1. Advanced Age Mortality Patterns and Longevity Predictors Natalia S. Gavrilova, Ph.D. Leonid A. Gavrilov, Ph.D. Center on Aging NORC and The University of Chicago Chicago, Illinois, USA

2. The growing number of persons living beyond age 80 underscores the need for accurate measurement of mortality at advanced ages.

3. Recent projections of the U.S. Census Bureau significantly overestimated the actual number of centenarians

4. Views about the number of centenarians in the United States 2009

5. New estimates based on the 2010 census are two times lower than the U.S. Bureau of Census forecast

6. The same story recently happened in the Great Britain Financial Times

7. Mortality at advanced ages is the key variable for understanding population trends among the oldest-old

8. Earlier studies suggested that the exponential growth of mortality with age (Gompertz law) is followed by a period of deceleration, with slower rates of mortality increase.

9. Mortality at Advanced Ages – more than 20 years ago Source: Gavrilov L.A., Gavrilova N.S. The Biology of Life Span: A Quantitative Approach, NY: Harwood Academic Publisher, 1991

10. Mortality at Advanced Ages, Recent Study Source: Manton et al. (2008). Human Mortality at Extreme Ages: Data from the NLTCS and Linked Medicare Records. Math.Pop.Studies

11. Problems with Hazard Rate Estimation At Extremely Old Ages 1. Mortality deceleration in humans may be an artifact of mixing different birth cohorts with different mortality (heterogeneity effect) 2. Standard assumptions of hazard rate estimates may be invalid when risk of death is extremely high 3. Ages of very old people may be highly exaggerated

12. Conclusions from our earlier study of Social Security Administration Death Master File Mortality deceleration at advanced ages among DMF cohorts is more expressed for data of lower quality Mortality data beyond ages 106-107 years have unacceptably poor quality (as shown using female-to-male ratio test). The study by other authors also showed that beyond age 110 years the age of individuals in DMF cohorts can be validated for less than 30% cases (Young et al., 2010) Source: Gavrilov, Gavrilova, North American Actuarial Journal, 2011, 15(3):432-447

13. Nelson-Aalen monthly estimates of hazard rates using Stata 11 Data Source: DMF full file obtained from the National Technical Information Service (NTIS). Last deaths occurred in September 2011.

14. Observed female to male ratio at advanced ages for combined 1887-1892 birth cohort

15. Selection of competing mortality models using DMF data Data with reasonably good quality were used: non-Southern states and 85-106 years age interval Gompertz and logistic (Kannisto) models were compared Nonlinear regression model for parameter estimates (Stata 11) Model goodness-of-fit was estimated using AIC and BIC

16. Fitting mortality with Kannisto and Gompertz models Kannisto model Gompertz model

17. Akaike information criterion (AIC) to compare Kannisto and Gompertz models, men, by birth cohort (non-Southern states) Conclusion: In all ten cases Gompertz model demonstrates better fit than Kannisto model for men in age interval 85-106 years

18. Akaike information criterion (AIC) to compare Kannisto and Gompertz models, women, by birth cohort (non-Southern states) Conclusion: In all ten cases Gompertz model demonstrates better fit than Kannisto model for women in age interval 85-106 years

19. The second studied dataset: U.S. cohort death rates taken from the Human Mortality Database

20. Selection of competing mortality models using HMD data Data with reasonably good quality were used: 80-106 years age interval Gompertz and logistic (Kannisto) models were compared Nonlinear weighted regression model for parameter estimates (Stata 11) Age-specific exposure values were used as weights (Muller at al., Biometrika, 1997) Model goodness-of-fit was estimated using AIC and BIC

21. Fitting mortality with Kannisto and Gompertz models, HMD U.S. data

23. Akaike information criterion (AIC) to compare Kannisto and Gompertz models, men, by birth cohort (HMD U.S. data) Conclusion: In all ten cases Gompertz model demonstrates better fit than Kannisto model for men in age interval 80-106 years

24. Akaike information criterion (AIC) to compare Kannisto and Gompertz models, women, by birth cohort (HMD U.S. data) Conclusion: In all ten cases Gompertz model demonstrates better fit than Kannisto model for women in age interval 80-106 years

25. Compare DMF and HMD data Females, 1898 birth cohort Hypothesis about two-stage Gompertz model is not supported by real data

26. Alternative way to study mortality trajectories at advanced ages: Age-specific rate of mortality change Suggested by Horiuchi and Coale (1990), Coale and Kisker (1990), Horiuchi and Wilmoth (1998) and later called ‘life table aging rate (LAR)’ k(x) = d ln µ(x)/dx  Constant k(x) suggests that mortality follows the Gompertz model.  Earlier studies found that k(x) declines in the age interval 80-100 years suggesting mortality deceleration.

27. Typical result from Horiuchi and Wilmoth paper (Demography, 1998)

28. Age-specific rate of mortality change Swedish males, 1896 birth cohort Flat k(x) suggests that mortality follows the Gompertz law

29. Study of age-specific rate of mortality change using cohort data Age-specific cohort death rates taken from the Human Mortality Database Studied countries: Canada, France, Sweden, United States Studied birth cohorts: 1894, 1896, 1898 k(x) calculated in the age interval 80-100 years k(x) calculated using one-year mortality rates

30. Slope coefficients (with p-values) for linear regression models of k(x) on age All regressions were run in the age interval 80-100 years. CountrySexBirth cohort 189418961898 slopep-valueslopep-valueslopep-value CanadaF-0.000230.9140.000040.9840.000660.583 M0.001120.7780.002350.4990.001090.678 FranceF-0.000700.681-0.001790.169-0.001650.181 M0.000350.907-0.000480.8080.002070.369 SwedenF0.000600.879-0.003570.240-0.000440.857 M0.001910.742-0.002530.6350.001650.792 USAF0.000160.8840.000090.9180.0000060.994 M0.000060.9650.000070.9460.000480.610

31. In previous studies mortality rates were calculated for five-year age intervals  Five-year age interval is very wide for mortality estimation at advanced ages.  Assumption about uniform distribution of deaths in the age interval does not work for 5-year interval  Mortality rates at advanced ages are biased downward

32. Simulation study of mortality following the Gompertz law Simulate yearly l x numbers assuming Gompertz function for hazard rate in the entire age interval and initial cohort size equal to 10 11 individuals Gompertz parameters are typical for the U.S. birth cohorts: slope coefficient (alpha) = 0.08 year -1 ; R 0 = 0.0001 year -1 Numbers of survivors were calculated using formula (Gavrilov et al., 1983): where Nx/N0 is the probability of survival to age x, i.e. the number of hypothetical cohort at age x divided by its initial number N0. a and b (slope) are parameters of Gompertz equation

33. Age-specific rate of mortality change with age, kx, by age interval for mortality calculation Simulation study of Gompertz mortality Taking into account that underlying mortality follows the Gompertz law, the dependence of k(x) on age should be flat

34. Simulation study of Gompertz mortality Compare Sacher hazard rate estimate and probability of death in a yearly age interval Sacher estimates practically coincide with theoretical mortality trajectory Probability of death values strongly undeestimate mortality after age 100

35. Conclusions Below age 107 years and for data of reasonably good quality the Gompertz model fits cohort mortality better than the Kannisto model (no mortality deceleration) for 20 studied single-year U.S. birth cohorts Age-specific rate of mortality change remains flat in the age interval 80-100 years for 24 studied single-year birth cohorts of Canada, France, Sweden and the United States suggesting that mortality follows the Gompertz law

36. Longevity Predictors Leonid A. Gavrilov Natalia S. Gavrilova Center on Aging NORC and The University of Chicago Chicago, USA

37. General Approach To study “success stories” in long-term avoidance of fatal diseases (survival to 100 years) and factors correlated with this remarkable survival success

38. Winnie ain’t quitting now. Smith G D Int. J. Epidemiol. 2011;40:537-562 Published by Oxford University Press on behalf of the International Epidemiological Association © The Author 2011; all rights reserved. An example of incredible resilience

39. Exceptional longevity in a family of Iowa farmers Father: Mike Ackerman, Farmer, 1865-1939 lived 74 years Mother: Mary Hassebroek 1870-1961 lived 91 years 1. Engelke "Edward" M. Ackerman b: 28 APR 1892 in Iowa 101 2. Fred Ackerman b: 19 JUL 1893 in Iowa 103 3. Harmina "Minnie" Ackerman b: 18 SEP 1895 in Iowa 100 4. Lena Ackerman b: 21 APR 1897 in Iowa 105 5. Peter M. Ackerman b: 26 MAY 1899 in Iowa 86 6. Martha Ackerman b: 27 APR 1901 in IA 95 7. Grace Ackerman b: 2 OCT 1904 in IA 104 8. Anna Ackerman b: 29 JAN 1907 in IA 101 9. Mitchell Johannes Ackerman b: 25 FEB 1909 in IA 85

40. Studies of centenarians require careful design and serious work on age validation The main problem is to find an appropriate control group

41. Approach Compare centenarians and shorter- lived controls, which are randomly sampled from the same data universe: computerized genealogies

42. Approach used in this study Compare centenarians with their peers born in the same year but died at age 65 years It is assumed that the majority of deaths at age 65 occur due to chronic diseases related to aging rather than injuries or infectious diseases (confirmed by analysis of available death certificates)

43. Case-control study of longevity Cases - 765 centenarians survived to age 100 and born in USA in 1890-91 Controls – 783 their shorter-lived peers born in USA in 1890-91 and died at age 65 years Method: Multivariate logistic regression Genealogical records were linked to 1900 and 1930 US censuses providing a rich set of variables

44. Age validation is a key moment in human longevity studies Death dates of centenarians were validated using the U.S. Social Security Death Index Birth dates were validated through linkage of centenarian records to early U.S. censuses (when centenarians were children)

45. Genealogies and 1900 and 1930 censuses provide three types of variables Characteristics of early-life conditions Characteristics of midlife conditions Family characteristics

46. Early-life characteristics Type of parental household (farm or non- farm, own or rented), Parental literacy, Parental immigration status Paternal (or head of household) occupation Number of children born/survived by mother Size of parental household in 1900 Region of birth

47. Midlife Characteristics from 1930 census Type of person’s household Availability of radio in household Person’s age at first marriage Person’s occupation (husband’s occupation in the case of women) Industry of occupation Number of children in household Veteran status, Marital status

48. Family Characteristics from genealogy Information on paternal and maternal lifespan Paternal and maternal age at person’s birth, Number of spouses and siblings Birth order Season of birth

49. Example of images from 1930 census (controls)

50. Parental longevity, early-life and midlife conditions and survival to age 100. Men Multivariate logistic regression, N=723 Variable Odds ratio 95% CIP-value Father lived 80+1.841.35-2.51<0.001 Mother lived 80+1.701.25-2.320.001 Farmer in 19301.671.21-2.310.002 Born in North-East2.081.27-3.400.004 Born in the second half of year 1.361.00-1.840.050 Radio in household, 19300.870.63-1.190.374

51. Parental longevity, early-life and midlife conditions and survival to age 100 Women Multivariate logistic regression, N=815 Variable Odds ratio 95% CIP-value Father lived 80+2.191.61-2.98<0.001 Mother lived 80+2.231.66-2.99<0.001 Husband farmer in 19301.150.84-1.560.383 Radio in household, 19301.611.18-2.200.003 Born in the second half of year 1.180.89-1.580.256 Born in the North-East region1.040.62-1.670.857

52. Variables found to be non-significant in multivariate analyses Parental literacy and immigration status, farm childhood, size of household in 1900, percentage of survived children (for mother) – a proxy for child mortality, sibship size, father-farmer in 1900 Marital status, veteran status, childlessness, age at first marriage Paternal and maternal age at birth, loss of parent before 1910

53. Season of birth and survival to 100 Birth in the first half and the second half of the year among centenarians and controls died at age 65 Significant difference P=0.008 Significant difference: p=0.008

54. Within-Family Study of Season of Birth and Exceptional Longevity Month of birth is a useful proxy characteristic for environmental effects acting during in-utero and early infancy development

55. Siblings Born in September-November Have Higher Chances to Live to 100 Within-family study of 9,724 centenarians born in 1880-1895 and their siblings survived to age 50

56. Possible explanations These are several explanations of season-of birth effects on longevity pointing to the effects of early-life events and conditions: seasonal exposure to infections, nutritional deficiencies, environmental temperature and sun exposure. All these factors were shown to play role in later-life health and longevity.

57. Conclusions Both midlife and early-life conditions affect survival to age 100 Parental longevity turned out to be the strongest predictor of survival to age 100 Information about such an important predictor as parental longevity should be collected in contemporary longitudinal studies

58. Acknowledgments This study was made possible thanks to: generous support from the National Institute on Aging (R01 AG028620) Stimulating working environment at the Center on Aging, NORC/University of Chicago

59. For More Information and Updates Please Visit Our Scientific and Educational Website on Human Longevity: http://longevity-science.org And Please Post Your Comments at our Scientific Discussion Blog: http://longevity-science.blogspot.com/

60. Which estimate of hazard rate is the most accurate? Simulation study comparing several existing estimates:  Nelson-Aalen estimate available in Stata  Sacher estimate (Sacher, 1956)  Gehan (pseudo-Sacher) estimate (Gehan, 1969)  Actuarial estimate (Kimball, 1960)

61. Simulation study of Gompertz mortality Compare Gehan and actuarial hazard rate estimates Gehan estimates slightly overestimate hazard rate because of its half-year shift to earlier ages Actuarial estimates undeestimate mortality after age 100

62. Simulation study of the Gompertz mortality Kernel smoothing of hazard rates

63. Monthly Estimates of Mortality are More Accurate Simulation assuming Gompertz law for hazard rate Stata package uses the Nelson- Aalen estimate of hazard rate: H(x) is a cumulative hazard function, d x is the number of deaths occurring at time x and n x is the number at risk at time x before the occurrence of the deaths. This method is equivalent to calculation of probabilities of death:

64. Sacher formula for hazard rate estimation (Sacher, 1956; 1966) l x - survivor function at age x; ∆x – age interval Hazard rate Simplified version suggested by Gehan (1969): µ x = -ln(1-q x )