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

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

Brief History and Background

Three scenarios for mortality at advanced ages Source: Gavrilov L.A., Gavrilova N.S. The Biology of Life Span: A Quantitative Approach, NY: Harwood Academic Publisher, 1991

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

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.

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.

Mortality Leveling-Off in House Fly Musca 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

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)

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

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

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.

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

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

Why do we see more indications for apparent limit to human lifespan?

Two Observations

No mortality improvement for centenarians Observation #1 No mortality improvement for centenarians Found for Swedish and UK centenarians Drefahl, S., H. Lundstrom, K. Modig, and A. Ahlbom. 2012. "The Era of Centenarians: Mortality of the Oldest Old in Sweden." Journal of Internal Medicine 272(1): 100--102. Continuous Mortality Investigation. 2015. "Initial Report on the Features of High Age Mortality. Working Paper 85.". London: Continuous Mortality Investigation Ltimited, UK

Recent scientific publications suggest that human longevity records stopped increasing. Our finding that the mortality of U.S. centenarians has not decreased noticeably in recent decades is consistent with this suggestion.

Mortality of U.S. centenarians does not decline over time Men Women

Mortality of 1898-1902 birth cohorts both sexes

Improvement of age reporting Observation #2 Improvement of age reporting

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

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

Quality Control Study of mortality for earlier and later single-year extinct birth cohorts: Records for later born persons are supposed to be of better quality due to improvement of age reporting over time.

Mortality for data with presumably different quality: Older and younger birth cohorts The degree of deceleration was evaluated using quadratic model

Historical Evolution of Mortality Trajectories 1880-1899 U. S Historical Evolution of Mortality Trajectories 1880-1899 U.S. birth cohorts. Men BIC values for fitting Gompertz and Kannisto models Fitting age-specific cohort death rates taken from the Human Mortality Database

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

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

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

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

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

Male to female ratio for survivors to specific age for 1898-1902 birth cohorts in DMF

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

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

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

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

Confirmation of birth date in early marriage record

Percent of records with questionable quality as a function of age 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.

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

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

Regression model for percentage of poor quality data Variable Regression coefficients P-value 95% confidence intervals 1898 cohort reference 1899 cohort 2.00 0.588 -6.55 - 10.55 1900 cohort -1.75 0.419 -6.69 - 3.19 1901 cohort -1.56e-15 1.000 -8.55 - 8.55 1902 cohort 4.75 0.057 -0.19 - 9.69 Age 100   Age 103 4.67 0.092 -1.03 - 10.37 Age 105 4.33 0.112 -1.37 - 10.03 Age 109 16.67 <0.001 10.97 - 22.37 Intercept 14.33 9.40-19.27

Force of mortality by the data quality score 1900 birth cohort, both sexes

Force of mortality after conducting data cleaning 1898-1902 birth cohort, both sexes

Is this assumption critical? Are monthly estimates of the force of mortality less subjected to mortality deceleration? 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?

1894 birth cohort from the Social Security Death Index 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

Simulation study of Gompertz mortality Compare 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

Force of mortality by monthly and yearly estimates 1898 birth cohort, both sexes

Force of mortality by monthly and yearly estimates after data cleaning 1898 birth cohort, both sexes

Regional mortality at advanced ages Study of mortality according to region of last residence and region of SSN application

Mortality, by region of last residence 1898-1902 birth cohort, women

Mortality, by region of SSN application 1898-1902 birth cohort, women

Conclusions Gompertzialization of old-age mortality trajectories over time. Mortality stagnation over time for ages 100 years and over. If continued, these trends may lead to accelerating pattern of mortality increase with age As a result, the number of centenarians in the future may be significantly lower than expected

Acknowledgments This study was made possible thanks to: generous support from the Society of Actuaries National Institute on Aging (R21 AG052670) Stimulating working environment at the Center on Aging, NORC/University of Chicago

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