Using

1
Using Interpreting the Single Decrement Life
Table

• Examples

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Plan

• Review Period Life Table Construction
• Ways of using the life table
• The life table as a Stationary Population
• Examples
• Life tables from South Africa
• Life tables from Zambia
• Life tables from the USA

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Creating a Period Life Table

• The data available are usually observed
  age-specific mortality rates, nMx
• Critical assumption is that nMx nmx
• The trick then is to convert these observed
  age-specific mortality rates into one of the
  columns of a life table
• The most convenient choice is to convert to nqx
• nMx to nqx conversion

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Strategies for Choosing nax

• nmx ? nqx requires nax where do we get nax ?
• From calculating it directly
• From smoothing (graduating) the death
  distribution within each age interval
• Borrowing values from another population
• Making one of two assumptions
• nax is half the length of the age interval (n/2),
  or
• nmx is constant in the interval which negates the
  necessity of using nax because there is a direct
  formula to calculate npx

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nax in Practice

• Usually use n/2 for all age groups except the
  first
• Mortality rate between ages 0 and 5 changes very
  rapidly, falling very quickly at first and then
  flattening out
• Consequently most deaths early in life occur
  closer to 0 than to 5 and hence nax is
  significantly less than n/2 in the first two age
  groups (0, 1-4)
• In general in other age groups where mortality is
  changing less rapidly, the overall life table is
  very insensitive to the exact choice of nax

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nax for Very Young Ages
7
Example Sensitivity of ex to nax
8
Life Table Columns nmx

• Death rate in the cohort between ages x and xn
• In constructing a period life table, we usually
  start by assuming that the observed mortality
  rates are equal to the life table mortality
  rates nmx nMx

9
Life Table Columns nax

• Average number of years lived in the age interval
  by those dying in the age interval
• We must acquire the nax values from somewhere,
  discussed previously

10
Life Table Columns nqx

• Probability of dying between ages x and xn
• This is where we usually start constructing the
  life table

11
Life Table Columns npx

• Probability of surviving from ages x to xn

12
Life Table Columns lx

• Survivors, number left alive at age xn

13
Life Table Columns ndx

• Number dying between ages x and xn

14
Life Table Columns nLx

• Person-years lived between ages x and xn
• Because n is effectively infinite for the open
  (last) age interval, we cannot calculate nLx
  given the formulas we have

15
Life Table Columns Tx

• Person-years lived at ages older than x

16
Life Table Columns ex

• Expectation of life at age x average additional
  years of life that someone who survives to age x
  can expect to live
• Single-Life-Table-Template.xls

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Additional Ways of Using a Life Table

• Probability of surviving from age x to age y
• Probability of dying between ages x and y
• Number of people dying between ages x and y
• Number of person years lived between ages x and y
• Probability that a newborn will die between ages
  x and xn

18
Additional Ways of Using a Life Table

• Probability that a newborn will experience their
  death between ages x and y
• Number of years that a newborn can expect to live
  between ages x and y
• Probability that newborn will survive to age x
• Probability that a newborn will die before age x

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The Life Table as Stationary Population

• A stationary population has
• Age-specific mortality constant through time
• The number of births constant through time
• Net migration 0 at all ages
• ? size and age structure that are constant
  through time

20
Stationary Population Life Table Columns

• is the number of births each year
• is the number at age x in each year
• is the number between age x and xn in each year
• is the number above age x in each year
• is the population size
• is the number dying between age x and xn each
  year
• is the mean age at death

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Stationary Population Relationships
22
Simple Examples

• Constant graduate student population of size 40
  with 10 new and 10 graduating each year
• Constant number of employees, average time spent
  in a job is five years

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• LIFE TABLES FROM SOUTH AFRICA
• Life-Tables_South-Africa.xls

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Life Table Template

• Examine life table template
• It is possible to calculate standard errors
  around life table values
• See
• Chiang, C.L. 1984. The Life Table and Its
  Applications. Malabar, FL Robert E. Krieger
  Publishing Company.
• Single-Life-Table-Template.xls

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• LIFE TABLES FROM ZAMBIA
• Life-Tables_Zambia.xls

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• LIFE TABLES FROM USA
• Male-USA-LTs-1959-2002.xls
• Human-Mortality-Database-1x1.mdb

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