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July 06, 2003


This is about death.

The crude death rate in a population is the number of deaths per head (or per thousand, etc) in a given period. As with the crude birth rate, it has its uses, but it is seriously affected by the age structure of the population.

For most purposes it is more useful to consider age-specific death (mortality) rates, i.e. the proportion of people in a specified age group who die in the given period. Mortality rates are also used to estimate ‘life expectancy’. The term ‘life expectancy’ is so widely used that we all like to think we know what it means, but there is scope for serious misunderstandings.

To calculate the ‘life expectancy’ for someone at a given age is in principle quite simple. Take a large hypothetical cohort of people of that age, and use the mortality rate for that age to estimate the number who will die in the next year. Then take the hypothetical survivors and repeat the process, using the mortality rate for people a year older than the starting age. Continue with the process until all of the hypothetical cohort are ‘dead’. Then add up the total years of survival for the entire cohort, and divide by the number of individuals at the start. This gives average life expectancy at the starting age.

It is easy to see that this single figure for life expectancy tells you very little. There can be enormous variation around the average. It should also be clear that the average (mean) is likely to be different from the median, especially for older age groups. The average is stretched out by the minority of people who live to a very old age. In calculating life expectancy at age 80, one person who lives to 100 has as much weight as 20 people who die at age 81.

Still, life expectancy can be a useful way of summarising and comparing mortality experience of different ages, times, or places. For example, here are life expectancies in 1900 and 2000 for white US males of various ages (expected age at death is in brackets).

0................48 (48)......75 (75)
10..............51 (61)......65 (75)
20..............42 (62)......56 (76)
30..............35 (65)......46 (76)
40..............28 (68)......37 (77)
50..............21 (71)......28 (78)
60..............14 (74)......20 (80)
70................9 (79)......13 (83)
80................5 (85)........8 (88)

This shows clearly how life expectancy at all ages has improved between 1900 and 2000. But it would be a mistake to infer from these figures that a group of people born in 1900 actually lived, on average, for 48 years. The standard calculation of life expectancy uses a ‘period life table’ based on age-specific mortality rates in the same short period of time. So ‘life expectancy’ at birth in 1900 uses the mortality rates prevailing in 1900 for 10-year-olds, 20-year-olds, etc. It is a highly artificial construct.

There is an alternative method, using ‘cohort life tables’, which traces the experience of a cohort of people retrospectively, using the mortality rates which prevailed at relevant periods during their life. So the rate applied at age 30 to someone born in 1900 would be the observed mortality rate for 30-year-olds in 1930, not in 1900, as in the standard method. ‘Life expectancy’ calculated in this way can be substantially different, because it takes account of changes in medicine, nutrition, etc., during the cohort’s lifetime. For example, the cohort method adds more than 5 years to life expectancy at birth in 1900. Unfortunately, it is not always stated which method has been used.

The most prevalent misunderstanding of ‘life expectancy’ is to take it as a reliable prediction of how long people will live in future. The very term ‘life expectancy’ encourages this interpretation. But this is unjustified unless we have good reasons for supposing that age-specific death rates will stay the same as they are now. Over the short-to-medium term this is reasonable, in modern Western societies, because death rates usually do not change very rapidly. But over the long term they do change substantially. So if someone says that a newborn baby can ‘expect’ to live (say) 75 years, without heavily qualifying that statement, he is just a snake-oil salesman.

We tend to assume that life expectancy will go on rising, thanks to medical progress, improved nutrition, less smoking, and so on. This is a plausible assumption, but it could turn out wrong. Apart from the possibility of unknown new viral diseases, antibiotic-resistant bacteria, etc., there is the possibility that the genetic quality of the population is deteriorating. Calculations of life expectancy tacitly assume that today’s newborn children will be as resistant to disease in 80 years’ time (if they live that long) as present-day 80-year-olds are. But present-day 80-year-olds were born in the 1920s, when there were no antibiotics, nutrition was poor, TB was rampant, and infant and child mortality were much higher than now. To have survived to their 80s, they must be tough cookies. There is no guarantee that today’s children (or ourselves) will be equally resistant.


Posted by David B at 03:51 AM

many ppl assume they'll live until they're 130 you know...don't rain on their parade david! randall, any opinions?

Posted by: razib at July 6, 2003 10:55 PM

Threescore and ten are the years allotted to man. True now, true 5000 years ago.

(at least for the non-slave classes back then--check out some of the ages of rich Romans/Greeks)


Posted by: David at July 8, 2003 09:52 AM