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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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

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:

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:

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

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

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

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:

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

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

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

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

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

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:

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