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Using & Interpreting the Single Decrement Life Table

Using & Interpreting the Single Decrement Life Table. Examples. 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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Using & Interpreting the Single Decrement Life Table

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  1. Using & Interpreting the Single Decrement Life Table Examples

  2. 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

  3. 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:

  4. 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:

  5. 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

  6. 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 x+n • 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. Probability of dying between ages x and x+n This is where we usually start constructing the life table: Life Table Columns: nqx

  11. Life Table Columns: npx • Probability of surviving from ages x to x+n

  12. Survivors, number left alive at age x+n Life Table Columns: lx

  13. Life Table Columns: ndx • Number dying between ages x and x+n

  14. Life Table Columns: nLx • Person-years lived between ages x and x+n • 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

  17. 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 x+n

  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

  19. 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 x+n in each year is the number above age x in each year is the population size is the number dying between age x and x+n each year is the mean age at death

  21. 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:

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

  24. 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

  25. LIFE TABLES FROM ZAMBIA Life-Tables_Zambia.xls

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