, Volume 51, Issue 1, pp 51–71 | Cite as

Mortality Deceleration and Mortality Selection: Three Unexpected Implications of a Simple Model

  • Elizabeth Wrigley-FieldEmail author


Unobserved heterogeneity in mortality risk is pervasive and consequential. Mortality deceleration—the slowing of mortality’s rise with age—has been considered an important window into heterogeneity that otherwise might be impossible to explore. In this article, I argue that deceleration patterns may reveal surprisingly little about the heterogeneity that putatively produces them. I show that even in a very simple model—one that is composed of just two subpopulations with Gompertz mortality—(1) aggregate mortality can decelerate even while a majority of the cohort is frail; (2) multiple decelerations are possible; and (3) mortality selection can produce acceleration as well as deceleration. Simulations show that these patterns are plausible in model cohorts that in the aggregate resemble cohorts in the Human Mortality Database. I argue that these results challenge some conventional heuristics for understanding the relationship between selection and deceleration; undermine certain inferences from deceleration timing to patterns of social inequality; and imply that standard parametric models, assumed to plateau at most once, may sometimes badly misestimate deceleration timing—even by decades.


Mortality deceleration Mortality selection Heterogeneity Methods Logistic models 



This research was supported by a graduate research fellowship from the National Science Foundation, a dissertation fellowship from the Ford Foundation, and core grants to the Center for Demography and Ecology (R24 HD047873) and Center for Demography of Health and Aging (P30 AG017266) at the University of Wisconsin–Madison. The author thanks, for helpful feedback, Felix Elwert, James Montgomery, Jenny Conrad, Michal Engelman, Duncan Gillespie, Jeffrey Grigg, Paul Hanselman, Anna Haskins, Michelle Niemann, Jenna Nobles, and Sarah Zureick-Brown, along with excellent reviewers and the Editor; and, for technical assistance, Russell Dimond, David Siegel, and the Social Science Computing Cooperative at the University of Wisconsin–Madison.

Supplementary material

13524_2013_256_MOESM1_ESM.doc (2.3 mb)
ESM 1 (DOC 2.34 mb)
13524_2013_256_MOESM2_ESM.docx (1.6 mb)
ESM 2 (DOCX 1.57 mb)
13524_2013_256_MOESM3_ESM.docx (345 kb)
ESM 3 (DOCX 345 kb)


  1. Beard, R. E. (1959). Notes on some mathematical mortality models. In G. E. W. Wolstenholme & M. O’Connor (Eds.), The lifespan of animals (pp. 302–311). Boston, MA: Little, Brown.Google Scholar
  2. Beard, R. E. (1971). Some aspects of theories of mortality, cause of death analysis, forecasting and stochastic processes. In W. Brass (Ed.), Biological aspects of demography (pp. 57–68). London, UK: Taylor & Francis.Google Scholar
  3. Bebbington, M., Lai, C.-D., & Zitikis, R. (2007). Modeling human mortality using mixtures of bathtub shaped failure distributions. Journal of Theoretical Biology, 245, 528–538.CrossRefGoogle Scholar
  4. Berkman, L., Singer, B., & Manton, K. (1989). Black/white differences in health status and mortality among the elderly. Demography, 26, 661–678.CrossRefGoogle Scholar
  5. Bongaarts, J. (2005). Long-range trends in adult mortality: Models and projection methods. Demography, 42, 23–49.CrossRefGoogle Scholar
  6. Brown, D. C., Hayward, M., Montez, J. K., Hidajat, M. M., Hummer, R. A., & Chiu, C.-T. (2012). The significance of education for mortality compression in the United States. Demography, 49, 819–840.CrossRefGoogle Scholar
  7. Carey, J. R., Liedo, P., Orozco, D., & Vaupel, J. W. (1992). Slowing of mortality rates at older ages in large medfly cohorts. Science, 258, 457–461.CrossRefGoogle Scholar
  8. Costa, D. L. (2012). Scarring and mortality selection among Civil War POWs: A long-term mortality, morbidity, and socioeconomic follow-up. Demography, 49, 1185–1206.CrossRefGoogle Scholar
  9. Curtsinger, J. W., Fukui, H. H., Townsend, D. R., & Vaupel, J. W. (1992). Demography of genotypes: Failure of the limited life-span paradigm in Drosophila melanogaster. Science, 258, 461–463.CrossRefGoogle Scholar
  10. Drapeau, M. D., Gass, E. K., Simison, M. D., Mueller, L. D., & Rose, M. R. (2000). Testing the heterogeneity theory of late-life mortality plateaus by using cohorts of Drosophila melanogaster. Experimental Gerontology, 35, 71–84.CrossRefGoogle Scholar
  11. Dupre, M. E., Franzese, A. T., & Parrado, E. A. (2006). Religious attendance and mortality: Implications for the black-white mortality crossover. Demography, 43, 141–164.CrossRefGoogle Scholar
  12. Edwards, R., & Tuljapurkar, S. (2005). Inequality in lifespans and a new perspective on mortality convergence across industrialized countries. Population and Development Review, 31, 645–674.CrossRefGoogle Scholar
  13. Engelman, M., Canudas-Romo, V., & Agree, E. (2010). The implications of increased survivorship for mortality variation in aging populations. Population and Development Review, 36, 511–539.CrossRefGoogle Scholar
  14. Finkelstein, M. (2012). Discussing the Strehler-Mildvan model of mortality. Demographic Research, 26(article 9), 191–206. doi: 10.4054/DemRes.2012.26.9 CrossRefGoogle Scholar
  15. Fukui, H. H., Xiu, L., & Curtsinger, J. W. (1993). Slowing of age-specific mortality rates in Drosophila melanogaster. Experimental Gerontology, 28, 585–599.CrossRefGoogle Scholar
  16. Gampe, J. (2010). Human mortality beyond age 110. In H. Maier, J. Gampe, B. Jeune, J.-M. Robine, & J. Vaupel (Eds.), Demographic Research Monographs 7: Supercentenarians (pp. 219–230). Berlin, Germany: Springer.Google Scholar
  17. Heathcote, C. R., Puza, B. D., & Roberts, S. P. (2009). The use of aggregate data to estimate Gompertz-type old-age mortality in heterogeneous populations. Australian & New Zealand Journal of Statistics, 51, 481–497.CrossRefGoogle Scholar
  18. Horiuchi, S. (1997). Postmenopausal acceleration of age-related mortality increase. Journals of Gerontology Series A: Biological Sciences, 52, B78–B92.CrossRefGoogle Scholar
  19. Horiuchi, S., & Coale, A. J. (1990). Age patterns of mortality for older women: An analysis using the age-specific rate of mortality change with age. Mathematical Population Studies, 2, 245–267.CrossRefGoogle Scholar
  20. Horiuchi, S., & Wilmoth, J. R. (1997). Age patterns of the life table aging rate for major causes of death in Japan, 1951–1990. Journals of Gerontology Series A: Biological Sciences and Medical Sciences, 52, B67–B77.CrossRefGoogle Scholar
  21. Horiuchi, S., & Wilmoth, J. R. (1998). Deceleration in the age pattern of mortality at older ages. Demography, 35, 391–412.CrossRefGoogle Scholar
  22. Human Mortality Database (HMD). (2011). University of California, Berkeley (USA), and Max Planck Institute for Demographic Research (Germany). Retrieved from or
  23. Kannisto, V. (1992). Frailty and survival. Genus, 47, 101–118.Google Scholar
  24. Kestenbaum, B. (1992). A description of the extreme aged population based on improved Medicare enrollment data. Demography, 29, 565–580.CrossRefGoogle Scholar
  25. Kulminski, A. M., Ukraintseva, S. V., Akushevich, I. V., Arbeev, K. G., & Yashin, A. I. (2007). Cumulative health deficiencies as a characteristic of long life. Journal of the American Geriatrics Society, 55, 935–940.CrossRefGoogle Scholar
  26. Lynch, S. M., & Brown, J. S. (2001). Reconsidering mortality compression and deceleration: An alternative model of mortality rates. Demography, 38, 79–95.CrossRefGoogle Scholar
  27. Lynch, S. M., Brown, J. S., & Harmsen, K. G. (2003). Black-white differences in mortality compression and deceleration and the mortality crossover reconsidered. Research on Aging, 25, 456–483.CrossRefGoogle Scholar
  28. Manton, K., Poss, S. S., & Wing, S. (1979). The black/white mortality crossover: Investigation from the perspective of the components of aging. The Gerontologist, 19, 291–300.CrossRefGoogle Scholar
  29. Masters, R. K. (2012). Uncrossing the U.S. black-white mortality crossover: The role of cohort forces in life course mortality risk. Demography, 49, 773–796.CrossRefGoogle Scholar
  30. Missov, T. I., & Finkelstein, M. S. (2011). Admissible mixing distributions for a general class of mixture survival models with known asymptotics. Theoretical Population Biology, 80, 64–70.CrossRefGoogle Scholar
  31. Mueller, L. D., Rauser, C. L., & Rose, M. R. (2011). Does aging stop? Oxford, UK: Oxford University Press.CrossRefGoogle Scholar
  32. Olshansky, S. J. (1998). On the biodemography of aging: A review essay. Population and Development Review, 24, 381–393.CrossRefGoogle Scholar
  33. Palloni, A. (2006). Reproducing inequalities: Luck, wallets, and the enduring effects of childhood health. Demography, 43, 587–615.CrossRefGoogle Scholar
  34. Preston, S. H., Heuveline, P., & Guillot, M. (2001). Demography: Measuring and modeling population processes. New York: Wiley-Blackwell.Google Scholar
  35. Rau, R., Muszynska, M., & Baudisch, A. (2009, May). At what age does mortality start to decelerate? Paper presented at the annual meeting of the Population Association of America, Detroit, MI.Google Scholar
  36. Rauser, C. L., Abdel-Aal, Y., Sheih, J. A., Suen, C. W., Mueller, L. D., & Rose, M. R. (2005). Lifelong heterogeneity in fecundity is insufficient to explain late-life fecundity plateaus in Drosophila melanogaster. Experimental Gerontology, 40, 660–670.CrossRefGoogle Scholar
  37. Robert, S. A., & House, J. S. (2000). Socioeconomic inequalities in health: An enduring sociological problem. In C. E. Bird, P. Conrad, & A. M. Fremont (Eds.), Handbook of medical sociology (5th ed., pp. 79–97). Upper Saddle River, NJ: Prentice Hall.Google Scholar
  38. Rodriguez, G. (1994). Statistical issues in the analysis of reproductive histories using hazard models. Annals of the New York Academy of Sciences, 709, 266–279.CrossRefGoogle Scholar
  39. Rogers, R. G. (2002). Mortality differentials in a diverse society. In N. A. Denton & S. Tolnay (Eds.), American diversity: A demographic challenge for the twenty-first century (pp. 129–154). Albany, NY: SUNY Press.Google Scholar
  40. Steinsaltz, D. (2005). Re-evaluating a test of the heterogeneity explanation for mortality plateaus. Experimental Gerontology, 40, 101–113.CrossRefGoogle Scholar
  41. Steinsaltz, D., & Evans, S. N. (2004). Markov mortality models: Implications of quasistationarity and initial distributions. Theoretical Population Biology, 65, 319–337.CrossRefGoogle Scholar
  42. Steinsaltz, D. R., & Wachter, K. W. (2006). Understanding mortality rate deceleration and heterogeneity. Mathematical Population Studies, 13, 19–37.CrossRefGoogle Scholar
  43. Strehler, B. L., & Mildvan, A. S. (1960). General theory of mortality and aging. Science, 132, 14–21.CrossRefGoogle Scholar
  44. Thatcher, A. R., Kannisto, V., & Vaupel, J. W. (1998). The force of mortality at ages 80 to 120. Odense, Denmark: Odense University Press.Google Scholar
  45. Vaupel, J. W. (1997). Trajectories of mortality at advanced ages. In K. W. Wachter & C. E. Finch (Eds.), Between Zeus and the salmon: The biodemography of longevity (pp. 17–37). Washington, DC: National Academy Press.Google Scholar
  46. Vaupel, J. W., & Carey, J. R. (1993). Compositional interpretations of medfly mortality. Science, 260, 1666–1667.CrossRefGoogle Scholar
  47. Vaupel, J. W., Manton, K. G., & Stallard, E. (1979). Impact of heterogeneity in individual frailty on the dynamics of mortality. Demography, 16, 439–454.CrossRefGoogle Scholar
  48. Vaupel, J. W., & Yashin, A. I. (1985). Heterogeneity’s ruses: Some surprising effects of selection on population dynamics. American Statistician, 39, 176–185.Google Scholar
  49. Vaupel, J. W., & Zhang, Z. (2010). Attrition in heterogeneous cohorts. Demographic Research, 23(article 26), 737–748. doi: 10.4054/DemRes.2010.23.26 CrossRefGoogle Scholar
  50. Wachter, K. W., & Finch, C. E. (Eds.). (1997). Between Zeus and the salmon: The biodemography of longevity. Washington, DC: National Academy Press.Google Scholar
  51. Zajacova, A., Goldman, N., & Rodriguez, G. (2009). Unobserved heterogeneity can confound the effect of education on mortality. Mathematical Population Studies, 16, 153–173.CrossRefGoogle Scholar
  52. Zheng, H., Yang, Y., & Land, K. C. (2011). Heterogeneity in the Strehler-Mildvan general theory of mortality and aging. Demography, 48, 267–290.CrossRefGoogle Scholar

Copyright information

© Population Association of America 2014

Authors and Affiliations

  1. 1.MadisonUSA

Personalised recommendations