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
What Do We Know About
Mortality of Centenarians?
A Study That Answered This Question
M. Greenwood, J. O. Irwin. BIOSTATISTICS OF SENILITY
Mortality at Advanced Ages
Source: Gavrilov L.A., Gavrilova N.S. The Biology of Life Span:
A Quantitative Approach, NY: Harwood Academic Publisher, 1991
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)
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.
hazard rate, log scale
0.1
Source:
Gavrilov & Gavrilova.
Handbook of the
Biology of Aging,
Academic Press,
2006, pp.3-42.
0.01
0.001
0
10
20
Age, days
30
40
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)
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
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
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
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.
Mortality when all data are used
Hypothesis
Mortality deceleration at advanced ages
should be less expressed for data of higher
quality
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)
Mortality for data with presumably different quality
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.
Mortality for data with presumably different quality
Internal Validation:
Mortality at Advanced Ages
by Sex
Mortality at Advanced Ages by Sex
SSDI Data Quality Evaluation
Female/Male ratio after age 100
1886 birth cohort
8
Female/Male Ratio
7
6
5
4
3
100
102
104
106
108
110
Age
Signal for age exaggeration in males after age 108 years
Is Gompertzian slope after age
90 lower than for the rest of
mortality curve?
Mortality at advanced ages:
Actuarial 1900 U.S. cohort life table
and SSDI 1887 cohort
0
log(hazard rate)
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
1900 cohort, U.S. life table
1887 cohort from SSDI
-1
-2
60
70
80
90
Age
100
110
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)
1900 cohort, U.S. life table
1887 cohort from SSDI
0
log(hazard rate)
1887 cohort, age interval 85-100
alpha=0.117 (0.116,0.118)
-1
80
85
90
95
Age
100
105
110
Crude Indicator
of Mortality Plateau (1)
Linearity of survival curves
in semi-log coordinates
(log survival – age)
Logarithm of Survival at Advanced Ages
Conclusion: This method produces misleading results (lack of aging)
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
Coefficient of variation of lifespan
Coefficient of variation for life expectancy as
a function of age
1.0
Males
Females
0.7
98
100
102
104
106
108
110
112
Age
Conclusion: Actuarial aging is more pronounced in women rather than
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 crosssectional collections of death certificates
7.9
life expectancy at age 80, years
1885 Birth Cohort
1891 Birth Cohort
7.8
7.7
7.6
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month of Birth
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
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

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/