Saturday, February 18, 2006

Actuarial Tables ARE Interesting

Most people when they hear the words "actuarial tables" think of statistical analysis and insurance and other boring subjects... But after reading a recent article about US biologist Shripad Tuljapurkar of Stanford University and his presentation at the American Association for the Advancement of Science annual meeting in St. Louis, I began to wonder if the way we create actuarial tables is all wrong. And if so, there will be enormous implications far beyond the insurance industry since we base many of our business decisions, political decisions, and personal life decisions on how long we think we will live.

According to the US Government, if you are born today you are likely to live to be about 74 years old as a male or about 80 as a female. Here is the statistical table from the social security website. What this means is that the average age at death for all people born today is 74 (I'll use the male statistics throughout this, but you can go look up the female statistics on the table if you are interested). This means that every infant that dies brings down the "average" life expectancy. Thus, as you would expect, as you grow older your "life expectancy" increases. At 20 years of age, the average life expectancy has increased to over 75 years. That is, of all the people still alive at 20, they will on average live another 55 years.

This method of calculating life expectancy assumes that relative lifespans are constant. Or, to quote the SSA website,

"The period life expectancy at a given age for 2001 represents the average number of years of life remaining if a group of persons at that age were to experience the mortality rates for 2001 over the course of their remaining life."

But this last point is precisely the one that Dr. Tuljapurkar brings into question in his report. He claims that at the current pace of medical advancement that we are adding one year of life expectancy each five years of medical research. Thus the life expectancy for someone born today should be 20 years longer than the "...mortality rates for 2001..." -- and this is just the average...

In his report he suggests that by 2050, we should be thinking that a retirement age of 85 is normal. Based on 2001 mortality rates, only the top quartile will live to be more than 85 years old. Even assuming that over the 50 years, we have added an average of 10 years of life (or, made 85 year olds as healthy as 75 year olds are today) only about half of all citizens live to be over 75 today. So these raises an interesting question about "retirement" age -- how should we think about these "golden years?" Who gets to participate? Only 50% of the population?

One of the interesting aspects of the actuarial table is looking for the "knee" in the graph. If you think about the primary causes of death you can group them largely into 3 categories -- accidents, self-inflicted, and disease. Most of the medical research that Dr. Tuljapurkar is talking about addresses disease, and in particular disease afflicting us in our old age. Thus even if the ultimate age at which we leave does not grow substantially, the "knee" in the curve could move dramatically.

91% of all US males make it past their 50th birthday. 85% are still alive at 60. At 65, when our parents think they should retire, 78% of american males are still alive. The die-off acclerates into the next few decades. 10 years later, at 75, only 58% are still alive, a 20% loss in 10 years. By comparison, between 50 and 60 only 6% die.

It seems reasonable to assume that a lot of these people are dying from preventable diseases. Even that changes in social behavior (the reduction of smoking, for example) already is going to have a big impact on this "knee" in the graph. Thus it may be reasonable to think that, rather than assuming an 85 year old in 2050 will be as healthy as a 75 year old is today, that as many as 78% of all Americans in that cohort are still alive at 85. This is a lot different than thinking that they are as healthy as 65 year olds. In fact, we may be a nation of hospital bound, breathing tube linked, living dead in 2050. The fact that medicine can keep us alive does not address the question of our quality of life at that age.

There is one male in the US out of every 100,000 born in 1906 that is alive today. The real question for the medical profession is not whether 100 years old will become, for our children, the average life expectancy. But rather, whether or not we will be living happy and healthy lives into our second centuries.

1 comment:

Damon said...

... and as you point out potentially deceiving. Past performance is no assurance of future performance.
Demographics, and the actuarial tables describing them, tend to be stable over short runs. Consider, for example, the effects of plague periods. Forecasting demographics, as suggested by Tuljapurkar ... now that gets interesting. A lot of the current interest and ongoing development of Bayesian statistical models is relevant.
Making the forecast personal, of course, is the most interesting by far