Appendix 5 - Calculating life expectancy from a life table

Summary

Life expectancy is calculated based on what we expect to happen to a hypothetical cohort of 100,000 newborn infants if they experience the same mortality rates that currently operate within the population. (The cohort size is often denoted I_x where x is the age of interest, thus at the start age = 0 and I₀ = 100,000.) The table shows the first and last few rows of a standard life table for Australian males based on mortality rates from 2005–7.

If the probability of a male dying before his first birthday (q_o) is 0.00527 then we would expect 527 deaths in our cohort in the first year of life (d₀ = I_o × q₀) leaving 99,473 survivors at age = 1 (i.e. I₁ = 99,473). We can also estimate the numbers of years of life lived between the ages of 0 and 1. Because most infant deaths occur shortly after birth this is estimated as 99,535 years, but for older ages we assume that those who died did so, on average, halfway through the year and thus contribute 0.5 years of life. Thus, for example, at age = 3 the total years of life L₃ = 99,409 – (19 ÷ 2) = 99,399. If we repeat these calculations for each year of age up to 100 we end up with 1,412 men from our original cohort of 100,000 who survive to age 100, 445 of whom will die before their 101st birthday.