, Volume 37, Issue 3, pp 253–265 | Cite as

Active life expectancy estimates for the U.S. elderly population: A multidimensional continuous-mixture model of functional change applied to completed Cohorts, 1982–1996

  • Kenneth G. Manton
  • Kenneth C. Land


An increment-decrement stochastic-process life table model that continuously mixes measures of functional change is developed to represent age transitions among highly refined disability states interacting simultaneously with mortality. The model is applied to data from the National Long Term Care Surveys of elderly persons in the years 1982 to 1996 to produce active life expectancy estimates based on completed-cohort life tables. At ages 65 and 85, comparisons with extant period estimates for 1990 show that our active life expectancy estimates are larger for both males and females than are extant period estimates based on coarse disability states.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Berkman, B., L.W.S. Foster, and E. Campion. 1989. “Failure to Thrive: Paradigm for the Frail Elderly.” The Gerontologist 29(50):654–59.Google Scholar
  2. Berkman, L., B. Singer, and K.G. Manton. 1989. “Black/White Differences in Health Status and Mortality Among the Elderly.” Demography 26:661–78.CrossRefGoogle Scholar
  3. Crimmins, E.M., Y. Saito, and D. Ingegneri. 1997. “Trends in Disability-Free Life Expectancy in the United States, 1970–90.” Population and Development Review 23:555–72.CrossRefGoogle Scholar
  4. Karlin, S. and L.S. Shapley. 1953. Geometry of Moment Spaces. Providence: American Mathematical Society.Google Scholar
  5. Katz, S. and C.A. Akpom. 1976. “A Measure of Primary Sociobiological Functions.” International Journal of Health Services 6:493–508.CrossRefGoogle Scholar
  6. Katz, S., L.G. Branch, M.H. Branson, J.A. Papsidero, J.C. Beck, and D.S. Greer. 1983. “Active Life Expectancy.” New England Journal of Medicine 309:1218–24.CrossRefGoogle Scholar
  7. Land, K.C., J.M. Guralnik, and D.G. Blazer. 1994. “Estimating Increment-Decrement Life Tables With Multiple Covariates From Panel Data: The Case of Active Life Expectancy.” Demography 31:297–319.CrossRefGoogle Scholar
  8. Lawton, M.P. and E.M. Brody. 1969. “Assessment of Older People: Self-Maintaining and Instrumental Activities of Daily Living.” Gerontology 9:179–86.Google Scholar
  9. Manton, K.G., L.S. Corder, and E. Stallard. 1993a. “Changes in the Use of Personal Assistance and Special Equipment 1982 to 1989: Results From the 1982 and 1989 NLTCS.” The Gerontologist 33:168–76.Google Scholar
  10. —. 1993b. “Estimates of Change in Chronic Disability and Institutional Incidence and Prevalence Rates in the U.S. Elderly Population From the 1982, 1984, and 1989 National Long Term Care Survey.” Journal of Gerontology: Social Sciences 47(4): S153–66.Google Scholar
  11. —. 1997. “Chronic Disability Trends in the U.S. Elderly Populations 1982 to 1994.” Proceedings of the National Academy of Sciences 94:2593–98.CrossRefGoogle Scholar
  12. Manton, K.G., E.S. Cornelius, and M.A. Woodbury. 1995. “Nursing Home Residents: A Multivariate Analysis of Their Medical, Behavioral, Psycho-Social, and Service Use Characteristics.” Journal of Gerontology: Medical Sciences 50(5):M242–51.Google Scholar
  13. Manton, K.G. and E. Stallard. 1996. “Longevity in the United States: Age and Sex Specific Evidence on Life Span Limits From Mortality Patterns: 1960–1990.” Journal of Gerontology: Biological Sciences 51A(5):B362–75.Google Scholar
  14. Manton, K.G., E. Stallard, and L.S. Corder. 1997. “Changes in the Age Dependence of Mortality and Disability: Cohort and Other Determinants.” Demography 34:135–57.CrossRefGoogle Scholar
  15. —. 1998. “The Dynamics of Dimensions of Age Related Disability 1982 to 1994 in the U.S. Elderly Population.” Journal of Gerontology: Biological Sciences 53A(1):B59–70.Google Scholar
  16. Manton, K.G., E. Stallard, and B.H. Singer. 1994. “Methods for Projecting the Future Size and Health Status of the U.S. Elderly Population.” Pp. 41–77 in Studies of the Economics of Aging, edited by D. Wise. Chicago: National Bureau of Economic Research and University of Chicago Press.Google Scholar
  17. Manton, K.G., E. Stallard, M.A. Woodbury, and J.E. Dowd. 1994. “Time-Varying Covariates in Models of Human Mortality and Aging: Multidimensional Generalization of the Gompertz.” Journal of Gerontology: Biological Sciences 49:B169–90.Google Scholar
  18. Manton, K.G. and M.A. Woodbury. 1983. “A Mathematical Model of the Physiological Dynamics of Aging and Correlate Mortality Selection II: Applications to the Duke Longitudinal Study.” Journal of Gerontology 38:406–13.Google Scholar
  19. Manton, K.G., M.A. Woodbury, and E. Stallard. 1991. “Statistical and Measurement Issues in Assessing the Welfare Status of Aged Individuals and Populations.” Journal of Econometrics 50:151–81.CrossRefGoogle Scholar
  20. Manton, K.G., M.A. Woodbury, and H.D. Tolley. 1994. Statistical Applications Using Fuzzy Sets. New York: Wiley.Google Scholar
  21. Matis, J.H. and T.E. Wehrly. 1979. “Stochastic Models of Compartmental Systems.” Biometrics 35:199–220.CrossRefGoogle Scholar
  22. Meltzer, D. 1997. “Accounting for Future Costs in Medical Cost-Effectiveness Analysis.” Journal of Health Economics 16:33–64.CrossRefGoogle Scholar
  23. Murray, C.J.L. and A.D. Lopez. 1996. The Global Burden of Disease: A Comprehensive Assessment of Mortality and Disability From Diseases, Injuries, and Risk Factors in 1990 and Projected to 2020. Geneva: World Health Organization.Google Scholar
  24. Nagi, S. 1976, “Epidemiology of Disability Among Adults in the United States.” Milbank Memorial Fund Quarterly 54:439–68.CrossRefGoogle Scholar
  25. Robine, J.M. 1994. “Disability-Free Life Expectancy Trends in France: 1981–1991, International Comparison.” Pp. 43–52 in Advances in Health Expectancies, edited by C. Mathers, J. McCallum, and J.M. Robine. Canberra: Australian Institute of Health and Welfare.Google Scholar
  26. Robine, J.M., C. Mathers, and N. Brouard. 1993. “Trends and Differentials in Disability-Free Life Expectancy.” Presented at the Conference on Health and Mortality Trends Among Elderly Populations: Determinants and Implications, Sendai, Japan.Google Scholar
  27. Rogers, A., R.G. Rogers, and L.G. Branch. 1989. “A Multistate Analysis of Active Life Expectancy.” Public Health Reports 104:222–26.Google Scholar
  28. Sanders, B.S. 1964. “Measuring Community Health Levels.” American Journal of Public Health 54:1063–70.CrossRefGoogle Scholar
  29. Schoen, R. 1988. Modeling Multigroup Populations. New York: Plenum.Google Scholar
  30. Singer, B. 1989. “Grade of Membership Representations: Concepts and Problems.” Pp. 317–34 in Festschreift for Samuel Karlin, edited by T.W. Anderson, K.B. Athreya, and D. Inglehart. Orlando: Academic Press.Google Scholar
  31. Social Security Administration. 1992. Life Tables for the United States Social Security Area 1900–2080 (Actuarial Study No. 107). SSA Pub. No. 11-11536. Baltimore, MD: Social Security Administration.Google Scholar
  32. Society of Actuaries. 1994. Group Annuity Mortality Table and 1994 Group Annuity Reserving Table. Schaumberg, IL: Society of Actuaries.Google Scholar
  33. Sullivan, D.F. 1971. “A Single Index of Mortality and Morbidity.” HSMHA Health Reports 86:347–54.CrossRefGoogle Scholar
  34. Talbot, L. 1996. “A Statistical Fuzzy Grade of Membership Approach to Unsupervised Clustering With Application to Remote Sensing.” PhD dissertation, Department of Statistics, Brigham Young University.Google Scholar
  35. Vaupel, J.W., J.R. Carey, K. Christensen, T.E. Johnson, A.I. Yashin, N.V. Holm, I.A. Iachine, V. Kannisto, A.A. Khazaeli, P. Liedo, V.D. Longo, Y. Zeng, K.G. Manton, and J.W. Curtsinger. 1998. “Biodemographic Trajectories of Longevity.” Science 280:855–60.CrossRefGoogle Scholar
  36. Vaupel, J.W., K.G. Manton, and E. Stallard. 1979. “The Impact of Heterogeneity in Individual Frailty on the Dynamics of Mortality.” Demography 16:439–54.CrossRefGoogle Scholar
  37. Weyl, H. 1949. “The Elementary Theory of Convex Polyhedra.” Pp. 3–10 in Contributions to the Theory of Games, edited by H. Kuhn and A. Tucker. Princeton, NJ: Princeton University Press.Google Scholar
  38. Wilkins, R. and O.B. Adams. 1983. “Health Expectancy in Canada, Late 1970s: Demographic, Regional, and Social Dimensions.” American Journal of Public Health 73:1073–80.CrossRefGoogle Scholar
  39. Woodbury, M.A. and J. Clive. 1974. “Clinical Pure Types as a Fuzzy Partition.” Journal of Cybernetics 4:111–21.CrossRefGoogle Scholar
  40. Woodbury, M.A., J. Clive, and A. Garson. 1978. “Mathematical Typology: A Grade of Membership Technique for Obtaining Disease Definition.” Computers and Biomedical Research 11:277–98.CrossRefGoogle Scholar
  41. Woodbury, M.A. and K.G. Manton. 1983a. “A Mathematical Model of the Physiological Dynamics of Aging and Correlated Mortality Selection I: Theoretical Development and Critiques.” Journal of Gerontology 38:398–405.Google Scholar
  42. —. 1983b. “A Theoretical Model of the Physiological Dynamics of Circulatory Disease in Human Populations.” Human Biology 55:417–41.Google Scholar
  43. World Health Organization. 1980. “International Classification of Impairments, Disabilities, and Handicaps: A Manual of Classification Relating to the Consequences of Disease.” Technical Report 706, World Health Organization, Geneva.Google Scholar
  44. Yashin, A.I. and K.G. Manton. 1997. “Effects of Unobserved and Partially Observed Covariate Processes on System Failure: A Review of Models and Estimation Strategies.” Statistical Science 12(1):20–34.CrossRefGoogle Scholar
  45. Yashin, A.I., K.G. Manton, M.A. Woodbury, and E. Stallard. 1995. “The Effects of Health Histories on Stochastic Process Models of Aging and Mortality.” Journal of Mathematical Biology 34(1):1–16.CrossRefGoogle Scholar

Copyright information

© Population Association of America 2000

Authors and Affiliations

  • Kenneth G. Manton
    • 1
  • Kenneth C. Land
    • 2
  1. 1.Center for Demographic StudiesDuke UniversityDurham
  2. 2.Department of SociologyDuke UniversityDurhamUSA

Personalised recommendations