Abstract
Longitudinal methods aggregate individual health histories to produce inferences about aging populations, but to what extent do these summaries reflect the experiences of older adults? We describe the assumption of gradual change built into several influential statistical models and draw on widely used, nationally representative survey data to empirically compare the conclusions drawn from mixed-regression methods (growth curve models and latent class growth analysis) designed to capture trajectories with key descriptive statistics and methods (multistate life tables and sequence analysis) that depict discrete states and transitions. We show that individual-level data record stasis irregularly punctuated by relatively sudden change in health status or mortality. Although change is prevalent in the sample, for individuals it occurs rarely, at irregular times and intervals, and in a nonlinear and multidirectional fashion. We conclude by discussing the implications of this punctuated equilibrium pattern for understanding health changes in individuals and the dynamics of inequality in aging populations.
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References
Abbott, A. (1995). Sequence analysis: New methods for old ideas. Annual Review of Sociology, 21, 93–113.
Abbott, A., & Tsay, A. (2000). Sequence analysis and optimal matching methods in sociology review and prospect. Sociological Methods & Research, 29, 3–33.
Armstrong, D. (2017). Clinical prediction and the idea of a population. Social Studies of Science, 47, 288–299.
Barban, N., & Billari, F. C. (2012). Classifying life course trajectories: A comparison of latent class and sequence analysis. Journal of the Royal Statistical Society, Series C: Applied Statistics, 61, 765–784.
Baynton, D. C. (2013). Disability and the justification of inequality in American history. In L. J. Davis (Ed.), The disability studies reader (4th ed., pp. 17–33). New York, NY: Routledge.
Ben-Shlomo, Y., & Kuh, D. (2002). A life course approach to chronic disease epidemiology: Conceptual models, empirical challenges and interdisciplinary perspectives. International Journal of Epidemiology, 31, 285–293.
Billari, F. C. (2001). Sequence analysis in demographic research. Canadian Studies in Population, 28, 439–458.
Bishop, N. J., Eggum-Wilkens, N. D., Haas, S. A., & Kronenfeld, J. J. (2016). Estimating the co-development of cognitive decline and physical mobility limitations in older U.S. adults. Demography, 53, 337–364.
Bolano, D., & Berchtold, A. (2016). General framework and model building in the class of hidden mixture transition distribution models. Computational Statistics & Data Analysis, 93, 131–145.
Bolano, D., Berchtold, D., & Bürge, E. (2018). The heterogeneity of disability trajectories in later life: Dynamics of activities of daily living performance among nursing home residents. Journal of Aging and Health, 31, 1315–1336.
Bollen, K. A., & Curran, P. J. (2006). Latent curve models: A structural equation perspective. Hoboken, NJ: Wiley.
Brown, T. H., O’Rand, A. M., & Adkins, D. E. (2012). Race-ethnicity and health trajectories: Tests of three hypotheses across multiple groups and health outcomes. Journal of Health and Social Behavior, 53, 359–377.
Clipp, E., Pavalko, E., & Elder, G., Jr. (1992). Trajectories of health: In concept and empirical pattern. Behavior, Health, and Aging, 2, 159–179.
Crimmins, E. M., Hayward, M. D., Hagedorn, A., Saito, Y., & Brouard, N. (2009). Change in disability-free life expectancy for Americans 70 years old and older. Demography, 46, 627–646.
Crimmins, E. M., Hayward, M. D., & Saito, Y. (1994). Changing mortality and morbidity rates and the health status and life expectancy of the older population. Demography, 31, 159–175.
Curran, P. J., Obeidat, K., & Losardo, D. (2010). Twelve frequently asked questions about growth curve modeling. Journal of Cognition and Development, 11, 121–136.
Dannefer, D. (2003). Cumulative advantage/disadvantage and the life course: Cross-fertilizing age and social science theory. Journals of Gerontology, Series B: Psychological Sciences & Social Sciences, 58, S327–S337.
DiPrete, T. A., & Eirich, G. M. (2006). Cumulative advantage as a mechanism for inequality: A review of theoretical and empirical developments. Annual Review of Sociology, 32, 271–297.
Elder, G. H., Jr. (1985). Life course dynamics: Trajectories and transitions, 1968–1980. Ithaca, NY: Cornell University Press.
Eldredge, N., & Gould, S. J. (1972). Punctuated equilibria: An alternative to phyletic gradualism. In T. J. M. Schopf (Ed.), Models in paleobiology (pp. 82–115). San Francisco, CA: Freeman Cooper.
Ferraro, K. F., Schafer, M. H., & Wilkinson, L. R. (2016). Childhood disadvantage and health problems in middle and later life: Early imprints on physical health? American Sociological Review, 81, 107–133.
Ferraro, K. F., & Shippee, T. P. (2009). Aging and cumulative inequality: How does inequality get under the skin? Gerontologist, 49, 333–343.
Fitzmaurice, G., & Molenberghs, G. (2009). Advances in longitudinal data analysis: An historical perspective. In G. Fitzmaurice, M. Davidian, G. Verbeke, & G. Molenbergs (Eds.), Longitudinal data analysis (pp. 3–30). Boca Raton, FL: CRC.
Gabadinho, A., Ritschard, G., Müller, N. S., & Studer, M. (2011). Analyzing and visualizing state sequences in R with TraMineR. Journal of Statistical Software, 40(4), 1–37.
George, L. K. (2009). Conceptualizing and measuring trajectories. In G. H. Elder, Jr. & J. Z. Giele (Eds.), The craft of life course research (pp. 163–186). New York, NY: Guilford Press.
Gill, T. M., Gahbauer, E. A., Han, L., & Allore, H. G. (2010). Trajectories of disability in the last year of life. New England Journal of Medicine, 362, 1173–1180.
Gould, S. J. (1985). The median isn’t the message. Discover, 6(6), 40–42.
Gueorguieva, R., Sindelar, J. L., Falba, T. A., Fletcher, J. M., Keenan, P., Wu, R., & Gallo, W. T. (2009). The impact of occupation on self-rated health: Cross-sectional and longitudinal evidence from the Health and Retirement Survey. Journals of Gerontology, Series B: Psychological Sciences & Social Sciences, 64, 118–124.
Haas, S. (2008). Trajectories of functional health: The “long arm” of childhood health and socioeconomic factors. Social Science & Medicine, 66, 849–861.
Han, L., Allore, H., Murphy, T., Gill, T., Peduzzi, P., & Lin, H. (2013). Dynamics of functional aging based on latent-class trajectories of activities of daily living. Annals of Epidemiology, 23, 87–92.
Hayward, M. D., & Gorman, B. K. (2004). The long arm of childhood: The influence of early-life social conditions on men’s mortality. Demography, 41, 87–107.
Hayward, M. D., Hummer, R. A., Chiu, C.-T., González-González, C., & Wong, R. (2014). Does the Hispanic paradox in U.S. adult mortality extend to disability? Population Research and Policy Review, 33, 81–96.
Holliday, R. (1995). Understanding ageing (Developmental and Cell Biology Series, Vol. 30). Cambridge, UK: Cambridge University Press.
Jackson, H., Engelman, M., & Bandeen-Roche, K. (2019). Robust respondents and lost limitations: The implications of nonrandom missingness for the estimation of health trajectories. Journal of Aging and Health, 31, 685–708.
Johnson-Hanks, J. A. (2015). Populations are composed one event at a time. In P. Kreager, B. Winney, S. Ulijaszek, & C. Capelli (Eds.), Population in the human sciences: Concepts, models, evidence (pp. 238–256). Oxford, UK: Oxford University Press.
Jung, T., & Wickrama, K. A. S. (2008). An introduction to latent class growth analysis and growth mixture modeling. Social and Personality Psychology Compass, 2, 302–317.
Juster, F. T., & Suzman, R. (1995). An overview of the Health and Retirement Study. Journal of Human Resources, 30(Special Issue), S7–S56.
Liang, J., Wang, C.-N., Xu, X., Hsu, H.-C., Lin, H.-S., & Lin, Y.-H. (2010a). Trajectory of functional status among older Taiwanese: Gender and age variations. Social Science & Medicine, 71, 1208–1217.
Liang, J., Xu, X., Bennett, J. M., Ye, W., & Quiñones, A. R. (2010b). Ethnicity and changing functional health in middle and late life: A person-centered approach. Journals of Gerontology, Series B: Psychological Sciences & Social Sciences, 65, 470–481.
Liang, J., Xu, X., Quiñones, A. R., Bennett, J. M., & Ye, W. (2011). Multiple trajectories of depressive symptoms in middle and late life: Racial/ethnic variations. Psychology and Aging, 26, 761–777.
Lynch, S. M., & Taylor, M. G. (2016). Trajectory models for aging research. In L. K. George & K. F. Ferraro (Eds.), Handbook of aging and the social sciences (8th ed., pp. 23–51). San Diego, CA: Academic Press.
Maddox, G. L. (1987). Aging differently. Gerontologist, 27, 557–564.
Mehta, P. D., & West, S. G. (2000). Putting the individual back into individual growth curves. Psychological Methods, 5, 23–43.
Muthén, B., & Asparouhov, T. (2008). Growth mixture modeling: Analysis with non-Gaussian random effects. In G. Fitzmaurice, M. Davidian, G. Verbeke, & G. Molenberghs (Eds.), Longitudinal data analysis (pp. 143–165). Boca Raton, FL: CRC.
Muthén, L., & Muthén, B. (2013). Mplus 7.11. Los Angeles, CA: Muthén & Muthén.
Nagin, D. S. (2005). Group-based modeling of development. Cambridge, MA: Harvard University Press.
Nagin, D. S., & Tremblay, R. E. (2001). Analyzing developmental trajectories of distinct but related behaviors: A group-based method. Psychological Methods, 6, 18–34.
Nagin, D. S., & Tremblay, R. E. (2005). Developmental trajectory groups: Fact or a useful statistical fiction? Criminology, 43, 873–904.
Namboodiri, K., & Suchindran, C. M. (1987). Life table techniques and their applications. Orlando, FL: Academic Press.
National Center for Health Statistics. (2016). Health, United States, 2015: With special feature on racial and ethnic health disparities (DHHS Publication No. 2016-1232). Hyattsville, MD: National Center for Health Statistics.
Nelson, E. A., & Dannefer, D. (1992). Aged heterogeneity: Fact or fiction? The fate of diversity in gerontological research. Gerontologist, 32, 17–23.
Nesselroade, J. R. (1991). Interindividual differences in intraindividual change. In L. M. Collins & J. L. Horn (Eds.), Best methods for the analysis of change: Recent advances, unanswered questions, future directions (pp. 92–105). Washington, DC: American Psychological Association.
O’Rand, A. M. (1996). The precious and the precocious: Understanding cumulative disadvantage and cumulative advantage over the life course. Gerontologist, 36, 230–238.
Quiñones, A. R., Liang, J., Bennett, J. M., Xu, X., & Ye, W. (2011). How does the trajectory of multimorbidity vary across black, white, and Mexican Americans in middle and old age? Journals of Gerontology, Series B: Psychological Sciences & Social Sciences, 66, 739–749.
Raudenbush, S. W., & Bryk, A. S. (2002). Hierarchical linear models: Applications and data analysis methods (Vol. 1, 2nd ed.). Thousand Oaks, CA: Sage.
Rose, T. (2016). The end of average: How we succeed in a world that values sameness. London, UK: Penguin.
Saperstein, A., & Penner, A. M. (2012). Racial fluidity and inequality in the United States. American Journal of Sociology, 118, 676–727.
Schweber, L. (2006). Disciplining statistics: Demography and vital statistics in France and England, 1830–1885. Durham, NC: Duke University Press.
Shuey, K. M., & Willson, A. E. (2008). Cumulative disadvantage and black-white disparities in life-course health trajectories. Research on Aging, 30, 200–225.
Smith, G. D. (2011). Epidemiology, epigenetics and the “gloomy prospect”: Embracing randomness in population health research and practice. International Journal of Epidemiology, 40, 537–562.
Taylor, M. G., & Lynch, S. M. (2011). Cohort differences and chronic disease profiles of differential disability trajectories. Journals of Gerontology, Series B: Psychological Sciences & Social Sciences, 66, 729–738.
Vaupel, J. W., Manton, K. G., & Stallard, E. (1979). The impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16, 439–454.
Verbrugge, M. L., & Jette, A. M. (1994). The disablement process. Social Science & Medicine, 38, 1–14.
Warner, D. F., & Brown, T. H. (2011). Understanding how race/ethnicity and gender define age-trajectories of disability: An intersectionality approach. Social Science & Medicine, 72, 1236–1248.
Warren, J. R., Luo, L., Halpern-Manners, A., Raymo, J. M., & Palloni, A. (2015). Do different methods for modeling age-graded trajectories yield consistent and valid results? American Journal of Sociology, 120, 1809–1856.
Wickrama, K. A. S., Mancini, J. A., Kwag, K., & Kwon, J. (2013). Heterogeneity in multidimensional health trajectories of late old years and socioeconomic stratification: A latent trajectory class analysis. Journals of Gerontology, Series B: Psychological Sciences & Social Sciences, 68, 290–297.
Wolf, D. (2016). Late-life disability trends and trajectories. In L. K. George & K. F. Ferraro (Eds.), Handbook of aging and the social sciences (8th ed., pp. 77–100). San Diego, CA: Academic Press.
Wolf, D. A., & Gill, T. M. (2009). Modeling transition rates using panel current-status data: How serious is the bias? Demography, 46, 371–386.
Yaffee, R. A., & McGee, M. (2000). An introduction to time series analysis and forecasting: With applications of SAS® and SPSS®. San Diego, CA: Academic Press.
Zimmer, Z., Martin, L. G., Nagin, D. S., & Jones, B. L. (2012). Modeling disability trajectories and mortality of the oldest-old in China. Demography, 49, 291–314.
Acknowledgments
This research was supported by the Steven H. Sandell Grant Program for Junior Scholars in Retirement Research, the Network on Life Course Health Dynamics and Disparities in 21st Century America (NIA R24AG045061), the Center for Demography of Health and Aging (NIA P30 AG17266) at the University of Wisconsin–Madison, and the Epidemiology and Biostatistics of Aging Training Grant (NIA T32AG000247) at the Johns Hopkins Center on Aging and Health. An earlier version of the manuscript was presented at the 2017 annual meeting of the Population Association of America. We thank Joshua Garoon, Douglas Wolf, and two anonymous reviewers for thought-provoking comments that strengthened this article.
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Engelman, M., Jackson, H. Gradual Change, Homeostasis, and Punctuated Equilibrium: Reconsidering Patterns of Health in Later Life. Demography 56, 2323–2347 (2019). https://doi.org/10.1007/s13524-019-00826-x
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DOI: https://doi.org/10.1007/s13524-019-00826-x