Mortality Patterns at Advanced Ages

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

2. Extremely Important Topic Because more and more people survive to advanced ages, we need to have more accurate and reliable estimates of mortality and mortality trends at extreme old ages

3. Brief History and Background

4. 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.

5. The Gompertz-Makeham Law Death rate is a sum of age-independent component (Makeham term) and age-dependent component (Gompertz function), which increases exponentially with age. μ(x) = A + R e αx A – Makeham term or background mortality R e αx – age-dependent mortality; x - age risk of death

6. Mortality deceleration at advanced ages After age 95, the observed risk of death [red line] deviates from the values predicted by the Gompertz law [black line]. Mortality of Swedish women for the period of 1990-2000 from the Kannisto-Thatcher Database on Old Age Mortality Source: Gavrilov, Gavrilova, “Why we fall apart. Engineering’s reliability theory explains human aging”. IEEE Spectrum. 2004.

7. Mortality Leveling-Off in House FlyMusca domestica Based on life table of 4,650 male house flies published by Rockstein & Lieberman, 1959 Source: Gavrilov, Gavrilova, Handbook of the Biology of Aging, 2006

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. 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

10. Study of the Social Security Administration Death Master File North American Actuarial Journal, 2011, 15(3):432-447

11. Birth cohort mortality, DMF data Nelson-Aalen monthly estimates of hazard rates using Stata 11

12. Gompertz model of old-age mortality Study of 20 single-year extinct U.S. birth cohorts based on the Social Security Administration Death Master File (DMF) found no mortality deceleration up to ages 105-106 years (Gavrilova, Gavrilov, 2011). However, data quality problems did not allow us to study mortality trajectories after age 107 or 110 years using this source of data.

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

14. Problem of mortality estimation at older ages Age misreporting

15. At what ages data have reasonably good quality? A study of age-specific mortality by gender using indirect measure of data quality

16. Women have lower mortality at advanced ages Hence number of males to number of females ratio should decrease with age

17. The validity of our method of gender assignment in DMF: No difference between gender-specific mortality estimates in DMF and vital statistics with known gender

18. Male-to-female ratio for survivors to specific age, by cohort and age in DMF

19. What is the quality of age reporting in DMF across ages and birth cohorts? A study of data quality for five single-year birth cohorts Supported by the Society of Actuaries

20. More details are available in a special report by the SOA Supported by the Society of Actuaries

21. Study Design Five single-year birth cohorts: 1898, 1899, 1900, 1901, 1902 Direct age validation of DMF samples randomly selected at ages 100, 103, 105 and 109+ ages Sample sizes: 100 records for ages 100-105 years For age group 109+ years – all records

22. Age validation procedure Age validation was conducted by linkage of DMF records to early historical sources (U.S. censuses, birth and marriage records, draft registration cards). DMF records were scored according to reliability of age reporting. The scoring system included the following scores: 1 – several early historical sources agree about birth date 2 – one early historical sources agrees about birth date 3 – later sources agree about birth date 4 – early sources disagree 5 – foreign-born individual arrived in the U.S. later in life 6 – not found in any sources

23. An Example of Age Validation using Ancestry service Finding person first in Ancestry database

24. Confirmation of birth date in early marriage record

25. Percent of records with questionable quality as a function of age. 1898, 1900 and 1902 birth cohorts Results of age validation study for samples of 100 records, by age group. For ages 109 and 110+ years sample sizes were slightly higher than 100.

26. Percent of records with questionable quality at extreme old ages. 1898-1902 birth cohorts

27. Regression model for percentage of poor quality records Percentage of poor records is modeled as a linear function of binary (dummy) variables representing birth cohorts and ages. where percent is percentage of poor quality records, AGE and COHORT represent sets of dummy variables (103, 105, 109 for AGE at death with 100 years used as a reference level and 1899, 1900, 1901, 1902 for COHORT birth year with 1898 used as a reference level), β1 and β2 are regression coefficients

28. Regression model for percentage of poor quality data

29. Force of mortality by the data quality score1900 birth cohort, both sexes

30. Hypothesis Mortality deceleration at advanced ages among DMF cohorts may be caused by poor data quality (age exaggeration) at very advanced ages If this hypothesis is correct then mortality deceleration at advanced ages should be less expressed for data with better quality

31. Further development Direct age validation of all records at ages 106 and over for those born in 1900

32. Mortality of U.S. men born in 1900 before and after data cleaning

33. Mortality of U.S. women born in 1900 before and after data cleaning

34. Conclusion: Age misreporting produces spurious mortality plateau

35. Is Mortality Deceleration Caused by Age Misreporting? It was demonstrated that age misstatement biases mortality estimates downwards at the oldest ages, which contributes to mortality deceleration (Preston et al., 1999). If this hypothesis is correct then mortality deceleration should be more prevalent among historically older birth cohorts

36. Historical Evolution of Mortality Trajectories1880-1899 U.S. birth cohorts. MenBIC values for fitting Gompertz and Kannisto models Fitting age-specific cohort death rates taken from the Human Mortality Database

37. 1880-1899 U.S. birth cohorts. WomenBIC values for fitting Gompertz and Kannisto models Fitting age-specific cohort death rates taken from the Human Mortality Database

38. 1880-1899 Canadian birth cohorts. AIC values for fitting Gompertz and Kannisto models Fitting age-specific cohort death rates taken from the Human Mortality Database

39. 1880-1899 UK birth cohorts. AIC values for fitting Gompertz and Kannisto models Fitting age-specific cohort death rates taken from the Human Mortality Database

40. Conclusion Mortality deceleration is more prevalent in historically older birth cohorts when age reporting was less accurate

41. Are monthly estimates of the force of mortality less prone to decelerate? We used actuarial estimate of hazard rate (calculated as central death rate). This estimate assumes uniform distribution of deaths in the age interval. Is this assumption critical?

42. Deaths at extreme ages are not distributed uniformly over one-year interval 85-year olds 102-year olds 1894 birth cohort from the Social Security Death Index

43. Simulation study of Gompertz mortalityCompare Gehan and actuarial hazard rate estimates Simplified Sacher estimates slightly overestimate hazard rate because of its half-year shift to earlier ages Actuarial estimates (death rates) undeestimate mortality after age 100

44. Force of mortality by monthly and yearly estimates1898 birth cohort, both sexes

45. Force of mortality by monthly and yearly estimates after data cleaning1898-1902 birth cohort, both sexes

46. CONTEMPORARY METHODS OF MORTALITY ANALYSIS Testing the Limit to Lifespan Hypothesis

47. Latest Developments Evidence of the limit to human lifespan (Dong et al., Nature, 2016) Evidence of mortality plateau after age 105 years (Barbi et al., Science, 2018)

48. Nature (2016) Based on data from the International Database on Longevity (IDL) Note: After 2000 number of supercentenarians exposed to death in IDL rapidly declines

49. If the limit to human lifespan exists then: No progress in longevity records in subsequent birth cohorts should be observed (Wilmoth, 1997) Mortality at extreme old ages should demonstrate an accelerating pattern (Gavrilov, Gavrilova, 1991)

50. Testing the “Limit-to-Lifespan” Hypothesis in the 1990s Source:Gavrilov L.A., Gavrilova N.S. 1991. The Biology of Life Span