1. Mortality Measurement at Advanced Ages Dr. Leonid A. Gavrilov, Ph.D. Dr. Natalia S. Gavrilova, Ph.D. Center on Aging NORC and The University of Chicago Chicago, Illinois, USA

2. What Do We Know About Mortality of Centenarians?

3. A Study That Answered This Question

4. M. Greenwood, J. O. Irwin. BIOSTATISTICS OF SENILITY

5. Mortality at Advanced Ages Source: Gavrilov L.A., Gavrilova N.S. The Biology of Life Span: A Quantitative Approach, NY: Harwood Academic Publisher, 1991

6. Mortality Deceleration in Other Species Invertebrates: Nematodes, shrimps, bdelloid rotifers, degenerate medusae (Economos, 1979) Drosophila melanogaster (Economos, 1979; Curtsinger et al., 1992) Medfly (Carey et al., 1992) Housefly, blowfly (Gavrilov, 1980) Fruit flies, parasitoid wasp (Vaupel et al., 1998) Bruchid beetle (Tatar et al., 1993) Mammals: Mice (Lindop, 1961; Sacher, 1966; Economos, 1979) Rats (Sacher, 1966) Horse, Sheep, Guinea pig (Economos, 1979; 1980) However no mortality deceleration is reported for Rodents (Austad, 2001) Baboons (Bronikowski et al., 2002)

7. Mortality Leveling-Off in House Fly Musca domestica Our analysis of the life table for 4,650 male house flies published by Rockstein & Lieberman, 1959. Source: Gavrilov & Gavrilova. Handbook of the Biology of Aging, Academic Press, 2006, pp.3-42.

8. Existing Explanations of Mortality Deceleration Population Heterogeneity (Beard, 1959; Sacher, 1966). “… sub-populations with the higher injury levels die out more rapidly, resulting in progressive selection for vigour in the surviving populations” (Sacher, 1966) Exhaustion of organism’s redundancy (reserves) at extremely old ages so that every random hit results in death (Gavrilov, Gavrilova, 1991; 2001) Lower risks of death for older people due to less risky behavior (Greenwood, Irwin, 1939) Evolutionary explanations (Mueller, Rose, 1996; Charlesworth, 2001)

9. Problems in Hazard Rate Measurement At Extremely Old Ages Mortality deceleration in humans may be an artifact of mixing different birth cohorts with different mortality (heterogeneity effect) Standard assumptions of hazard rate estimates may be invalid when risk of death is extremely high Ages of very old people may be highly exaggerated

10. Social Security Administration Death Master File (SSA DMF) Helps to Alleviate the First Two Problems Allows to study mortality in large, more homogeneous single-year or even single-month birth cohorts Allows to study mortality in one-month age intervals narrowing interval of hazard rates estimation

11. What Is SSA DMF ? SSA DMF (Social Security Administration Death Master File) is a publicly available data resource (available at Rootsweb.com) Covers 93-96 percent deaths of persons 65+ occurred in the United States in the period 1937-2008. Coverage improves over time. Some birth cohorts covered by DMF could be studied by method of extinct generations Considered superior in data quality compared to vital statistics records by some researchers

12. Social Security Administration Death Master File (DMF) Was Used in This Study: (1) Study of cohort mortality at advanced ages: Estimation of hazard rates for each month of age for single-year extinct birth cohorts. (2) Month-of-birth and mortality after age 80: Using single-month birth cohorts to estimate of life expectancy according to month of birth.

13. Mortality when all data are used

14. Hypothesis Mortality deceleration at advanced ages should be less expressed for data of higher quality

15. Quality Control (1) Study of mortality in states with different quality of age reporting: Records for persons applied to SSN in the Southern states, Hawaii and Puerto Rico were suggested to have lower quality (Rosenwaike, Stone, 2003)

16. Mortality for data with presumably different quality

17. Quality Control (2) Study of mortality for earlier and later single-year extinct birth cohorts: Records for later born persons were suggested to have higher quality due to more accurate age reporting.

18. Mortality for data with presumably different quality

20. Internal Validation: Mortality at Advanced Ages by Sex

21. Mortality at Advanced Ages by Sex

22. SSDI Data Quality Evaluation Signal for age exaggeration in males after age 108 years

23. Is Gompertzian slope after age 90 lower than for the rest of mortality curve?

24. Mortality at advanced ages: Actuarial 1900 U.S. cohort life table and SSDI 1887 cohort Source for actuarial life table: Bell, F.C., Miller, M.L. Life Tables for the United States Social Security Area 1900-2100 Actuarial Study No. 116

25. Mortality at advanced ages: Actuarial U.S. cohort life table and SSDI 1887 cohort Estimating Gompertz slope parameter 1900 cohort, age interval 50-100 alpha = 0.092 (0.092,0.093) 1887 cohort, age interval 85-100 alpha=0.117 (0.116,0.118)

26. Crude Indicator of Mortality Plateau (1) Linearity of survival curves in semi-log coordinates (log survival – age)

27. Logarithm of Survival at Advanced Ages Conclusion: This method produces misleading results (lack of aging)

28. Crude Indicator of Mortality Plateau (2) Coefficient of variation for life expectancy is close to, or higher than 100% CV = σ/μ where σ is a standard deviation and μ is mean lifespan

29. Coefficient of variation for life expectancy as a function of age Conclusion: Actuarial aging is more pronounced in women rather than men before age 108 years

30. Month-of-Birth and Mortality at Advanced Ages SSA Death Master File allows researchers to study mortality in real birth cohorts by month-of-birth Provides more accurate and unbiased estimates of life expectancy by month of birth compared to usage of cross- sectional collections of death certificates

33. Conclusions Late-life mortality deceleration appears to be not that strong - cohort mortality at advanced ages continues to grow exponentially up to age 105 years The higher the data quality the less mortality deceleration is observed Life expectancy at age 80 depends on month of birth

34. Acknowledgments This study was made possible thanks to: generous support from the National Institute on Aging The Society of Actuaries grant Stimulating working environment at the Center on Aging, NORC/University of Chicago

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