Life Tables contd.

1
Life Tables contd.

• Questions?
• Review
• Today
• Life Table Review
• Survival Rates
• The essence of cohort survival
• Introduction to Fertility/Births component

2
Cohort Survival

• Mortality, fertility and mobility
• Survival and Life Tables - today
• Fertility and births - Thursday
• Net Migration as a residual and migration rates -
  Tuesday

3
Mortality and Life Tables

• We need to determine s -- the sex-specific and
  age-cohort-specific survival rate
• For live births
• For each cohort to the next
• For the last, open-ended cohort
• Life Table is the key to determining s

4
How to Get a Life Table

• http//0-www.statcan.ca.darius.uleth.ca/english/fr
  eepub/84-537-XIE/tables.htm
• Course page
• Alberta Male Life Table
• Alberta Female Life Table
• These are complete current life tables for
  1995-1997 they are also linked directly to the
  course web page

5
Anatomy of a Current Life Table I

• Age x (age interval x to just before,x1), one
  year time interval between exact age, the period
  when one is x years of age
• Radix of 100,000
• lx the number living on their xth birthday
• When they are exactly x years of age
• The number surviving at the start of the age
  interval
• dx the number dying who survived to reach age x
  but died before they reached age x1
• Note that l1 l0-d0

6
Anatomy of a Current Life Table II

• px the proportion of survivors at exact age x
  that are expected to survive until their next
  birthday
• The probability of those aged exactly x, living
  to their next birthday
• qx the proportion of survivors at exact age x
  that are not expected to survive until their next
  birthday
• The probability that someone of exact age x will
  die before they are x1
• Note that pxqx 1.0

7
For the Next Two Columns, We Assume a Stationary
Population

• A hypothetical population that does not grow or
  decline
• 100,000 person are born and die each year
• Proportion dying each year corresponds to qx
• Assume no migration
• Births and deaths evenly distributed through the
  year
• Thus number of persons in each age interval
  remains the same year-round.

8
Anatomy of a Current Life Table III

• Lx the total number of persons in the stationary
  population in the x to x1 age interval
• The number of person-years lived by the
  stationary population in each age interval
• average population of age x, alive, between
  birthdays
• Note that Lx (lx lx1)/2

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Anatomy of a Current Life Table IV

• Tx the total number of persons in the
  stationary population for each age interval and
  all subsequent intervals
• Cumulative value of Lx and all older Lx
• Total number of person-years that will be lived
  by the stationary population in the x to x1
  interval and all later intervals
• Note that Tx Tx1 Lx1

10
Anatomy of a Current Life Table V

• ex average remaining lifetime for a person who
  has survived up to an exact age x
• Life expectancy at age x
• Average number of years remaining to be lived by
  persons surviving to exact age x
• Note that ex Tx/lx
• And e0 is the male or female life expectancy at
  birth, an index commonly used as a measure of
  quality of life and human development.

11
Now We Know Enough to Compute Survival Rates

• For a complete life table, there is one row for
  each exact year age,
• We can easily compute one year survival rates s
  n,n1 where n represents the number of a one year
  cohort
• Recall

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Computing one year Survival Rates I
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Computing one year Survival Rates II

• For the two special cohorts

Survival into 1st age interval (Note correction
to last lecture and the text book, p. 72)
Survival within last, open-ended cohort
Caution! We are dealing with Tn not Tx, n is
cohort number not age, x
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But these are one year survival rates!

• We need multiple year survival rates to be
  consistent with the size of cohort, typically 5
  year or ten year cohorts
• Easy if we had abridged 10 year life table
• We must compute a new set of n-year cohort
  values, Dn based on Tx

15
Computing Multiple Year Survival Rates I

• Where n is the cohort number
• And x is the start of the age interval
  corresponding to n

16
Computing Multiple Year Survival Rates II

• For the two special cohorts

Survival into 1st age interval
Survival within last, open-ended cohort
17
Easy - Peasy!
18
Class Exercise

• Using the Alberta Male Life Tables 1995-1997,
  Compute
• S1,2 cohort 1 to cohort 2, 0-9, 10-19
• S0,1 birth to 0-9 cohort
• S8,8 open-ended 70 cohort
• Hint Use Table 5.2 of your text as a template

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Cohort Survival

• We now know s -- the sex-specific and
  age-cohort-specific survival rate
• For live births
• For each cohort to the next
• For the last, open-ended cohort
• Given 3,995 males in the 0-9 cohort in Lethbridge
  in 2002, how many will survive until 2012?

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Compute

• 3995 0.9970 3983
• Of course this is an expected number based on
  probabilities derived from 1995-97.

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For next week

• Read Chapters 6, 7, 8
• Issues to face
• Computing average number of women per fecund
  cohort including a very important migration
  component!
• Computing fertility rate
• Sex assignment