Every so often I’l hear on the news something like: Babies born this year will live an average of 80.5 years.
I don’t see how you can predict such a thing. There is no way of knowing what medical treatments will be created in the intervening years. Likewise, we can’t predict societal trends. For instance, what if the obesity epidemic accelerates? What if if the Atkins thing really works, and there is no obesity in ten years? What if we have cures, or preventions, for heart disease, stroke, every type of cancer and drug addiction in ten years?
Are these numbers just based on assuming that current trends will continue as they have in the recent past, or is there something else I’m missing here?
Life expectancy is based on the current statistics. So , when they say a baby is going to live 80.5 years, they aren’t making any prediction. It’s just that, on average, people currently live 80.5 years (I assume it would be a baby girl. The life expectancy of males is below 80 years in all countries, AFAIK, except perhaps Japan, but I don’t think so).
Also, quite consistently, the average age at death has been rising at two years per decade for the past fifty years or so. Assuming that the average life expectancy continues to rise at the same rate into the future is no different than assuming that Moore’s Law will continue to operate for the forseeable future. Moore’s Law says that computer power will double every year and a half. It is possible to make a reasonable guess at future life expectancy.
>Life expectancy is based on the current statistics. So , when they say a baby is going to live 80.5 years, they aren’t making any prediction. It’s just that, on average, people currently live 80.5 years…
Well, no, it’s more complicated than that. Statisticians certainly understand that average age at death is something that gradually drifts over the decades, such that more people born in 1900 saw their 80th birthday than did people born in 1800, and can predict that an even greater fraction born in 2000 would do so.
What does “people currently live 80.5 years” mean? That people born today will live an average of 80.5? That half the people born 80.5 years ago are still alive (actually this would be a remark about medians and not means, but I couldn’t think of a simple statement remarking about means)?
They also appreciate that average life expectancy is influenced by people dying young. That’s why the older YOU get, the greater your life expectancy gets also. In other words, now that I am 47, I’m guaranteed I won’t die before the age of 46, whereas 30 years ago I didn’t know that. The life expectancy of people that are now over 90 years old is, obviously, somewhat more than 90 years, maybe 93 or 98 or something.
There are many ways of modeling the age a person would die and taking into consideration various demographics including the year of birth. They are all reasonable in some sense. Generally they assume a distribution of some sort, such as a Weibull (IIRC), and try to include various causes.
The word “average” is one of those very tricksy bits, that can be used to mean lots of different things. Generally, “average life expectancy” is neither mode nor mean nor median, but is expected value (from a probablistic sense.)
An average (mean) life expectancy would be taking all the people who died (let’s say in the last five years), finding their age at death, and dividing by the number of people who did die.
An average (mode) life expenctancy would be taking all the people who died (let’s say in the last five years), and finding the most common age at death.
An average (median) life expectancy would be taking the ages of all the people who died (let’s say in the last five years), and finding the age that’s in the middle (the 50th percentile.)
None of those are what is generally meant by actuaries, insurance companies, and statisticians when they talk about “average life expectancy.” Instead, they mean the expected value. The expected value is found by multipying, for each age, the probability of death at that age (as determined by actuarial tables) by the number of people who lived up to that age; and then summing all those values. In non-mathematics, it’s the expected (average) outcome if you started a zillion people at age 0 today, and if your probabilities were accurate.
If you like, let me use the analogy that we’ve got data on 100 million rolls of one die. We can therefore find the mean, or median, or mode for the 100 million rolls… but the expected value of rolling a 3 is still 1/6.
Actuarial life tables (from which life expectancy figures are derived) are normally compiled from the most recent population mortality statistics. The Australian Life Tables are produced every 5 years by the Commonwealth Government Actuary , using the results of the quinquennial population census.
The census data is analysed to produce age-specific mortality rates for both males and females. These mortality rates are then applied to a hypothetical initial population (say 100,000), from birth. The total lifespans of the hypothetical population are then projected, from which an average life-span is derived. It’s obviously not, and is certainly not intended to be, a “predictor” of future mortality rates. It’s simply a method of producing an average age at death for a population born today, and assumed to experience (over the lives of the whole cohort, which could be as much as 120 years), the current population mortality rates.
I can’t see calling this an average life expectancy. Even if the distribution of age of death were constant, this will be biased by variations in birth rates in the past, including a long-term tendency for birth rates to increase as population grows.
Josh, I was just trying to point out that the word “average” has several interpretations (outside of mathematics, where it means mean). The actual “average life expectancy” is an expected value, not a mean, nor a median, nor a mode.
I didn’t mean the birth rate per woman, I meant the total number of births per year. I presume that that has tended in the long term to increase with increasing population (though at particular times it has been decreasing, for example during the decline of the “baby boom” in the U.S.). If it were actually decreasing, my point would still stand (the bias would be in the opposite direction).
Then you should use the words more carefully. The “birth rate” means the number of babies born relative to the number of people alive in a given year (so that we might talk about how there were 893 babies born per 100,000 people alive in a given year). One could also talk about the average number of babies born to each woman over her lifetime (so that we might talk about how the average woman had 2.31 babies in her lifetime). (Those two numbers just made up at random.) I don’t see how either of these numbers, nor the raw number of babies born in a year, show anything about the difference in average life expectancy.
OK, I used “birth rate” incorrectly. Thank you for the polite correction.
I was addressing a particular statistic mentioned by C K Dexter Haven. Suppose for simplicity that the distribution of lifespan does not change over time. Let’s tabulate the ages of all people who die over some period of time. This will have some distribution. Will this be the same as the distribution of lifespan? It will if and only if the number of birth per unit time has been constant in the past. If, for example, there was a sharp peak in baby production sixty years earlier, there will be peak at sixty in the distribution of those who died, but this will not correspond to a peak in mortality rates for sixty year-olds.