Transcript Reliability-Theory Approach to Epidemiological Studies of

Reliability-Theory Approach
to Epidemiological Studies of
Aging, Mortality and Longevity
Dr. Leonid A. Gavrilov, Ph.D.
Dr. Natalia S. Gavrilova, Ph.D.
Center on Aging
NORC and The University of Chicago
Chicago, Illinois, USA
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What Is Reliability-Theory Approach?
Reliability-theory approach is based on
ideas, methods, and models of a general
theory of systems failure known as
reliability theory.
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Reliability theory was historically
developed to describe failure and aging
of complex electronic (military)
equipment, but the theory itself is a very
general theory based on probability
theory and systems approach.
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Why Do We Need
Reliability-Theory Approach?



Because it provides a common scientific
language (general paradigm) for scientists
working in different areas of aging research,
including epidemiological studies.
Reliability theory helps to overcome disruptive
specialization and it allows researchers to
understand each other.
Provides useful mathematical models allowing
to explain and interpret the observed
epidemiological data and findings.
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Some Representative Publications
on Reliability-Theory Approach
to Epidemiological Studies of Aging,
Mortality and Longevity
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Gavrilov, L., Gavrilova, N.
Reliability theory of
aging and longevity.
In: Handbook of the
Biology of Aging.
Academic Press, 6th
edition, 2006, pp.3-42.
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The Concept of System’s Failure

In reliability theory
failure is defined as
the event when a
required function is
terminated.
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Failures are often classified into
two groups:


degradation failures, where
the system or component no
longer functions properly
catastrophic or fatal failures the end of system's or
component's life
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Definition of aging and non-aging
systems in reliability theory



Aging: increasing risk of failure with
the passage of time (age).
No aging: 'old is as good as new'
(risk of failure is not increasing with
age)
Increase in the calendar age of a
system is irrelevant.
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Aging and non-aging systems
Perfect clocks having an ideal
marker of their increasing age
(time readings) are not aging
Progressively failing clocks are aging
(although their 'biomarkers' of age at
the clock face may stop at 'forever
young' date)
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Mortality in Aging and Non-aging Systems
3
3
aging system
non-aging system
Risk of death
Risk of Death
2
1
2
1
0
0
2
4
6
8
10
Age
12
0
2
4
6
8
10
12
Age
Example: radioactive decay
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According to Reliability Theory:
Aging is NOT just growing old
Instead
Aging is a degradation to failure:
becoming sick, frail and dead


'Healthy aging' is an oxymoron like
a healthy dying or a healthy disease
More accurate terms instead of
'healthy aging' would be a delayed
aging, postponed aging, slow aging,
or negligible aging (senescence)
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Reliability-Theory Approach to
Epidemiology of Aging (I)



Focus on adverse health outcomes,
“health failures” (disability, disease,
death) rather than any age-related
changes
Focus on incidence of “health
failures” rather than prevalence
measures
Focus on age-specific incidence rates
rather than age-aggregated (ageadjusted) measures
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Reliability-Theory Approach to
Epidemiology of Aging (II)
Very inclusive system approach (not
limited to humans). Extensive use of
modeling:



Mathematical models
Animal models
Failure models for manufactured
items
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Aging is a Very General Phenomenon!
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
Particular mechanisms of aging may be
very different even across biological
species (salmon vs humans)
BUT

General Principles of Systems Failure and
Aging May Exist
(as we will show in this presentation)
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Further plan of presentation



Empirical laws of failure and aging in
epidemiology
Explanations by reliability theory
Links between reliability theory and
epidemiologic studies
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Empirical Laws of Systems
Failure and Aging
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Stages of Life in Machines and Humans
The so-called bathtub curve for
technical systems
Bathtub curve for human mortality as
seen in the U.S. population in 1999
has the same shape as the curve for
failure rates of many machines.
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Failure (Mortality) Laws
1.
Gompertz-Makeham law of mortality
2.
Compensation law of mortality
3.
Late-life mortality deceleration
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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
risk of death
Non-aging
component
αx
Aging
component
A – Makeham term or background mortality
R e αx – age-dependent mortality; x - age
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Gompertz Law of Mortality in Fruit Flies
Based on the life
table for 2400
females of
Drosophila
melanogaster
published by Hall
(1969).
Source: Gavrilov,
Gavrilova, “The
Biology of Life Span”
1991
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Gompertz-Makeham Law of Mortality
in Flour Beetles
Based on the life table for
400 female flour beetles
(Tribolium confusum
Duval). published by Pearl
and Miner (1941).
Source: Gavrilov, Gavrilova,
“The Biology of Life Span”
1991
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Gompertz-Makeham Law of Mortality in
Italian Women
Based on the official
Italian period life table
for 1964-1967.
Source: Gavrilov,
Gavrilova, “The
Biology of Life Span”
1991
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Compensation Law of Mortality
(late-life mortality convergence)
Relative differences in death rates are
decreasing with age, because the
lower initial death rates are
compensated by higher slope of
mortality growth with age (actuarial
aging rate)
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Compensation Law of Mortality
Convergence of Mortality Rates with Age
1
2
3
4
– India, 1941-1950, males
– Turkey, 1950-1951, males
– Kenya, 1969, males
- Northern Ireland, 19501952, males
5 - England and Wales, 19301932, females
6 - Austria, 1959-1961, females
7 - Norway, 1956-1960, females
Source: Gavrilov, Gavrilova,
“The Biology of Life Span” 1991
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Compensation Law of Mortality (Parental Longevity Effects)
Mortality Kinetics for Progeny Born to Long-Lived (80+) vs Short-Lived Parents
1
Log(Hazard Rate)
Log(Hazard Rate)
1
0.1
0.01
0.1
0.01
short-lived parents
long-lived parents
short-lived parents
long-lived parents
Linear Regression Line
Linear Regression Line
0.001
40
50
60
70
Age
Sons
80
90
100
0.001
40
50
60
70
80
90
100
Age
Daughters
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Compensation Law of Mortality in
Laboratory Drosophila
1 – drosophila of the Old Falmouth,
New Falmouth, Sepia and Eagle
Point strains (1,000 virgin
females)
2 – drosophila of the Canton-S
strain (1,200 males)
3 – drosophila of the Canton-S
strain (1,200 females)
4 - drosophila of the Canton-S
strain (2,400 virgin females)
Mortality force was calculated for
6-day age intervals.
Source: Gavrilov, Gavrilova,
“The Biology of Life Span” 1991
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Epidemiological Implications
Be prepared to a paradox that higher
actuarial aging rates may be associated
with higher life expectancy in compared
populations (e.g., males vs females)
Be prepared to violation of the
proportionality assumption used in hazard
models (Cox proportional hazard models)
Relative effects of risk factors are agedependent and tend to decrease with age
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The Late-Life Mortality Deceleration
(Mortality Leveling-off, Mortality Plateaus)
The late-life mortality deceleration
law states that death rates stop to
increase exponentially at advanced
ages and level-off to the late-life
mortality plateau.
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Mortality deceleration at
advanced ages.
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After age 95, the observed
risk of death [red line]
deviates from the value
predicted by an early
model, 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.
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M. Greenwood, J. O. Irwin. BIOSTATISTICS OF SENILITY
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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:
0.01
Gavrilov & Gavrilova.
Handbook of the
Biology of Aging,
Academic Press,
2006, pp.3-42.
0.001
0
10
20
30
40
Age, days
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Non-Aging Mortality Kinetics in Later Life
If mortality is constant then log(survival)
declines with age as a linear function
Source:
Economos, A. (1979).
A non-Gompertzian
paradigm for mortality
kinetics of metazoan
animals and failure
kinetics of
manufactured
products.
AGE, 2: 74-76.
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Non-Aging Failure Kinetics
of Industrial Materials in ‘Later Life’
(steel, relays, heat insulators)
Source:
Economos, A. (1979).
A non-Gompertzian
paradigm for mortality
kinetics of metazoan
animals and failure
kinetics of
manufactured
products.
AGE, 2: 74-76.
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Testing the “Limit-to-Lifespan” Hypothesis
Source: Gavrilov L.A., Gavrilova N.S. 1991. The Biology of Life Span
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Epidemiological Implications
There is no fixed upper limit to human
longevity - there is no special fixed
number, which separates possible and
impossible values of lifespan.

This conclusion is important, because it
challenges the common belief in existence
of a fixed maximal human life span.

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Additional Empirical Observation:
Many age changes can be explained by
cumulative effects of cell loss over time


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Atherosclerotic inflammation - exhaustion
of progenitor cells responsible for arterial
repair (Goldschmidt-Clermont, 2003; Libby,
2003; Rauscher et al., 2003).
Decline in cardiac function - failure of
cardiac stem cells to replace dying
myocytes (Capogrossi, 2004).
Incontinence - loss of striated muscle cells
in rhabdosphincter (Strasser et al., 2000).
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Like humans,
nematode
C. elegans
experience
muscle loss
Herndon et al. 2002.
Stochastic and genetic
factors influence tissuespecific decline in ageing
C. elegans. Nature 419,
808 - 814.
“…many additional cell types
(such as hypodermis and
intestine) … exhibit agerelated deterioration.”
Body wall muscle sarcomeres
Left - age 4 days. Right - age 18 days
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What Should
the Aging Theory Explain

Why do most biological species including
humans deteriorate with age?

The Gompertz law of mortality

Mortality deceleration and leveling-off at
advanced ages

Compensation law of mortality
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The Concept of Reliability Structure

The arrangement of components
that are important for system
reliability is called reliability
structure and is graphically
represented by a schema of
logical connectivity
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Two major types of system’s
logical connectivity

Components
connected in
series
Ps = p1 p2 p3

…
pn =
Fails when the first component fails
pn
Components
connected in
parallel
Fails when
all
components
fail
Qs = q1 q2 q3 … qn = qn
 Combination of two types – Series-parallel system
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Series-parallel
Structure of
Human Body
• Vital
organs are
connected in series
• Cells in vital organs
are connected in
parallel
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Redundancy Creates Both Damage Tolerance
and Damage Accumulation (Aging)
System without
redundancy dies
after the first
random damage
(no aging)
System with
redundancy
accumulates
damage
(aging)
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Reliability Model
of a Simple Parallel System
Failure rate of the system:
( x) =
d S ( x)
nk e
=
S ( x ) dx
1
kx
(1
e
kx n
(1
e
kx n
)
1
)
 nknxn-1 early-life period approximation, when 1-e-kx  kx
 k
late-life period approximation, when 1-e-kx  1
Source: Gavrilov L.A., Gavrilova N.S. 1991. The Biology of Life Span
Elements fail
randomly and
independently
with a constant
failure rate, k
n – initial
number of
elements
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Failure Rate as a Function of Age
in Systems with Different Redundancy Levels
Source: Gavrilov, Gavrilova, IEEE Spectrum. 2004.
Failure of elements is random
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Standard Reliability Models Explain


Mortality deceleration and
leveling-off at advanced ages
Compensation law of mortality
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Standard Reliability Models
Do Not Explain


The Gompertz law of mortality
observed in biological systems
Instead they produce Weibull
(power) law of mortality
growth with age:
μ(x) = a xb
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An Insight Came To Us While Working
With Dilapidated Mainframe Computer

The complex
unpredictable
behavior of this
computer could
only be described
by resorting to such
'human' concepts
as character,
personality, and
change of mood.
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Reliability structure of
(a) technical devices and (b) biological systems
Low redundancy
Low damage load
Fault avoidance
High redundancy
High damage load
Fault tolerance
X - defect
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Models of systems with
distributed redundancy
Organism can be presented as a system
constructed of m series-connected blocks
with binomially distributed elements within
block (Gavrilov, Gavrilova, 1991, 2001)
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Model of organism
with initial damage load
Failure rate of a system with binomially distributed
redundancy (approximation for initial period of life):
n
(x ) Cmn (q k )
where
x0 =
q
1
qk
q
1
qk
n
+ x
1
=
n
(x 0 + x )
1
Binomial
law of
mortality
- the initial virtual age of the system
The initial virtual age of a system defines the law of
system’s mortality:
x0 = 0 - ideal system, Weibull law of mortality
x0 >> 0 - highly damaged system, Gompertz law of mortality
Source: Gavrilov L.A., Gavrilova N.S. 1991. The Biology of Life Span
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People age more like machines built with lots of
faulty parts than like ones built with pristine parts.

As the number
of bad
components,
the initial
damage load,
increases
[bottom to top],
machine failure
rates begin to
mimic human
death rates.
Source: Gavrilov, Gavrilova, IEEE Spectrum. 2004
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Statement of the HIDL hypothesis:
(Idea of High Initial Damage Load )
"Adult organisms already have an
exceptionally high load of initial damage,
which is comparable with the
amount of subsequent aging-related
deterioration, accumulated during
the rest of the entire adult life."
Source: Gavrilov, L.A. & Gavrilova, N.S. 1991. The Biology of Life Span:
A Quantitative Approach. Harwood Academic Publisher, New York.
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Why should we expect high initial damage load in
biological systems?


General argument:
-- biological systems are formed by self-assembly
without helpful external quality control.
Specific arguments:
1. Most cell divisions responsible for DNA copy-errors
occur in early development leading to clonal expansion
of mutations
2. Loss of telomeres is also particularly high in early-life
3. Cell cycle checkpoints are disabled in early development
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Birth Process is a Potential
Source of High Initial Damage



Severe hypoxia and asphyxia just
before the birth.
oxidative stress just after the birth
because of acute reoxygenation
while starting to breathe.
The same mechanisms that produce
ischemia-reperfusion injury and the
related phenomenon, asphyxiareventilation injury known in
cardiology.
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Mutation Frequencies
are Already High Early in Life
Spontaneous mutant frequencies with age in heart and small intestine of mouse
Small Intestine
Heart
35
-5
Mutant frequency (x10 )
40
30
25
20
15
10
5
0
0
5
10
15
20
Age (months)
25
30
35
Source: Presentation by Jan Vijg at the IABG Congress, Cambridge, 2003
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Practical implications from
the HIDL hypothesis:
"Even a small progress in optimizing the
early-developmental processes can
potentially result in a remarkable
prevention of many diseases in later life,
postponement of aging-related morbidity
and mortality, and significant extension
of healthy lifespan."
Source: Gavrilov, L.A. & Gavrilova, N.S. 1991. The Biology of Life Span:
A Quantitative Approach. Harwood Academic Publisher, New York.
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Implications for
Epidemiological Studies
If the initial damage load is really
important, then we may expect
significant effects of early-life
conditions (like season-of-birth,
birth order, or paternal age at
conception) on late-life morbidity
and mortality
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Life Expectancy and Month of Birth
life expectancy at age 80, years
7.9
1885 Birth Cohort
1891 Birth Cohort
Data source:
Social Security
Death Master File
7.8
Published in:
7.7
Gavrilova, N.S.,
Gavrilov, L.A. Search
for Predictors of
Exceptional Human
Longevity. In: “Living
to 100 and Beyond”
Monograph. The
Society of Actuaries,
Schaumburg, Illinois,
USA, 2005, pp. 1-49.
7.6
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Month of Birth
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Birth Order and Chances
to Become a Centenarian
Cases - centenarians born in the United States
between 1890 and 1899
Controls – their siblings born in the same time
window
Model:
Log(longevity odds ratio)= ax + bx2 + cz + d
where x – birth order; z – family size; a, b, c, d – parameters of
polynomial regression model
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Birth Order and Survival to 100
0.8
Odds to become a centenarian
0.7
Females
Males
Source:
0.6
Gavrilova, N.S.,
Gavrilov, L.A. Search
for Predictors of
Exceptional Human
Longevity. In: “Living
to 100 and Beyond”
Monograph. The
Society of Actuaries,
Schaumburg, Illinois,
USA, 2005, pp. 1-49.
0.5
0.4
0.3
0.2
0.1
1
2
3
4
5
6
7
8
9
10
Birth order
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Genetic Justification for
Paternal Age Effects
Advanced paternal age
at child conception is
the main source of new
mutations in human
populations.
James F. Crow, geneticist
PNAS USA, 1997, 94(16): 8380-6
Professor Crow (University of Wisconsin-Madison) is recognized as
a leader and statesman of science. He is a member of the National
Academy of Sciences, the National Academy of Medicine, The
American Philosophical Society, the American Academy of Arts and
Sciences, the World Academy of Art and Science.
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Paternal Age and Risk of
Schizophrenia


Estimated cumulative
incidence and
percentage of
offspring estimated
to have an onset of
schizophrenia by age
34 years, for
categories of paternal
age. The numbers
above the bars show
the proportion of
offspring who were
estimated to have an
onset of
schizophrenia by 34
years of age.
Source: Malaspina et
al., Arch Gen
Psychiatry.2001.
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Daughters' Lifespan (30+) as a Function
of Paternal Age at Daughter's Birth
6,032 daughters from European aristocratic families born in 1800-1880
1

Life expectancy of adult
women (30+) as a function of
father's age when these
women were born (expressed
as a difference from the
reference level for those born
to fathers of 40-44 years).

The data are point
estimates (with standard
errors) of the differential
intercept coefficients adjusted
for other explanatory variables
using multiple regression with
nominal variables.

Daughters of parents who
survived to 50 years.
Lifespan Difference (yr)
0
-1
-2
-3
p = 0.04
-4
15-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59
Paternal Age at Reproduction
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Contour plot for daughters’ lifespan (deviation from cohort
mean) as a function of paternal lifespan (X axis) and
paternal age at daughters’ birth (Y axis)
65
Paternal Age at Person's Birth, years
60
55
3
2
1
0
-1
-2
-3
7984 cases
1800-1880 birth
cohorts
50
45
European
aristocratic
families
40
35
Distance weighted
least squares
smooth
30
25
20
40
50
60
70
80
90
Pate rnal Life span, ye ars
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Daughters’ Lifespan as a Function of
Paternal Age at Daughters’ Birth
Data are adjusted for other predictor variables
4
1
2
Lifespan Difference (yr)
Lifespan Difference (yr)
0
-1
-2
0
-2
-3
-4
-4
15-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59
15-24 25-29 30-34 35-39 40-44 45-49 50-54 55-59
Paternal Age at Person's Birth
Paternal Age at Person's Birth
Daughters of shorter-lived
fathers (<80), 6727 cases
Daughters of longer-lived
fathers (80+), 1349 cases
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Preliminary Conclusion
Being conceived to old father is a risk factor,
but it is moderated by paternal longevity
It is OK to be conceived to old father if he
lives more than 80 years
Epidemiological implications: Paternal
lifespan should be taken into account in the
studies of paternal-age effects
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Conclusions (I)


Redundancy is a key notion for understanding
aging and the systemic nature of aging in
particular. Systems, which are redundant in
numbers of irreplaceable elements, do
deteriorate (i.e., age) over time, even if they are
built of non-aging elements.
An apparent aging rate or expression of aging
(measured as age differences in failure rates,
including death rates) is higher for systems with
higher redundancy levels.
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Conclusions (II)


Redundancy exhaustion over the life course explains the
observed ‘compensation law of mortality’ (mortality
convergence at later life) as well as the observed late-life
mortality deceleration, leveling-off, and mortality
plateaus.
Living organisms seem to be formed with a high load of
initial damage, and therefore their lifespans and aging
patterns may be sensitive to early-life conditions that
determine this initial damage load during early
development. The idea of early-life programming of aging
and longevity may have important practical implications
for developing early-life interventions promoting health
and longevity.
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Acknowledgments
This study was made possible
thanks to:
generous support from the
National Institute on Aging, and


stimulating working environment
at the Center on Aging,
NORC/University of Chicago
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For More Information and Updates
Please Visit Our
Scientific and Educational Website
on Human Longevity:
 http://longevity-science.org
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Possible Change of Paradigm in
Epidemiology
Mortality of Swedish females
10-1
10-2
1900
1920
1930
1940
1950
1960
10-3
10-4
Log (Hazard Rate)
Log (Hazard Rate)
10-1
1960
1970
1980
1990
2000
10-2
10-3
10-4
0
20
40
60
Age
Before the 1960s
80
0
20
40
60
80
Age
After the 1960s
Columbia University - Research Seminars in Epidemiology
Mortality Before the 1960s
Can be Modeled Using the
Gompertz-Makeham law
By studying the historical
dynamics of the mortality
components in this law:
μ(x) = A + R e
Makeham component
αx
Gompertz component
Columbia University - Research Seminars in Epidemiology
Historical Stability of the Gompertz
Mortality Component Before the 1980s
Historical Changes in Mortality for 40-year-old Swedish Males
1.
2.
3.
Total mortality, μ40
Background
mortality (A)
Age-dependent
mortality (Reα40)
Source:
Gavrilov, Gavrilova, “The
Biology of Life Span” 1991
Columbia University - Research Seminars in Epidemiology
Predicting Mortality Crossover
Historical Changes in Mortality for
40-year-old Women in Norway and Denmark
1.
2.
3.
4.
Norway, total mortality
Denmark, total
mortality
Norway, agedependent mortality
Denmark, agedependent mortality
Source: Gavrilov, Gavrilova,
“The Biology of Life Span”
1991
Columbia University - Research Seminars in Epidemiology
Predicting Mortality Divergence
Historical Changes in Mortality for
40-year-old Italian Women and Men
1.
2.
3.
4.
Women, total
mortality
Men, total mortality
Women, agedependent mortality
Men, age-dependent
mortality
Source: Gavrilov, Gavrilova,
“The Biology of Life
Span” 1991
Columbia University - Research Seminars in Epidemiology
Hypothesis of Death Quota for Total Mortality
The Idea of Non-Specific Vulnerability Intermediate State
Normal state of
organism
Extreme
situations
producing
background
mortality
Aging
(limiting stage)
Death
State of nonspecific
vulnerability
Various
diseases
and
“causes”
of death
Columbia University - Research Seminars in Epidemiology
Mortality Decline After the 1960s May Be a Result of
Improvement in Early-Life Conditions
Mortality Rate, log scale
0.100
0.010
1880 Birth Cohort
1890 Birth Cohort
1900 Birth Cohort
1910 Birth Cohort
1920 Birth Cohort
0.001
40
50
60
70
80
90
Age
Birth cohorts of Swedish women (Source of data: HMD)
Columbia University - Research Seminars in Epidemiology
Extension of the Gompertz-Makeham
Model Through the
Factor Analysis of Mortality Trends
Mortality force (age, time) =
= a0(age) + a1(age) x F1(time) + a2(age) x F2(time)
Where:
• ai(age) – a set of numbers; each number is fixed for specific age group
• Fj(time) – “factors,” a set of standardized numbers; each number is fixed for
specific moment of time (mean = 0; st. dev. = 1)
Columbia University - Research Seminars in Epidemiology
Factor Analysis of Mortality Trends
Swedish Females
Mortality factor score
4
Makeham-like factor 1
("young ages")
Gompertz-like factor 2
("old ages")
“Factor analysis of the
time series of mortality
confirms the preferential
reduction in the
mortality of old-aged
and senile people [in
recent years]…”
Gavrilov, Gavrilova, The
Biology of Life Span,
1991.
2
0
Data source for the
current slide: Human
-2
Mortality Database
1900
1920
1940
1960
1980
2000
Calendar Year
Columbia University - Research Seminars in Epidemiology
Testing hypothesis of statistical independence
between causes of death
Based on 179 values of male mortality at age 55-64 from 26 countries (WHO)
Cause of death
Correlation coefficient with
total mortality
Coefficient of
mortality
amplification
(2)/(1)
Expected
value*
(1)
Observed
value
(2)
Ischaemic heart disease (A83)
+0.770
+0.606
0.79
Cerebrovascular disease
+0.246
+0.345
1.40
Lung cancer (A51)
+0.215
+0.601
2.80
Cirrhosis of liver (A102)
+0.139
+0.027
0.19
Bronchitis, emphysema, asthma
(A93)
+0.121
+0.603
4.98
Stomach cancer (A47)
+0.114
+0.148
1.30
Diseases of arteries, arterioles
and capillaries (A86)
+0.036
+0.680
18.89
VIIIth revision of ICD
* Expected
value = std(cause of death)/std(all causes) Preston, Nelson, 1974
Columbia University - Research Seminars in Epidemiology
A Broader View on the
Historical Changes in Mortality
10-1
Log (Hazard Rate)
1925
1960
1980
2000
Swedish Females
10-2
Data source: Human
Mortality Database
10-3
10-4
0
20
40
60
80
Age
Columbia University - Research Seminars in Epidemiology
Preliminary Conclusions



There was some evidence for ‘ biological’
mortality limits in the past, but these
‘limits’ proved to be responsive to the
recent technological and medical progress.
Thus, there is no convincing evidence for
absolute ‘biological’ mortality limits now.
Analogy for illustration and clarification: There was
a limit to the speed of airplane flight in the past (‘sound’
barrier), but it was overcome by further technological
progress. Similar observations seems to be applicable to
current human mortality decline.
Columbia University - Research Seminars in Epidemiology