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					Longevity
 Human Development 117
    Entomology 117

University of California, Davis
       Fall Quarter, 2001




         Instructor:

       James R. Carey
  Department of Entomology
      Instructor: Prof. James R. Carey                     Office: 67 Briggs Hall
      Email: jrcarey@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-      Population 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    Thu    Dec. 6                  The future of human life span
   Grading:

    (1) tests—2 midterms and a final exam. These
will be combination of short-answer and objective
questions (T/F & multiple choice).
    (2) problem sets—a total of 3 problem sets,
discussion questions, and/or short essays.
    (3) discussion—email response to questions in
class; possible quizzes
    (4) term paper--a 2,500 word term paper

    Weightings will be as follows: 2 midterms
@15% each (total 30%), discussion=5%, 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.
TTerm Paper:
1. Purpose
2. Subject
3. Procedures
4. Specific Requirements
5. Grading
What Learn in Course

1. Longevity (i.e. course topic)


2. Science (i.e. questions and process)


3. Writing (i.e. quality over quantity)
   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 disciplines—biology 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.
  Additional Course Details and Expectations

1. No course book or syllabus. All lecture notes
2. Responsible for 100% of material presented in
   class; all is fair game on tests
3. Difficult tests; requires understanding both
   details and concepts
4. Some unannounced ‗quizzes‘; mostly for
   attendance (+, -, 0)
5. Please try not to come late
6. Please do not talk when I start lecture
7. Notify me before lecture if must leave early
8. No late homework or papers accepted
    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
―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
     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
     Test of Actuarial Knowledge


2. What is the record lifespan in humans?

     a) 115 years     b) 117 years

     c) 119 years     d) 122 years
     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
     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%
    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%)
     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
      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
 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
   Sources of Knowledge


1. Observation

2. Experimentation

3. Inductive and deductive reasoning
    Most Important Numbers
         in the Universe
1. Zero (0)

2. One (1)

3. e (exponent)

4. i (imaginary number)

5. pi (ratio circumference to radius)
Longitudinal survey (e.g. death rate)
        (1900 birth cohort)

  0      1      2             99     100
 1900   1901   1902           1999   2000
    Cross-sectional survey (e.g. death rate)
             1999     2000

1999 birth
  cohort      0        0
1998 birth
  cohort      1        1

              2        2




              99       99

              100      100
                 Arithmetic Series
                               Age (x)
Series       0             1             2                3

A            3             6             9                12

B            1.1           1.2           1.3              1.4

C            .001          .002          .003         .004

Common Difference: 6-3=3; 9-6=3, etc.             A

                                                  B
                                         #
                                                  C
                                                Age (x)
                 Geometric Series
                               Age (x)
Series       0             1             2                  3

A            2             4              8                 16

B            1.1           1.21          1.33          1.46

C            .0001         .0002          .0004      .0008

Common Ratio: 4/2=2; 8/2=2, etc.
                                                        A

                                         #              B

                                                        C
                                                  Age (x)
          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
                           RATES
Absolute rate of change:

Nx+1 – Nx = difference

75 – 6 5 = 10
                  Relative rate of change:

                  Nx+1 / Nx = ratio

                  75/65 = 1.15
                                  Proportional rate of change:

                                  (Nx+1 - Nx )/ Nx = proportional

                                  (75 – 65)/65 = 0.15 (or 15%)
        Longevity
            Lecture #2
      Tuesday, October 4, 2001

Part I:
1. Additional background (terms; concepts)
2. Life course
Part II:
1. Life table definition and concepts
2. Five main life table parameters
3. U.S. Life table
                Terms and Concept

•Cohort—group of individuals of same age
  (e.g. birth cohort; marriage cohort; college cohort)

•Life expectancy—average length of life (newborn)

•Life span (individual)—age at death

•Life span (species)—theoretical limit to life span
               Probability
•Probability—the likelihood of occurrence; ratio of
the number of observations of a particular type or
event to the number of all possible types or events

•a priori probability—predictable before (e.g. coin
 flips; card decks)

• a posteriori probability—predictable only after
  observation (e.g. sex ratio at birth; death rate;
  marriage probability)
              Probability
Number dead = 20
Number alive = 80
Number at risk = 100

Probability of dying = number dead/number at risk

                   = 20/100

                   = 0.20
                  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      >1 yr      Crawl; babble
Toddler       14-24 mo     <1 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
                  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      >1 yr      Crawl; babble
Toddler       14-24 mo     <1 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
                  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      >1 yr      Crawl; babble
Toddler       14-24 mo     <1 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
                  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      >1 yr      Crawl; babble
Toddler       14-24 mo     <1 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
OLDEST AGES:
Septuagenarian=70s
Octogenarian=80s
Nonagenarian=90s
Centenarian=100s
Supercentenarians>110
      Decacentenarian=110s
      Dodecacentenarian=120s
        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
             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
                Life Tables



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

Cohort life table—provides longitudinal perspective


Current life table—is 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.
                Life Tables

Single decrement—lumps all deaths into one
decrement

Multiple decrement life table—disaggregates
deaths by cause.
                    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
                   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
                    Life Tables
Column 3: This column contains cohort survival, lx
defined as the fraction of the original cohort surviving
to age x.                   Nx
                     lx 
                            N0
     N0                                     N3
l0                                    l3 
     N0                                     N0
     100,000
                                           40,000
     100,000                             
                                           100,000
    10000
      .
                                          0.4000
                       Life Tables
          Both of these are radices

         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
                            U.S. Population 2000

                                 Survival
Proportion Surviving
1.2

 1

0.8

0.6

0.4

0.2

 0
      0   10    20     30   40   50   60    70   80   90   100   110
                                 AGE (years)
                    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 x+1.
The general formula is:
                        l x 1
                   px 
                         lx

       p0 
              l1
              l0
                       
                         0.90
                                     090
                                       .
                          .
                         100

            l4            .
                         010
       p3 
            l3
                       
                         0.40
                                     0.25
                  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 x+1.
                                     l x 1
   qx  1  px              qx  1 
                                       lx
q0  1  p0                        q3  1  p3
    100  090
      .     .                           100  0.25
                                          .

    010
      .                                 0.75
            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
                      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
                       U.S. Population 2000
                      Age-specific Mortality
Mortality
1.2

 1

0.8

0.6

0.4

0.2

 0
      0     10   20   30   40   50   60   70   80   90   100   110
                                AGE (years)
                   Life Tables
Column 6: The parameter contained in this column
Is the fraction of the original cohort that dies in the
Interval x to x+1 and is denoted dx. It is the frequency
Distribution of deaths given by the general formula:
                   d x  lx  lx 1

  d0  l0  l1                        d3  l3  l4

      100  090
        .     .                           0.40  0.10
      010
        .                                  030
                                             .
                      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
                      U.S. Population 2000


             Frequency Distribution o f Deaths
Proportion Dying at Age x
0.04


0.03


0.02


0.01


   0
       0   10    20   30    40   50   60   70   80   90   100   110
                                 AGE (years)
                        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.
                  1 lx 1  lx  2  lx  3 ... l
              ex  
                  2                lx

     1 l  l  l ... l                                  1 l4  l5
 e0   1 2 3                                     e3        
     2        l0                                           2    l3
    1 0.90  0.50  0.40  010
                            .                              1 010  0.00
                                                               .
                                                          
    2            .
                100                                        2     0.40


    2.40                                                 0.75
                     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.
                    U.S. Population 2000

                         Expectation of Life
Years
100


 80


 60


 40


 20


  0
      0   10   20   30     40   50   60   70   80   90   100   110
                                AGE (years)
         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

				
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