1. Samuel Clark Department of Sociology, University of Washington Institute of Behavioral Science, University of Colorado at Boulder Agincourt Health and Population Unit, University of the Witwatersrand Using & Interpreting the Single Decrement Life Table Examples

2. 1 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. 2 Creating a Period Life Table  The data available are usually observed age-specific mortality rates, n M x  Critical assumption is that n M x ~ n m x  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 n q x  n M x to n q x conversion:

4. 3 Strategies for Choosing n a x  n m x  n q x requires n a x … where do we get n a x ?  From calculating it directly  From smoothing (graduating) the death distribution within each age interval  Borrowing values from another population  Making one of two assumptions: – n a x is half the length of the age interval (n/2), or – n m x is constant in the interval which negates the necessity of using n a x because there is a direct formula to calculate n p x:

5. 4 n a x 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 n a x 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 n a x

6. 5 n a x for Very Young Ages

7. 6 Example Sensitivity of e x to n a x

8. 7 Life Table Columns: n m x  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 : n m x ~ n M x

9. 8 Life Table Columns: n a x  Average number of years lived in the age interval by those dying in the age interval  We must acquire the n a x values from somewhere, discussed previously

10. 9 Life Table Columns: n q x  Probability of dying between ages x and x+n  This is where we usually start constructing the life table:

11. 10 Life Table Columns: n p x  Probability of surviving from ages x to x+n

12. 11 Life Table Columns: l x  Survivors, number left alive at age x+n

13. 12 Life Table Columns: n d x  Number dying between ages x and x+n

14. 13 Life Table Columns: n L x  Person-years lived between ages x and x+n  Because n is effectively infinite for the open (last) age interval, we cannot calculate n L x given the formulas we have:

15. 14 Life Table Columns: T x  Person-years lived at ages older than x

16. 15 Life Table Columns: e x  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. 16 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. 17 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. 18 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. 19 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. 20 Stationary Population Relationships

22. 21 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. 22 LIFE TABLES FROM SOUTH AFRICA Life-Tables_South-Africa.xls

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38. 37 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 Single-Life-Table-Template.xls

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45. 44 LIFE TABLES FROM ZAMBIA Life-Tables_Zambia.xls

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52. 51 LIFE TABLES FROM USA Male-USA-LTs-1959-2002.xls Human-Mortality-Database-1x1.mdb

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