An excel spreadsheet template for calculating life expectancy is available.
tables conceptually trace a cohort of newborn babies through their entire life
Interval (x to x+n)
The period of life between two exact ages; e.g. “20 to 25” means the 5-year interval between the 20th and 25th birthdays.
Specific Mortality Rate (nMx)
The age specific mortality rate , nMx = nDx/nPx where nDx is the number of deaths occurring to persons aged n to x+n, and nPx is the number of persons aged x to x+n alive at the mid-point of the period under consideration. Mortality rates are usually presented as deaths per x persons per year, where x is a convenient population base, e.g. 10,000. If a longer period is used to count the number of deaths (e.g. 5 years as in the life table template) then an adjustment must accordingly be made to calculate the annual age specific mortality rate by dividing the derived rate by the period of observation years.
of Dying (nqx)
To estimate the exact probability of dying between age x and x+n (nqx) the deaths to persons aged x to x+n must be related to the true population at risk. The mid-period population estimate must be adjusted by adding half the number of deaths occurring over the period to it. This assumes that deaths are evenly spread throughout the time period and across the period of life under consideration.
general for age groups; nqx
= 2 x n(nMx)
assumption that deaths are spread evenly across the time period of life under
consideration is particularly unrealistic in the case of infants, where the
majority of deaths occur within the first few days of life.
To calculate the probability of dying for infants therefore, the infant
mortality rate is used, as the number of livebirths is an exact estimate of the
population at risk of dying. Therefore
for infant deaths we have;
B = number of livebirths over period of consideration.
exception occurs in the final open-ended age group (85+ in the lifetable
templates). As everybody within
this age group must die, the probability of dying is equal to 1,
The number of persons living at the beginning of the indicated age interval (x) out of the total number of births assumed as the radix of the life table.
number of persons alive at the beginning of an age interval (lx+n) is
equal to the number alive at the beginning of the previous age interval (lx),
minus the numbers of persons dying within that previous age interval
over the time period considered (ndx);
= lx - ndx
The number of persons dying within the indicated age interval (x to x+n) out of the total number of births assumed in the table.
number of persons dying within a particular age interval (ndx)
is equal to the number persons alive at the beginning of that age interval (lx)
multiplied by the probability of dying within that age interval (nqx),
= lx x nqx
Lived in Age Interval (nLx)
The number of person-years that would be lived within the indicated age interval (x to x+n) by the assumed cohort of 100,000 births. Again, assuming that deaths are spread equally across the age intervals and also across the period of consideration, then the number of person-years lived in an age interval is calculated as the mean of the populations at the beginning and end of each age interval, multiplied by the length of each age interval in years i.e. nLx = n/2 x (lx + lx+n)
difficulty arises with the estimation of 1L0,that is the
average number of infants alive who have not yet reached their first birthday.
Again the problem is that it cannot be assumed that infant deaths occur
uniformly throughout the 0 to 1 age interval.
For this reason ‘separation factors’ are used to weight the average
of l0 and l1 as follows;
= 0.3l0 + 0.7l1
additional problem lies with ¥L85,
the average number of persons alive over age 85.
This is approximated from ¥L85
Years Lived From Age x (Tx)
The total number of person-years that would be lived after the beginning of the indicated age interval by the assumed cohort of 100,000 births. This is calculated by simply cumulating the nLx column from the oldest to the youngest age.
The average remaining lifetime (in years) for a person who survives to the beginning of the indicated age interval. Calculated by dividing the total number of person-years lived from age x (Tx) by the number of persons alive at age x (lx)
i.e. ex = Tx/lx
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