Except for income, values are the percentage of patients. NS = not significant; IADL = Instrumental Activities of Daily Living.
Orthopedics
The effects of total knee arthroplasty on physical functioning in the older population
Article first published online: 29 SEP 2008
DOI: 10.1002/art.23888
Copyright © 2008 by the American College of Rheumatology
Additional Information
How to Cite
George, L. K., Ruiz, D. and Sloan, F. A. (2008), The effects of total knee arthroplasty on physical functioning in the older population. Arthritis & Rheumatism, 58: 3166–3171. doi: 10.1002/art.23888
Publication History
- Issue published online: 29 SEP 2008
- Article first published online: 29 SEP 2008
- Manuscript Accepted: 17 JUN 2008
- Manuscript Received: 8 JUL 2007
Funded by
- Institute for Health Technology Studies
- Abstract
- Article
- References
- Cited By
Abstract
Objective
Clinical research provides convincing evidence that total knee arthroplasty (TKA) is safe and improves joint-specific outcomes. However, higher-level functioning associated with self care and independent living has not been studied. Furthermore, most previous studies of the effects of TKA relied on relatively small clinical samples. We undertook this study to estimate the effects of TKA on 3 levels of physical functioning in a national sample of older adults.
Methods
Data were obtained from the Medicare Current Beneficiary Survey from 1992 to 2003. Medicare claims data identified participants with osteoarthritis of the knee who received TKA (n = 259) or no TKA (n = 1,816). Propensity scores were used to match treatment and no-treatment groups according to demographic characteristics, comorbid conditions, and baseline functioning. Three levels of physical functioning were examined as outcomes of TKA. These levels were represented by items on the Nagi Disability Scale, the Instrumental Activities of Daily Living (IADL) Scale, and the Activities of Daily Living (ADL) Scale. These items were measured after TKA and at comparable intervals for the no-treatment group. Average treatment effects were calculated for relevant Nagi Disability Scale, IADL Scale, and ADL Scale tasks.
Results
Between baseline and outcome assessments, TKA recipients improved on all 3 levels of physical functioning; the no-treatment group declined. Statistically significant average treatment effects for TKA were observed for one or more tasks for each measure of physical functioning.
Conclusion
TKA is associated with sizeable improvements in 3 levels of physical functioning among elderly Medicare beneficiaries.
Clinical trials and observational studies convincingly demonstrate that total knee arthroplasty (TKA) is safe and improves joint-specific outcomes, including pain and range of motion (1–3). Levels of patient satisfaction are also high, exceeding 75% (4, 5). It is less clear whether TKA improves overall physical functioning. In a clinical study, Jones et al examined both joint-specific outcomes and general physical functioning 6 months after TKA (4). They reported significant improvements in joint pain and mobility, but improvements in physical functioning were less common and were not highly correlated with joint-specific outcomes. Noble et al compared multiple indicators of physical functioning between TKA recipients who were at least 1 year postsurgery and age- and sex-matched adults with no history of knee disorders (6). They reported no differences between groups for most activities, but TKA recipients reported significantly greater dysfunction on tasks that place greater demands on the knee (e.g., kneeling, carrying loads). Note, however, that this study did not compare functioning before and after TKA. Similar results were reported in a survey-based study in France (7).
TKA may be one factor accounting for declining disability rates in the US (8, 9). To document this, however, improvements in physical functioning resulting from TKA must be observed at the population level. Given the high cost of TKA, a question also remains whether its benefits exceed joint-specific outcomes and translate into improved capacity for self care and maintenance activities, although studies based on health-related quality of life show that TKA is cost-effective (10, 11). The present study examined the effects of TKA on 3 levels of physical functioning that vary in severity of impairment in a national sample of Medicare beneficiaries. To our knowledge, this is the first study to examine the effects of TKA using national data, although similar samples have been used in studies of the epidemiology of TKA (12–14).
Rates of TKA have increased dramatically since 1990 (12). Kurtz and colleagues reported that rates of primary TKA nearly tripled between 1990 and 2002 (13). Despite the dramatic increase in primary TKAs, the National Institutes of Health Consensus Statement on Total Knee Replacement estimated that only 13% of women and 9% of men who are candidates for this surgical procedure choose TKA (5). Similarly, in a county-level study in Ontario, Canada, only 33.5% of persons for whom joint replacement was clinically appropriate reported that they would “definitely” or “probably” be willing to consider joint replacement as a treatment option (15). Increasing rates of TKA and the very large potential pool of candidates for TKA highlight the importance of documenting the effects of TKA on physical functioning.
PATIENTS AND METHODS
Sample.
This study used data from the Medicare Current Beneficiary Survey (MCBS) Cost and Use files. The MCBS sample is selected from Medicare beneficiaries using a multistage, stratified random sampling procedure. Disabled persons ages ≤64 years and beneficiaries ages ≥80 years are oversampled. The Medicare program covers 96% of the US population ages ≥65 years as well as seriously disabled persons younger than this. Participants are interviewed 3 times each year. The interviews focus on demographic and socioeconomic characteristics, health, cognitive status, physical functioning, and health service use. However, the physical functioning items are asked only once a year. Medicare claims data are merged with the survey data. The MCBS uses a rotating panel design in which one-third of the sample is replaced annually. Study participants are interviewed for 4 years or until they die or drop out. The sample size in any given year is ∼12,500 (16).
The present study used MCBS and claims data collected between 1992 and 2003. National data indicate that ∼95% of TKAs in the older population are performed because of arthritis of the knee (17). The sample for this study consisted of individuals who 1) reported no TKA prior to entering an MCBS cohort and 2) had been diagnosed as having osteoarthritis of the knee (International Classification of Diseases, Ninth Revision, Clinical Modification codes 715.16, 715.96, 715.06, 715.26, 715.36, and 715.86). The sample was further classified into members who did and did not undergo unilateral TKA between their baseline and final interviews (Current Procedural Terminology code 27447). After eliminating respondents for whom data were missing (including respondents enrolled in health maintenance organizations for whom information about medical diagnoses and procedures was lacking), there were 259 persons in the treatment group and 1,816 persons in the no-treatment group (see Figure 1 for the types and numbers of losses to attrition). The vast majority of sample loss was due to lack of an interview within the appropriate time frame, resulting in part from the fact that the physical functioning items were asked only once a year. Creation of propensity scores is described below. The Institutional Review Board at Duke University approved this study.
Measurement.
The primary independent variable was receipt versus nonreceipt of unilateral TKA. For TKA recipients, baseline measures were taken from the interview immediately prior to surgery; followup data were taken from the first interview that occurred at least 80 days postsurgery and included the physical functioning items. For the no-treatment group, baseline interviews were randomly selected with the qualification that there was a followup interview at least 6 months after the baseline interview that included the physical functioning items. The average interval between baseline and followup interviews was slightly less than 13 months for the treatment group and slightly less than 16 months for the no-treatment group. Time between baseline and followup interview was a control variable in the multivariate analysis.
Three levels of physical functioning were examined as outcomes of TKA. We examined 3 items from the Nagi Disability Scale that were especially relevant to knee function: stooping/crouching, walking 2–3 blocks, and lifting objects weighing up to 10 pounds (18). Respondents reported the amount of difficulty they had performing these tasks (no difficulty, a little difficulty, some difficulty, a lot of difficulty, and not able to do it). Persons who reported “a lot of difficulty” and “not able to do it” were compared with those who reported “no difficulty,” “a little difficulty,” and “some difficulty.”
We examined 4 items from the Instrumental Activities of Daily Living (IADL) Scale: performing light housework, performing heavy housework, preparing meals, and personal shopping (19). The omitted IADL tasks—taking medicine, handling money, and using the telephone—were unlikely to be affected by TKA. We examined 5 items from the Activities of Daily Living (ADL) Scale: bathing/showering, getting dressed, getting in and out of a chair, walking, and using the toilet (20). The omitted ADL tasks—eating and personal grooming—were also unlikely to be affected by TKA. Response categories for IADL and ADL items focused on difficulty performing the task (no difficulty, have difficulty, and do not do). Respondents who reported having difficulty or “do not do” because of health or physical problems were compared with those who reported “no difficulty.”
These 3 scales require different levels of strength, mobility, and stamina. The Nagi Disability Scale items require the highest levels of functional capacity, IADL Scale items are intermediate, and ADL Scale items require the least functional capacity (21). Metric values of the functional measures were used as baseline measures of the outcomes. Changes in scores between interview dates were the dependent variables.
Analytical methods.
Percentages and means (for income) for the independent variables were compared for the treatment and no-treatment groups. We used t-tests to assess statistically significant differences between treatment and no-treatment groups in physical functioning outcomes and to compare presurgical–postsurgical measures of physical functioning within groups. Propensity score methods were used to predict the average treatment effects of TKA on physical functioning.
In a first step, we estimated a logit model for which the dependent variable was 1 if the individual received a TKA and 0 if otherwise. We included as covariates several variables demonstrated in previous research to predict either receipt or outcome of TKA. Demographic characteristics included sex (male = 1, female = 0), a set of binary variables representing race/ethnicity (American Indian, Asian, African American, Other, and White, the omitted category in the analysis), and baseline age, which was coded in 3 groups: 60–74 years (omitted category), 75–84 years, and ≥85 years. Socioeconomic characteristics included education (<9 years [the omitted category], 9–12 years, and ≥13 years), income (coded in hundreds of dollars), and insurance coverage in addition to Medicare, which included private insurance and Medicaid. We also included baseline measures of self-rated health and comorbid conditions that limit mobility. Self-rated health was coded in 5 categories: poor, fair, good, very good, and excellent (omitted category). Binary variables indicated the presence of Parkinson's disease, osteoporosis, Alzheimer's disease, hardening of arteries, stroke, congestive heart disease, other heart conditions, and whether a respondent had a body mass index >30. For the baseline Nagi Disability Scale, IADL Scale, and ADL Scale, “no difficulty” was the omitted category.
In a second step, a no-treatment group was defined by matching treated patients with “controls” based on the predicted probabilities of receiving a TKA. The purpose was to match the controls as closely as possible to the treated patients based on the predicted probabilities of receiving a TKA. The propensity score procedure defines block groups. Within each block group, the average predicted probability of receiving the procedure does not differ significantly between the treated patients and the controls. In our analysis, the 6 resulting blocks of treatment and no-treatment persons were generated using the kernel matching method to compute the average treatment effect of TKA on physical functioning measures (22). Standard errors were calculated using the bootstrapping method. All analyses were performed using Stata 9.0 software (StataCorp, College Station, TX).
There is consensus among statisticians that conventional significance tests are inappropriate for assessing the fit of propensity score matching (23, 24). The Stata software used in this analysis splits the sample into the number of intervals required to ensure that the balancing hypothesis is met (i.e., that the means of each characteristic do not differ between treated and untreated units) (22). If necessary, subjects will be dropped from the sample to meet the balancing criterion. As shown in Figure 1, in this analysis, 3 TKA recipients and 1 untreated respondent were dropped from the sample for this reason.
In lieu of conventional significance testing, Austin et al (23), among others, propose the use of standardized difference scores for assessing the adequacy of the balance between treated and untreated groups in observational studies. They recommend that a standardized difference score of >10% represents meaningful imbalance between groups. Of the 1,816 matches generated by the propensity score analysis, only 3 pairs had standardized difference scores of >10%. Overall, the balancing criterion was well met.
RESULTS
Table 1 presents percentages (and means for income) for the independent variables for the treatment and no-treatment groups at baseline. Neither sex nor race/ethnicity differed significantly across groups. Respondents ages ≥85 years or with <9 years of education were significantly less likely to receive TKA. Self-rated health and comorbid conditions did not differ across groups. Two of the 3 Nagi Disability Scale activities (stooping and walking) and 3 of the ADL Scale tasks (bathing, walking, and using the toilet) differed significantly across groups. As expected, the treatment group was more impaired than the no-treatment group. IADL Scale limitations were not significantly related to receipt of TKA.
| Treatment group (n = 259) | No-treatment group (n = 1,816) | P† | |
|---|---|---|---|
| |||
| Demographic characteristics | |||
| Male | 33.98 | 33.37 | NS |
| Race/ethnicity | |||
| American Indian | 1.16 | 0.39 | NS |
| Asian | 0.39 | 1.43 | NS |
| African American | 6.56 | 9.86 | NS |
| White | 90.73 | 86.62 | NS |
| Other | 1.16 | 1.71 | NS |
| Married | 53.28 | 50.17 | NS |
| Age, years | |||
| 60–74 | 44.40 | 38.88 | <0.001 |
| 75–84 | 50.97 | 46.37 | <0.001 |
| ≥85 | 4.63 | 14.76 | <0.001 |
| Socioeconomic characteristics | |||
| Education attained | |||
| <9 years | 14.67 | 21.42 | <0.05 |
| 9–12 years | 50.97 | 48.51 | NS |
| ≥13 years | 34.36 | 30.07 | NS |
| Income, mean $ (×100) | 261.08 | 277.91 | NS |
| Other coverage | |||
| Private insurance | 81.85 | 77.75 | NS |
| Medicaid | 11.58 | 16.13 | NS |
| Health and comorbidities | |||
| Self-reported health | |||
| Excellent/very good/good | 74.52 | 66.96 | NS |
| Fair | 18.53 | 21.70 | NS |
| Poor | 6.95 | 8.59 | NS |
| Comorbidities | |||
| Parkinson's disease | 1.54 | 1.43 | NS |
| Osteoporosis | 21.24 | 20.93 | NS |
| Alzheimer's disease | 1.54 | 2.04 | NS |
| Artery hardening | 12.74 | 13.66 | NS |
| Stroke | 9.65 | 10.96 | NS |
| Other heart conditions | 28.96 | 35.02 | NS |
| Congestive heart disease | 15.44 | 16.63 | NS |
| Baseline physical functioning | |||
| Nagi Disability Scale activities | |||
| No difficulty stooping | 23.17 | 45.87 | <0.01 |
| Difficulty stooping | 30.50 | 28.25 | NS |
| Not able to stoop | 46.33 | 25.88 | <0.01 |
| No difficulty lifting | 71.43 | 74.67 | NS |
| Difficulty lifting | 10.42 | 11.40 | NS |
| Not able to lift | 18.15 | 13.93 | NS |
| No difficulty walking | 45.56 | 56.72 | <0.01 |
| Difficulty walking | 15.44 | 14.15 | NS |
| Not able to walk | 39.00 | 29.13 | <0.01 |
| IADL Scale activities | |||
| Light housework | 26.25 | 21.31 | NS |
| Heavy housework | 59.85 | 55.12 | NS |
| Preparing meals | 21.24 | 18.12 | NS |
| Shopping | 25.87 | 24.50 | NS |
| ADL Scale activities | |||
| Bathing | 25.48 | 18.72 | <0.01 |
| Getting in/out of chair | 29.34 | 24.01 | NS |
| Dressing | 13.51 | 11.40 | NS |
| Walking | 51.74 | 40.69 | <0.001 |
| Use of toilet | 16.22 | 10.74 | <0.01 |
Table 2 presents descriptive statistics for changes in physical functioning scores between the presurgical and postsurgical interviews. Metric-based change scores are presented, and significance tests are reported for both within-group changes and cross-group differences. Differences between groups were significant for 9 of the 12 physical functioning tasks (all but heavy housework, getting in/out of a chair, and dressing); the treatment group members reported significantly better functioning than members of the no-treatment group. There was a clear pattern: physical functioning of treatment group members improved over time and that of persons who did not receive TKA declined over time. Examining changes within the treatment group, 10 of the 12 change scores represented statistically significant improvements in functioning. Within the no-treatment group, there were significant declines in functioning for 5 of the 12 tasks.
| Treatment group (n = 259) | No-treatment group (n = 1,816) | P† | |
|---|---|---|---|
| |||
| Nagi Disability Scale activities | |||
| Stooping | 20.85‡ | −2.53 | <0.001 |
| Walking | 30.12‡ | −2.53 | <0.001 |
| Lifting | 11.20§ | −2.59¶ | <0.01 |
| IADL Scale limitations | |||
| Light housework | 5.79¶ | −0.83¶ | <0.05 |
| Heavy housework | 5.41¶ | −1.49 | NS |
| Preparing meals | 4.25¶ | −1.93¶ | <0.05 |
| Shopping | 6.18§ | −1.65¶ | <0.01 |
| ADL Scale limitations | |||
| Bathing | 5.41¶ | −3.02‡ | <0.001 |
| Dressing | 0.00 | −0.88 | NS |
| Getting in/out of chair | 4.25 | 0.06 | NS |
| Use of toilet | 5.41§ | 0.11 | <0.01 |
| Walking | 10.42§ | 0.50 | <0.001 |
Table 3 presents the average treatment effect of TKA for each Nagi Disability Scale, IADL Scale, and ADL Scale activity. The average treatment effects were statistically significant for 2 of the 3 Nagi Disability Scale activities (lifting and walking) and for 3 of the 4 IADL Scale tasks (light housework, heavy housework, and shopping). In contrast, only 1 of the average treatment effects for the 5 ADL Scale tasks (bathing) was significant.
| Baseline covariate (range) | Treatment effect, % |
|---|---|
| |
| Nagi Disability Scale activities (−3 to 3) | |
| Stooping | 7.8 (−0.02 to 0.16) |
| Lifting | 14.0 (0.61 to 0.22)† |
| Walking | 27.6 (0.15 to 0.37)† |
| IADL Scale activities (−1 to 1) | |
| Light housework | 5.3 (0.00 to 0.10)† |
| Heavy housework | 6.1 (0.00 to 0.14)† |
| Preparing meals | 4.6 (−0.00 to 0.10) |
| Shopping | 7.8 (0.04 to 0.13)† |
| ADL Scale activities (−1 to 1) | |
| Bathing | 6.9 (0.01 to 0.13)† |
| Dressing | 0.5 (−0.03 to 0.055) |
| Getting in/out of chair | 3.6 (−0.00 to 0.10) |
| Walking | 6.9 (−0.01 to 0.15) |
| Use of toilet | 4.2 (−0.00 to 0.10) |
DISCUSSION
This study demonstrates that TKA is associated with improvements in both basic and advanced activities of daily living—known prerequisites for self care and living independently. Recipients of TKA improved significantly in 1 basic aspect of self care (bathing), 3 more difficult tasks (light housework, heavy housework, and shopping), and 2 advanced activities of daily living (walking 2–3 blocks and lifting weights up to 10 pounds). In contrast, persons who did not have TKA exhibited overall patterns of decline in physical functioning. It is not surprising that improvements in Nagi Disability Scale activities and IADL Scale tasks were more common than those for ADL Scale tasks because the latter represent very basic indicators of physical functioning. If an individual is disabled in one or more ADL Scale tasks, the odds of recovery of function are especially low (8, 9).
This study has several strengths. The effects of TKA on physical functioning were examined using data from a national sample. Physical functioning was measured at 3 levels of severity, all of which improved after TKA. Propensity scores were used to match TKA and no-TKA groups on demographic factors, self-rated health, comorbid medical conditions, and baseline levels of functioning. Propensity scores are generally superior to analysis of covariance procedures when estimating treatment effects using observational data (25). The propensity matching worked very well in these data. This was probably because even at the bivariate level, only 2 of the sociodemographic variables and none of the health variables differed significantly between the treatment and no-treatment groups (see Table 1).
We acknowledge the study's limitations. Although the MCBS sample was large, fewer than 300 participants received TKA and met the criteria for inclusion in the analysis. The interval between baseline and followup interviews was ∼2 months longer for the no-treatment group than for the treatment group. We controlled for interval length in the multivariate logit model, however, and it was not a significant predictor. Use of propensity scores was helpful for establishing equivalence between the TKA and no-TKA groups, but this procedure does not permit use of sample weights, precluding population estimates. The measures of physical functioning were based on participants' self reports rather than on performance tests. Previous research strongly suggests, however, that older adults accurately report their functional capacities (19, 26).
Rates of disability in the older population have declined steadily since the 1980s (8, 9). Manton and Gu reported that the prevalence of disability cumulatively declined by 25%, from 26.2% to 19.7% of the older population, between 1982 and 1999 (9). Moreover, the rate of decline is increasing over time. This pattern is typically attributed to the long-term effects of public health measures introduced in the 20th century, rising levels of socioeconomic status, and historical trends of better health habits (26). Improvements in medical care are only rarely suggested as contributors to declining disability rates (27), although substantial research has reported the importance of improvements in health care for longevity (28, 29). Research on disability transitions indicates that, although transitions to a disabled status are most common, some older adults transition from disability to no disability—and transitions out of disability appear to be increasing over time (26, 30). Joint replacement is one likely way that medical care is contributing to declining rates of disability in the older population. The results of the present study are compatible with this conclusion. Additional research that examines the effects of medical procedures on overall disability status at the population level is a high priority for future efforts.
AUTHOR CONTRIBUTIONS
Dr. George had full access to all of the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis.
Study design. George, Ruiz, Sloan.
Acquisition of data. Sloan.
Analysis and interpretation of data. George, Ruiz, Sloan.
Manuscript preparation. George, Ruiz.
Statistical analysis. Ruiz.
REFERENCES
- 1, , , , , . A comparison of outcomes in osteoarthritis patients undergoing total hip and knee replacement surgery. Osteoarthritis Cartilage 2001; 9: 37–146.
- 2, , , . The effect of age on pain, function, and quality of life after total hip and knee arthroplasty. Arch Intern Med 2001; 161: 454–60.
- 3, , , , , . Health-related quality of life after elective surgery: measurement of longitudinal changes. J Gen Intern Med 1997; 12: 686–97.Direct Link:
- 4, , . Health-related quality of life outcomes after total hip and knee arthroplasties in a community-based population. J Rheumatol 2000; 27: 745–52.
- 5National Institutes of Health. NIH consensus statement on total knee replacement. NIH Consens State Sci Statements 2003; 20: 1–36.
- 6, , , , , . Does total knee replacement restore normal knee function? Clin Orthop 2005; 431: 157–65.
- 7, , , , , , et al. Social and personal consequences of disability in adults with hip and knee arthroplasty: a French national community based survey. J Rheumatol 2004; 31: 759–66.
- 8, , . Recent trends in disability and functioning among older adults in the United States. JAMA 2002; 288: 3137–46.
- 9, . Changes in the prevalence of chronic disability in the United States black and non-black population above age 65 from 1982 to 1999. Proc Natl Acad Sci U S A 2001; 98: 6354–9.
- 10, , . Cost effectiveness and quality of life in knee arthroplasty. Clin Orthop Relat Res 1997; 345: 134–9.
- 11, , , , , , et al. Effectiveness of hip and knee replacement surgery in terms of quality-adjusted life years and costs. Acta Orthop 2007; 78: 108–115.
- 12, , , , , , et al. Trends in epidemiology of knee arthroplasty in the United States, 1990–2000. Arthritis Rheum 2005; 52: 3928–33.Direct Link:
- 13, , , , , . Prevalence of primary and revision total hip and knee arthroplasty in the United States from 1990 through 2002. J Bone Joint Surg Am 2005; 87: 1487–97.
- 14, , , , , , et al. Racial/ethnic differences in surgical outcomes in veterans following knee or hip arthroplasty. Arthritis Rheum 2005; 52: 3143–51.Direct Link:
- 15, , , , for the Toronto Arthroplasty Health Services Research Consortium. Perceptions of, and willingness to consider, total joint arthroplasty in a population-based cohort of individuals with disabling hip and knee arthritis. Arthritis Rheum 2004; 51: 635–41.Direct Link:
- 16
- 17, , , , . Indications for total hip and total knee arthroplasties—results of orthopaedic surveys. J Arthroplasty 1996; 11: 34–46.
- 18World Health Organization. International classification of impairments, disabilities, and handicaps. Geneva: World Health Organization; 1980.
- 19. Multidimensional functional assessment of older adults: the Duke older Americans resources and services procedures. Mahwah (NJ): Lawrence Erlbaum; 1988.
- 20, , , , . Studies of illness of the aged. The index of ADL: a standardized measure of biological and psychosocial functions. JAMA 1963; 185: 914–9.
- 21, . Equating health status measures with item response theory: illustrations with functional status items. Med Care 2000; 38: 1143–59.
- 22, . Estimation of average treatment effects based on propensity scores. Stata J 2002; 2: 358–77.
- 23, , . A comparison of the ability of different propensity score models to balance measured variables between treated and untreated subjects: a Monte Carlo study. Stat Med 2007; 26: 734–53.Direct Link:
- 24, , . Misunderstandings among experimentalists and observationalists: balance test fallacies in causal inference. Technical report; Princeton University. Available from: URL: http://imai.princeton.edu/research/balance.html.
- 25, Estimating treatment effects using observational data. JAMA 2007; 297: 314–6.
- 26, , . Further evidence on recent trends in the prevalence and incidence of disability among older Americans from two sources: the LSOA and the NHIS. J Gerontol B Psychol Sci Soc Sci 1997; 52: S59–71.
- 27. The reduction in disability among the elderly. Proc Natl Acad Sci U S A 2001; 98: 6546–7.
- 28, . The value of life and the rise in health care spending. Q J Econ 2007; 122: 39–72.
- 29, . The value of health and longevity. J Political Economy 2006; 114: 871–904.
- 30, , , . Transitions between states of disability and independence among older persons. Am J Epidemiol 2005; 161: 575–84.

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