## What Does Life Expectancy Represent?

August 25, 2008

Every year, the new life expectancy figures come out to grand fanfare. “Life expectancy is now XXX, up YYY years from last year”, but what does this number actually represent? Is it meaningful? You might think you know, but you’re probably wrong. I know I was…

I became curious about life expectancy statistics because my grandfather died a few years ago at the age of 94. It got me thinking, how long were people expected to live when he was born? Given all the scientific advances we’ve made in the last hundred years, how long did people of his generation actually live? Did he outlive his expected life span?

#### Life Expectancy vs. Expected Lifetime

Life expectancy for 2005 in the U.S. was 77.8. So, the assumption is that, on average, anyone born in 2005 can expect, on average, to live to the age of 77.8, right? Wrong.

In mathematics, expectancy is a term used to describe the expected future value of something, based on current knowledge. For example, if you flip a coin 10 times and you win \$1 for heads and lose a \$1 for tails, the expectancy for this game is \$0 because you expect, on average, an equal number of heads and tails.

So life expectancy then is the expected average lifetime of someone born today, based on what we know today – i.e. the death rates for today. The way they calculate this (and have since the 17th century) is by using life tables. Life tables give you, based on your current age, the probability of living one more year. For example, they tell you that if you were 39 in 2004, that you had a 99.82% chance of making it to 40.

The problem is, to calculate the 77.8 life expectancy figure for 2005, they’re applying those chances of someone making it from 39 to 40 in 2005, and projecting them 39 years in the future to calculate future survivability. So, 77.8 is really a fictional number that says that for someone born in 2005, if death rates at a given age were to remain as they were in 2005, this is how long they’d live on average.

We can probably all agree that it’s likely a lot of things are going to change in the next hundred years that will impact mortality rates. For example, there may be some big scientific breakthroughs on cancer or heart disease, there could be another world war or infectious disease pandemic, or we could be attacked by aliens…

Either way, life expectancy is not the same as expected lifetime.

#### Life Expectancy vs. Actual Lifetime

So if life expectancy is a projection of present knowledge on future longevity, we should be able to see how far off these figures were. For example, life expectancy for someone born in 1900 was 49.2; what was their actual average lifetime?

As I was trying to find actual longevity information, I came across a text book called “Development Through Life” by Newman & Newman that said that current life expectancy values are calculated using life tables, whereas life expectancy values for someone born in 1900 are now based on actual rates of death. This completely confused me because it implied that life expectancy was a dynamic number. That somehow life expectancy values from previous years would be recalculated using actual death rates. This would also imply that comparing the life expectancy for someone born in 1900 vs. someone born in 2000 would be completely bogus because we’d be comparing apples and oranges.

Fortunately, this assertion doesn’t seem to be true. Going back to the life tables from the CDC published in 1900, the numbers appear the same as the numbers reported for 1900 today, so I’m not sure what Newman & Newman were talking about…

In the end, I couldn’t find the numbers I was looking for, so I calculated them myself. To estimate the actual average lifetime for someone born in 1900 you can incrementally use all the life tables produced over the last hundred years because those life tables are calculated based on actual death rates for that year. For example, if you managed to survive to the age of 40, then the life tables from 1940 for someone aged 40 will tell you what the chances were of living to the age of 41. The biggest limitation to this approach is we can’t control for things like immigration and migration. Oh well, c’est la vie.

From my calculations, the average lifetime for someone born in 1900 was actually something like 55 years, rather than the original life expectancy of 49.2. Notice that over time, average lifetime seems to consistently be about 10 years longer than life expectancy.

[Note that the lines converge because as we get closer to the present, more and more people are still alive, which means I had to use more and more life table data rather than actual death data. As we progress into the future, I expect the average lifetime to retroactively creep as people continue to live beyond their original expectancy (as least as long as life expectancy continues to rise).]

#### Life Span

Life span usually refers to the maximum lifetime of a species. So, given that life expectancy is going up, you might ask if human life spans also being extended? It doesn’t appear so. The maximum life span for humans still seems to be about 110 years.

So the fact that my grandfather lived to the age of 94 wasn’t really statistically extraordinary; it was just a lot less likely than me living to the age of 94.

#### Usefulness?

So now that we understand life expectancy, what can we do with it? You and me personally, probably not much. The fact that overall life expectancy was 77.8 years in 2005 is pretty meaningless because it’s a composite number for everyone alive in 2005. It’s not that useful for a new baby, because the figures don’t attempt to predict the future. And it’s not relevant to someone born 40 years ago because how do you combine it with the life expectancy from 40 years ago? The number might as well be 75, 80, or 85.

But the change in the expectancy figure year to year can tell us something. Namely, if life expectancy is going up, it tells us that we’re all currently, on average, living longer – which is probably a good thing (assuming we have reasonable quality of life).

What about the fact that the life expectancy for someone who was 80 in 2005 was 9 years? Medical science isn’t likely to change significantly in the next 9 years, so the number is at least relevant. That said, your remaining lifetime at that age is probably more heavily affected by your current health rather than these general averages, so maybe that’s not all that useful either…

What about retirement? Can you make financial plans using these life expectancy numbers? If you do, you may be in for an unpleasant surprise… If the current trend continues, life expectancy will continue to under-estimate actual lifetimes. Life expectancy was off by 6 years for people born in 1900. How far off will it be for your generation?

1. I have a question rather than a comment. In the Social Security Life Table, 2007, the male life expectancy at birth is 75.38 years. But if I look down the column showing the number of males still alive out of 100,000 I find that 50,951 are still alive at age 79, meaning that more than half the males are still alive 4 years after their life expectancy. Why doesn’t life expectancy represent a 50/50 chance of dying?

• That’s the difference between median and mean.

The median life expectancy would the age at which half of people live shorter, and half live longer. So in the stats you cited, the median life expectancy for men is about 79, and the median life expectancy for women is about 84.

The mean (average) life expectancy on the other hand, is calculated by adding up everyone’s actual life span and dividing by the number of people. Since life expectancy drops off fairly quickly into our 70s and 80s, median life expectancy is going to be longer than average life expectancy.

2. Thanks for the explanation.

In looking at the data in the Social Security Life Table though, it appears to me that median life expectancy is a more accurate predictor than mean life expectancy since a person has a 50% chance of dying at the median life expectancy age, but has greater than a 60% chance of being alive at the mean life expectancy age. However, mean life expectancy seems to be the one universally used. What am I missing?

• I agree. Median life expectancy does seem to be the more useful number. I’m not sure why the mean would be the preferred value, other than maybe the average person doesn’t know the median means. 😉

3. What about the fact that our average length of life is gradually declining. People of earlier generations lived longer than our generations. What measurements do you have about that. Is it stable or declining?

• I don’t see any evidence that average length of life is declining (in the U.S at least), or that earlier generations are living longer than the current generation – although we won’t be able to prove it either way until we’re all dead.

From the CDC (http://www.cdc.gov/nchs/fastats/lifexpec.htm), the stats indicate that life expectancy is still increasing, and mortality rates are still decreasing.

Life expectancy was:
– 2005: 77.8
– 2009: 78.5
– 2011: 78.8

4. if it says when symptoms start life expectancy is 10 years had symptoms for years but was just diagnosed what would that mean?