Problems of 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

Mortality measurement at advanced ages suffers from several problems small numbers of survivors to advanced age, which requires mixing different birth cohorts with different mortality. As a result, the observed mortality deceleration may be at least partially an artifact of this heterogeneity effect.

Mortality measurement at advanced ages suffers from several problems extremely high and rapidly growing risks of death at old ages, which make the standard assumptions of hazard rate estimation to be invalid age misreporting (usually exaggeration) by old persons

The advantage of this data source is that some birth cohorts covered by DMF could be studied by the method of extinct generations. Availability of month of birth and month of death information provides a unique opportunity to obtain more precise estimates of hazard rates for every month of age, which is important given extremely high mortality after age 100 years.

The first study of late-life mortality in humans

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

Mortality Deceleration in Animal 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)

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)

Challenges in Hazard Rate Estimation At Extremely Old Ages Mortality deceleration 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

Social Security Administration Death Master File Helps to Relax 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

What Is SSA DMF ? SSA DMF is a publicly available data resource (available at Rootsweb.com) Covers percent deaths of persons 65+ occurred in the United States in the period 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

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 extinct birth cohorts. (2) Month-of-birth and mortality after age 80: Estimation of life expectancy in real birth cohort according to month of birth.

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

Resolving the Problem of Age Misreporting at Older Ages A recent study of age validation among supercentenarians (Rosenwaike, Stone, 2003) showed that age reporting among supercentenarians in the SSA database is rather accurate, with the exception of persons born in the Southern states. In order to improve the quality of our dataset when estimating hazard rates, we excluded records for those persons who applied for Social Security numbers in the Southeast (AR, AL, GA, MS, LA, TN, FL, KY, SC, NC, VA, WV) and Southwest (AZ, NM, TX, OK) regions, Puerto Rico and Hawaii.

Less reliable data for Southern states, Puerto Rico and Hawaii are excluded

Mortality at Advanced Ages by Sex

Crude Indicators of Mortality Plateaus 1. Linearity of survival curves in semi-log coordinates (log survival – age) 2. Coefficient of variation for life expectancy is close to, or higher than 100%

Logarithm of Survival at Advanced Ages

Coefficient of variation for life expectancy as a function of age

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 death certificates

Month-of-Birth effects disappear at age 100+

Conclusions Late-life mortality deceleration appears to be not that strong - cohort mortality at advanced ages continues to grow up to age 105 years Late-life mortality plateau is likely not an artifact and is expressed earlier in males than females Month of birth effects on mortality exist at age 80 but then fade and disappear by age 100+

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

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