The overweight female cohort does better than the obese female cohort, but worse than the normal weight female cohort with life expectancy of 84.72, and healthy life expectancy of 72.38. T-test indicated that both life expectancy and healthy life expectancy among the cohort who were in normal weight range at 65 is statistically significantly higher than other cohorts who are underweight, overweight, or obese at baseline (P < 0:05). Concerning the changes of BMI during the aging process, we plot the average simulated BMI among the survivors in different baseline weight categories by age (see Fig. 4). The result inspires confidence because we find the average BMI among the survivors of the cohort who are underweight at age 65 increases with age, but the average BMI among the survivors of the cohorts who are overweight or obese decreases with age. Finally, the average BMI of the survivors who are in the normal weight range at age 65 does not change over time up until age 85 at approximate 24. After that, it starts to decrease to approximate 22 if they survive to 100. The average BMI of survivors in the cohorts with different baseline weight converges over time to 22 at age 100, which is very close to the observed results from descriptive analysis depicted in Fig. 2(middle panel), where the average BMI among survivors at age 98–100 is close to 22. 5. Discussion By using a dynamic approach, this study implicitly assumes that weight itself relates to other health outcome measures, and is partially under behavioral control, and therefore could change in response to other health care events and behaviors. Prior research has not investigated the relationship between body weight and health outcomes using a longitudinal model to

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address these dynamic features. Hence, this study provides some insight into the weight related health issues among the aging population. The results of this study suggest that optimal BMI at age 65 appears to be within the normal weight spectrum from 18.5 to 25. Individuals with normal weight at 65 not only survive the longest, but also enjoy the longest healthy life expectancy. The underweight and obese people have the lowest survival rates, and the obese people experience the worst quality of life with shortest expectancy of healthy life. The differences in life expectancy between the normal weight and overweight cohorts are minor (within 1 year), but differences in the healthy life expectancies between these two cohorts are greater at close to 1.4 years for both men and women. Different from some other studies of obesity that rely on contemporaneous weight and survival data, this study does not find overweight to be a protective factor against mortality or functional disability among the elderly population. The convergence of BMI toward normal weight shows the dynamic relationship between changes of weight and survival. Based on the simulation of life expectancy, one explanation for the convergence of BMI toward normal weight is that it is based on survival such that the lightest and heaviest people die earlier leaving survivors in older age who are closer and closer to the healthy weight. Given the maximum 5 year follow-up in MCBS data, such results are population based, which indicates that at aggregate level, the average body weight of the elderly survivors will converge into normal weight level. It interesting that the average weight of survivors with different baseline weights did not converge to an underweight level as most people lose weight before death. Instead, the average weight of survivors converge to the recommended healthy BMI at 22 as recommended by previous research. On average, the elderly in healthy body weight at age 65 are more likely to keep their healthy body weight into older age (their average weight goes down a bit from 24 to 22) and survive longer than to lose weight and die earlier. In addition, to put the health gains in perspective, Table 5 suggests potential gains of about 1.4 years of healthy life expectancy for being normal weight instead of obese. Although there is no universally agreed upon estimate for the dollar value of a year of life, many have assumed a value of a quality adjusted life year (QALY) may exceed $100,000 (French and Mauskopt, 1992; Ubel et al., 2003). Thus the value of being normal weight instead of obese could be estimated at $160,000 because of the implied QALY benefits. A 65 year old obese person contemplating investments in altered lifestyle or stomach bypass surgery, would discount these gains 30 years into the future. At a discount rate of 3%, the monetary value of the health gains from attaining normal weight have a present value of $67,000 and would justify many of the current treatment options for obesity.

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