Longevity

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Longevity   Human Development 117 Entomology
117   University of California, Davis Fall
Quarter, 2001         Instructor   James R.
Carey Department of Entomology  
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Instructor Prof. James R. Carey Office 67
Briggs Hall Email jrcarey_at_ucdavis.edu Phone
752-6217 Office Hours Monday 10-11a
Wk Day Date Themes Topic(s) 1 1 Tue Oct.
2 Overview of concepts and course 2 Thur Oct. 4
Life Table Life tables I basic concepts and
techniques 2 2 Tue Oct. 9 Life tables II sex
differences cause of death 3 Thur Oct.
11 Mortality Mortality models and
concepts 3 4 Tue Oct. 16 Model systems Fruit
fly/insect models 5 Thu Oct. 18 Aging Senescence
origins theories of aging 4 6 Tue Oct.
23 Synopsis and overview of aging 7 Thu Oct.
25 1st Midterm 5 8 Tue Oct. 30 Natural- Populatio
n biology of the elderly 9 Thu Nov.
1 history Record life spans primate
patterns 6 10 Tue Nov. 6 Evolution of
longevity 11 Thu Nov. 8 Genetics of longevity
7 12 Tue Nov. 13 Biodemo- General biodemographic
principles 13 Thu Nov. 15 graphy Theory of
longevity extension 8 14 Tue Nov. 20 2nd
Midterm 15 Thu Nov. 22 THANKSGIVING HOLIDAY
9 16 Tue Nov. 27 Human Mortality trends in
oldest-old 17 Thu Nov. 29 longevity Centenarians
and supercentenarians 10 18 Tue Dec.
4 Successful aging longevity determinants 19 Th
u Dec. 6 The future of human life span
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Grading (1) tests2 midterms and a final exam.
These will be combination of short-answer and
objective questions (T/F multiple choice). (2)
problem setsa total of 3 problem sets,
discussion questions, and/or short essays.
(3) discussionemail response to questions in
class possible quizzes (4) term paper--a 2,500
word term paper Weightings will be as follows 2
midterms _at_15 each (total 30), discussion5,
problem sets 20, term paper 20, final exam
25. Grades will be assigned on a curve
though never lower than 90, 80, 70 etc. for A,
B, C etc.
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TTerm Paper 1.      Purpose 2.     
Subject 3.      Procedures 4.      Specific
Requirements 5.      Grading
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• What Learn in Course
• Longevity (i.e. course topic)
• Science (i.e. questions and process)
• Writing (i.e. quality over quantity)

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Course Goals (1) to introduce a general
framework for understanding longevity in both
humans and nonhuman species (2) to integrate
the literature in two historically and
disciplinarily separate disciplinesbiology whose
roots are in the natural sciences and demography
whose historical roots are more in the social and
analytical sciences (3) to foster abstract
and integrative thought on topics concerned with
aging and longevity that are of national and
international concern.
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• Additional Course Details and Expectations
• No course book or syllabus. All lecture notes
• Responsible for 100 of material presented in
  class all is fair game on tests
• Difficult tests requires understanding both
  details and concepts
• Some unannounced quizzes mostly for attendance
  (, -, 0)
• Please try not to come late
• Please do not talk when I start lecture
• Notify me before lecture if must leave early
• No late homework or papers accepted

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Importance of Understanding Longevity (1) Aging
world population (2) Fundamental to life and
species (3) Personal and family
health (4) Emerging biotechnical
revolution (5) Business, politics, and economics
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From birth to 18, a girl needs good parents
from 18 to 35 good looks, from 35 to 55 a good
personality, and from 55 on, cash. Sophie
Tucker
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Test of Actuarial Knowledge
1. What is the life expectancy of U.S.
females? a) 73 years b) 75 years c) 77
years d) 79 years
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Test of Actuarial Knowledge
2. What is the record lifespan in humans? a)
115 years b) 117 years c) 119 years d) 122
years
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Test of Actuarial Knowledge
3. A cure for all cancers would increase current
life expectancy by how many years? a) 2
years b) 5 years c) 10 years d) 20 years
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Test of Actuarial Knowledge
4. What is the probability of a 65 year old
woman in the U.S. surviving to age 90? a)
5 b) 15 c) 20 d) 35
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Test of Actuarial Knowledge
5. Between the ages of 30 and 75 years old,
the odds of dying within a 1-year period
increase by what factor at each birthday? a)
1.02-fold (2) b) 1.04-fold (4) c)
1.08-fold (8) d) 1.16-fold (16)
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Test of Actuarial Knowledge
6. If everyone was subjected to the mortality
rate for 11-years olds, at what age would there
be 10 of the original cohort living? a) 500
years b) 1,300 years c) 6,000 years d) 14,000
years
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Test of Actuarial Knowledge
7. Suppose mortality was eliminated in U.S.
women until age 50, at which time they were
subject to the prevailing mortality rates for
each of the subsequent age classes. How much
would life expectancy be increased with this
elimination of mortality? a) 2 years b) 4
years c) 6 years d) 10 years
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Test of Actuarial Knowledge
8. The greatest total number of male deaths
occur at which age? a) 57 years b) 63
years c) 68 years d) 79 years
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Sources of Knowledge

• Observation
• Experimentation
• Inductive and deductive reasoning

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Most Important Numbers in the Universe

• Zero (0)
• One (1)
• e (exponent)
• i (imaginary number)
• pi (ratio circumference to radius)

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Longitudinal survey (e.g. death rate) (1900 birth
cohort)
0
1
2
100
99
1900
1901
1902
2000
1999
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Cross-sectional survey (e.g. death rate)
1999
2000
1999 birth cohort
0
0
1998 birth cohort
1
1
2
2
99
99
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Arithmetic Series
Common Difference 6-33 9-63, etc.
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Geometric Series
Common Ratio 4/22 8/22, etc.
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NOTATION
x always denotes age Some other letter will
denote a number or rate For example, let N
denote number alive then Nx denotes the number
alive at age x Examples N3 number alive at
age 3 N10 number alive at age 10
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RATES
Absolute rate of change Nx1 Nx
difference 75 6 5 10
Relative rate of change Nx1 / Nx
ratio 75/65 1.15
Proportional rate of change (Nx1 - Nx )/ Nx
proportional (75 65)/65 0.15 (or 15)
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Longevity Lecture 2 Tuesday, October 4, 2001

• Part I
• Additional background (terms concepts)
• Life course
• Part II
• Life table definition and concepts
• Five main life table parameters
• U.S. Life table

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Terms and Concept

• Cohortgroup of individuals of same age (e.g.
  birth cohort marriage cohort college cohort)
• Life expectancyaverage length of life (newborn)
• Life span (individual)age at death
• Life span (species)theoretical limit to life
  span

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Probability

• Probabilitythe likelihood of occurrence ratio
  ofthe number of observations of a particular
  type orevent to the number of all possible
  types or events
• a priori probabilitypredictable before (e.g.
  coin flips card decks)
• a posteriori probabilitypredictable only after
• observation (e.g. sex ratio at birth death
  rate marriage probability)

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Probability
Number dead 20 Number alive 80 Number
at risk 100 Probability of dying number
dead/number at risk 20/100
0.20
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Stages of human life course Life Phase Age
Interval Duration Example Event(s) Prebirth Zygote
Conception -- Genetic union Embryo 1 day-2
mo 2 mo Development Fetus 2-9 mo 7
mo Growth Preadult Infant 0-14 mo gt1 yr Crawl
babble Toddler 14-24 mo lt1 yr Walk single
words  Preschool 2-5 yrs 4 yrs Pre-school
vocabulary develop Childhood 6-12 7
yrs Elementary school Adolescent 13-17 5 yrs Jr
High School Pre-adult 18-21 4 yrs College
career Adult Young Adult 22-35 14 yrs Marry
first job, kids Middle Age 36-55 20 yrs Child
rearing mid-level Senior Young-old 56-65 10
yrs first grandkids job seniority
Middle-old 66-85 20 yrs active senior years
Oldest-old 86-100 15 yrs onset of chronic
diseases Super-seniors Centenarians 100-110 10
yrs usually quite frail Super-centenarians110
12 yrs very rare individuals
 

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Stages of human life course Life Phase Age
Interval Duration Example Event(s) Prebirth Zygote
Conception -- Genetic union Embryo 1 day-2
mo 2 mo Development Fetus 2-9 mo 7
mo Growth Preadult Infant 0-14 mo gt1 yr Crawl
babble Toddler 14-24 mo lt1 yr Walk single
words  Preschool 2-5 yrs 4 yrs Pre-school
vocabulary develop Childhood 6-12 7
yrs Elementary school Adolescent 13-17 5 yrs Jr
High School Pre-adult 18-21 4 yrs College
career Adult Young Adult 22-35 14 yrs Marry
first job, kids Middle Age 36-55 20 yrs Child
rearing mid-level Senior Young-old 56-65 10
yrs first grandkids job seniority
Middle-old 66-85 20 yrs active senior years
Oldest-old 86-100 15 yrs onset of chronic
diseases Super-seniors Centenarians 100-110 10
yrs usually quite frail Super-centenarians110
12 yrs very rare individuals
 

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Stages of human life course Life Phase Age
Interval Duration Example Event(s) Prebirth Zygote
Conception -- Genetic union Embryo 1 day-2
mo 2 mo Development Fetus 2-9 mo 7
mo Growth Preadult Infant 0-14 mo gt1 yr Crawl
babble Toddler 14-24 mo lt1 yr Walk single
words  Preschool 2-5 yrs 4 yrs Pre-school
vocabulary develop Childhood 6-12 7
yrs Elementary school Adolescent 13-17 5 yrs Jr
High School Pre-adult 18-21 4 yrs College
career Adult Young Adult 22-35 14 yrs Marry
first job, kids Middle Age 36-55 20 yrs Child
rearing mid-level Senior Young-old 56-65 10
yrs first grandkids job seniority
Middle-old 66-85 20 yrs active senior years
Oldest-old 86-100 15 yrs onset of chronic
diseases Super-seniors Centenarians 100-110 10
yrs usually quite frail Super-centenarians110
12 yrs very rare individuals
 

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Stages of human life course Life Phase Age
Interval Duration Example Event(s) Prebirth Zygote
Conception -- Genetic union Embryo 1 day-2
mo 2 mo Development Fetus 2-9 mo 7
mo Growth Preadult Infant 0-14 mo gt1 yr Crawl
babble Toddler 14-24 mo lt1 yr Walk single
words  Preschool 2-5 yrs 4 yrs Pre-school
vocabulary develop Childhood 6-12 7
yrs Elementary school Adolescent 13-17 5 yrs Jr
High School Pre-adult 18-21 4 yrs College
career Adult Young Adult 22-35 14 yrs Marry
first job, kids Middle Age 36-55 20 yrs Child
rearing mid-level Senior Young-old 56-65 10
yrs first grandkids job seniority
Middle-old 66-85 20 yrs active senior years
Oldest-old 86-100 15 yrs onset of chronic
diseases Super-seniors Centenarians 100-110 10
yrs usually quite frail Super-centenarians110
12 yrs very rare individuals
 

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OLDEST AGES Septuagenarian70s Octogenarian80s N
onagenarian90s Centenarian100s Supercentenarians
gt110 Decacentenarian110s Dodecacentenarian120s
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Review of Key Concepts

• Arithmetic/geometric series of numbers
• Longitudinal vs cross-sectional
• Probability
• Three different rates
• Basic terms (e.g. life expectancy)
• Notation (x Nx)
• Classification of stages in life course oldest
  old

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The Life Table

• Life tables are important because they
• serve as barometer of current health in a
  population
• identify trends in health and mortality
• provides a baseline for prediction

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Life Tables
Definitiona detailed description of the
age- specific mortality, survival and expectation
of life of a population
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Life Tables

• Answers questions
• What is the life expectancy of a newborn?
• How many years remains for the average woman?
• Over what age groups do most deaths occur?
• What is the probability of an 18 year old
• dying in the next year?
• What is this probability at age 80?
• What fraction of newborn in 2000 will live to 85?

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Life Tables

• Cohort life tableprovides longitudinal
  perspective
• Current life tableis cross sectional assumes a
• hypothetical cohort subject throughout its
  lifetime
• to the age-specific mortality rates prevailing
  for
• the actual population over a specified period.
  Is
• to construct a synthetic cohort.

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Life Tables

• Single decrementlumps all deaths into one
• decrement
• Multiple decrement life tabledisaggregates
• deaths by cause.

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Life Tables
Column 1 The first column of a life table
contains all age classes, denoted x, and ranges
from 0 (newborn) through The oldest possible age,
x (1) (2) (3)
(4) (5) (6) (7) 0 1 2 3 4 5
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Life Tables
Column 2 This column gives the number of the
original cohort alive at age x, and is denoted
Nx. The initial number is typically 100,000 and
is known as the life table radix.
x Nx (1) (2) (3)
(4) (5) (6) (7) 0 100,000 1
90,000 2 50,000 3 40,000 4
10,000 5 0
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Life Tables
Column 3 This column contains cohort survival,
lx defined as the fraction of the original cohort
surviving to age x.
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Life Tables
x Nx lx px qx
dx ex (1) (2) (3)
(4) (5) (6) (7) 0 100,000
1.000 1 90,000 .900 2 50,000
.500 3 40,000 .400 4 10,000
.100 5 0 .000
In words l3 the fraction of the initial cohort
that survives to age 3 is 0.40
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U.S. Population 2000
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Life Tables
Column 4 The parameter defined in this column
is known at period survival, px, defined as the
fraction of individuals alive at age x that
survive to age x1. The general formula is
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Life Tables
Column 5 This column contains the complement
of Period survival and is known as period or
age-specific Mortality, qx, defined as the
fraction of individuals Alive at age x that die
prior to age x1.
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Life Tables
x Nx lx px qx
dx ex (1) (2) (3)
(4) (5) (6) (7) 0 100,000 1.000
.900 1 90,000 .900 .556 2
50,000 .500 .800 3 40,000 .400
.250 4 10,000 .100 .000 5
0 .000
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Life Tables
x Nx lx px qx
dx ex (1) (2) (3)
(4) (5) (6) (7) 0 100,000 1.000
.900 .100 1 90,000 .900 .556
.444 2 50,000 .500 .800 .200 3
40,000 .400 .250 .750 4 10,000
.100 .000 1.000 5 0 .000
In words p3 the fraction of individuals alive
at age 3 that survive to age 4 is 0.250
q3 the fraction of individuals alive at age 3
that die prior to age 4 is 0.750
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U.S. Population 2000
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Life Tables
Column 6 The parameter contained in this
column Is the fraction of the original cohort
that dies in the Interval x to x1 and is
denoted dx. It is the frequency Distribution of
deaths given by the general formula
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Life Tables
x Nx lx px qx
dx ex (1) (2) (3)
(4) (5) (6) (7) 0 100,000 1.000
.900 .100 .100 1 90,000 .900 .556
.444 .400 2 50,000 .500 .800
.200 .100 3 40,000 .400 .250 .750
.300 4 10,000 .100 .000 1.000
.100 5 0 .000
In words d3 the fraction of all individuals in
the cohort that die in the interval 3 to 5
is 0.300
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U.S. Population 2000
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Life Tables
Column 7 This column contains the life table
parameter expectation of life, ex, defined as the
average number of years (days, weeks) remaining
to an individual age x.
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Life Tables
x Nx lx px qx
dx ex (1) (2) (3)
(4) (5) (6) (7) 0 100,000 1.000
.900 .100 .100 2.40 1 90,000
.900 .556 .444 .400 1.61 2 50,000
.500 .800 .200 .100 1.50 3 40,000
.400 .250 .750 .300 .75 4 10,000
.100 .000 1.000 .100 .50 5
0 .000
In words e3 the number of years remaining to
the average individual age 3 is 0.75.
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U.S. Population 2000
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Hypothetical Life Table
x Nx lx px qx
dx ex (1) (2) (3)
(4) (5) (6) (7) 0 100,000 1.000
.900 .100 .100 2.40 1 90,000
.900 .556 .444 .400 1.61 2 50,000
.500 .800 .200 .100 1.50 3 40,000
.400 .250 .750 .300 .75 4
10,000 .100 .000 1.000 .100 .50 5
0 .000