21 replies to this topic

[DJS]

I saw this article posted on the WTA list and thought some of you might enjoy reading it.

---

Fear Of Death And Muddled Thinking




Dept. of Economics, George Mason University.
http://hanson.gmu.edu/home.html
rhanson@gmu.edu

Edited by DonSpanton, 26 August 2005 - 10:57 PM.

[sjayo]

Don: A very interesting article -- congratulations! Overall I would have to agree with your thesis, especially the suggestion that most of what goes wrong with us gets better on its own. In fact, when I was in the Dept. of Internal Medicine at the University of Chicago my physician colleagues who were geriatricians used to whisper that message in my ear all the time. However, there are a couple of other points in your paper worth noting.

1) You made reference to an exponential decline in death rates and listed two manuscripts as references. Neither of those papers suggest exponential decline --they demonstrate linear increases in life expectancy. Big difference.

2) We do know why we live so much longer today than a century ago -- of that there is no doubt. Reductions in death rates from infectious diseases expressed early in life. The effect of this reduction has been demonstrated repeatedly in the scientific literature. Where there is uncertainty is in why death rates from some infectious diseases declined before the introduction of antibiotics, but standard improvements in public health (clean water, sewage disposal, hand washing, etc.) correspond perfectly with the observed phenomenon.

3. Contrary to your statement, death rates have not fallen as rapidly in the last third of the century as they have in the first third or even two thirds of the century. I'm not sure how you came to believe this. To the contrary, in the U.S. life expectancy at older ages among females has stagnated most of the last quarter century -- indicating little or no reduction in mortality. We documented this in our NEJM article a few months ago. Death rates at younger ages are already so low that they can't decline much more, so it's not possible to achieve more rapid declines in death rates at younger ages now than that observed early in the 20th century. This we documented in our Science article in 1990.

4. If, as you say, we don't know why death rates are declining, then what is the basis for your recommendation that we exercise, smoke less, and live in rural areas? I agree we should do these things because they have been demonstrated to reduce the risk of death, but that conclusion seems to contradict your earlier statement that we don't know why death rates are declining.

Aside from these points, I think this is an excellent article -- well worth reading. My colleague Bruce Carnes and I spent the better part of the first chapter of our book dealing with the issue of the fear of death. Fascinating topic.
Best,
S. Jay Olshansky

[DJS]

[bl:)] Unfortunately the article was written by Robin Hanson. (I wish I could put something together that cogent)...maybe someday, maybe someday...

I will send him your response though. I'm sure he would be interested to hear your comments.

[sjayo]

Don: It's interesting, because most people use made-up names here and rarely if ever sign their posts -- for reasons that are mysterious to me. I never know who anyone is. Is Don Spanton your actual name?
S. Jay Olshansky

[advancedatheist]

I have to question some of Robin's epidemiology. The Japanese live in dense urban concentrations and they have nearly nearly the highest per capita cigarette consumption in the world (mostly unfiltered ones, I gather), yet they also have the highest healthy life expectancy.

Apart from that anomaly, in general Robin has correctly identified the mythological thinking underlying the belief in medical "progress." Many countries considerably poorer than the U.S. have healthier and longer-lived populations, despite all the propaganda we get in this country about the benefits of modern medicine and how we should feel thankful when the healthcare system confiscates our life savings to pay for them.

[DJS]

SJay

Don:  It's interesting, because most people use made-up names here and rarely if ever sign their posts -- for reasons that are mysterious to me.  I never know who anyone is.  Is Don Spanton your actual name?
S. Jay Olshansky

Yes Jay, I use to have a pen name, but I have since switched it over to my actual name.

I guess I will be the go liaison for this conversation. Or perhaps I will invite Robin over here to dialog directly.

Here is Robin's reply:

I wrote at http://hanson.gmu.edu/feardie.pdf :
in the developed nations it seems that age specific death rates have
fallen at a steady exponential rate for at least a century (Lee &
Carter, 1992; Tuljapurkar, Li, & Boe, 2000)

S. Jay Olshansky wrote:
>1) You made reference to an exponential decline in death rates and
>listed two manuscripts as references. Neither of those papers
>suggest exponential decline --they demonstrate linear increases in
>life expectancy. Big difference.

Huh?  Those papers look at mortality rates, not life
expectancy.  Look at the graphs in the '92 paper; the "y" axis is log
in mortality rates, and the "x" axis is in years.  The graphs show
roughly falling lines.  (That Lee-Carter paper is *the* classic paper
in modeling changing mortality trends, by the way.  For example, see
it cited prominently in http://www.popcounci...pdfs/wp/192.pdf )

>2) We do know why we live so much longer today than a century ago --
>of that there is no doubt. Reductions in death rates from infectious
>diseases expressed early in life.
>The effect of this reduction has been demonstrated repeatedly in the
>scientific literature. Where there is uncertainty is in why death
>rates from some infectious diseases declined before the introduction
>of antibiotics, but standard improvements in public health (clean
>water, sewage disposal, hand washing, etc.) correspond perfectly
>with the observed phenomenon.

"correspond perfectly" is a pretty strong claim.  Yes, both events
happened roughly from 1850 to 1950.  But can you point me to a data
paper showing any closer correspondence than this?

>3. Contrary to your statement, death rates have not fallen as
>rapidly in the last third of the century as they have in the first
>third or even two thirds of the century. I'm not sure how you came
>to believe this. To the contrary, in the U.S. life expectancy at
>older ages among females has stagnated most of the last quarter
>century -- indicating little or no reduction in mortality.

Death rates are not the same thing as life expectancy.  Because of
the changing distribution of population across ages, age specific
death rates can fall exponentially without implying a linear or even
steady increase in life expectancy.

>4. If, as you say, we don't know why death rates are declining, then
>what is the basis for your recommendation that we exercise, smoke
>less, and live in rural areas? I agree we should do these things
>because they have been demonstrated to reduce the risk of death, but
>that conclusion seems to contradict your earlier statement that we
>don't know why death rates are declining.

Looking across people at the same time, exercising more, smoking
less, and living more in rural areas correlate with lower death
rates.  But they can't explain the time trend because we are not in
fact exercising more, smoking less, and living more in rural areas
than people long ago.

Robin Hanson

[sjayo]

Robin: The Lee and Carter paper does show declining death rates, but I'm curious what leads you to believe the decline is "exponential" as you claim? Your observation that "the graphs show roughly declining lines" is not sufficient evidence that the declines are occurring exponentially. I'm quite familiar with the Lee and Carter methodology since I was the discussant at the PAA session in which it was first presented. The Tulja article also does not claim "exponentially" declining death rates -- perhaps you can show me where in those articles they suggest this. With regard to the causes of declining death rates and the rise in life expectancy, I would encourage you to read the book by James C. Riley entitled Rising Life Expectancy: A Global History (Cambridge University Press, 2001). If you want additional references, go to his reference section. You're the first person I've ever heard claim that they don't understand why life expectancy rose so rapidly. Your comment that "death rates are not the same thing as life expectancy" and that "because of the changing distribution of population across ages, age specific death rates can fall exponentially without implying a linear or even steady increase in life expectancy" is, for want of a better phrase, dead wrong. Life expectancy is insensitive to age distribution because it's calculation is based on age-specific death rates. If life expectancy stagnates, then death rates are not declining, unless of course you believe it is possible that the two can occur simultaneously. Have you ever worked with a life table? With regard to your final comment, subgroups of the population certainly do smoke less and exercise more, and they have been shown to live longer -- take a look at the work of Ken Manton who explored mortality differentials among Seventh Day Adventists and Mormons and the rest of the population. The right question was raised by advancedathiest who notes that the Japanese smoke like crazy, live in urban areas, and live much longer than us. However, the Japanese mortality structure is far different from ours -- they have practically no heart disease but very high stroke mortality, so it's hard to compare the U.S. and Japan.
S. Jay Olshansky

[robinhanson]

S. Jay Olshansky wrote:

Robin: The Lee and Carter paper does show declining death rates, but I'm curious what leads you to believe the decline is "exponential" as you claim? Your observation that "the graphs show roughly declining lines" is not sufficient evidence that the declines are occurring exponentially. I'm quite familiar with the Lee and Carter methodology since I was the discussant at the PAA session in which it was first presented. ...

I'll quote from their more web-accessible review article:
http://www.soc.upenn...ings/lee00t.pdf

Let m_xt  be the central death rate for age x at time t. The model
used for mortality is: ln(m_xt) = a + b_x k_t + e_xt . ... In most
applications so far, k_t is well-modeled as a random walk with drift:
k_t = c +  k_(t-1) + u_t. In this case, the forecast of k changes
linearly and each forecasted death rate changes at a constant
exponential rate. ... Figure 2 shows past values of k for the U.S.
from 1900 to 1989 and their forecasts from 1990 to 2065. Note that the
estimated values of k over the base period change in a linear fashion.
In fact, the change in k over the first half of the period almost
exactly equals its change in the second half. This contrasts with our
usual understanding that the pace of mortality decline has decelerated
over time, an understanding based on the trends in life expectancy at birth

[ag24]

There is a nicely memorable relation, which I think (correct me if I'm wrong please, Jay) was first noted by Vaupel, to the effect that a decline of n% per year in age-specific mortality rates across the whole life table equates rather accurately to a rise of n years per decade in life expectancy. (The most interesting value of n is of course 10, equating to my "escape velocity" concept. The human mortality rate doubling time of 7-8 years nicely demonstrates the relationship, since 1.1 to the power 7.5 is very close to 2.) As is well known, Vaupel and Jim Oeppen published a couple of years ago the observation that the "best practice" life expectancy has risen very linearly indeed over the past 160 years, by 2.5 years per decade. While there are plenty of ways to show that that trend does not constitute strong evidence that mortality rates and life expectancy will continue to progress at that same rate, I think it is what Robin was getting at in his remark, and it certainly seems to me to mean that Jay's statement "Neither of those papers suggest exponential decline -- they demonstrate linear increases in life expectancy. Big difference." is questionable, since the two things are not different at all -- they imply each other.

[robinhanson]

Mark Plus, statistical trends do not predict every case exactly. A single case is not evidence against a purported trend.

[advancedatheist]

Mark Plus, statistical trends do not predict every case exactly.  A single case is not evidence against a purported trend.

Science advances by looking at the anomalies, and Japan does have a population of 127 million, hardly a trivial sample. I don't smoke and I don't recommend that people take up the habit, but I do find the Japanese exception interesting.

BTW, Robin, have you looked at the role of egalitarianism in health and longevity? For example, what do you make of Dr. Stephen Bezruchka's claims in his Changesurfer appearances:

http://radio4all.net...nfo.php?id=8689

[robinhanson]

Mark Plus, if you told me that within Japan those who smoke more live longer, that would be a lot of data I agree. But telling me that Japan on average smokes more than other countries and lives longer, that is just one data point.

It seems that diminishing returns at the individual level is sufficient to explain correlations between inequality and poor health. No need to invoke any group level effects.

[sjayo]

Greetings Aubrey -- I'm preparing for my trip to Oxford. I think I'll be there during the same time as your meeting -- perhaps I'll stop by. I'm giving a plenary at the actuary meeting run by the Oxford Centre on Ageing.

The linkage between a percent reduction in mortality and the rise in life expectancy at birth to which you refer is from our Science article in 1990. However, it seems to me that Nathan Keyfitz seems to have thought of everything well before everyone else in this field, so it wouldn't surprise me if the idea appears in one of his publications decades ago. The mortality rate doubling time is 7-8 years depending on whether you're talking about total mortality or intrinsic mortality. I hope that's not what Robin is thinking of. Of course mortality and life expectancy do not progress at the same rate -- the rate of increase in life expectancy must decelerate as it rises because the person-years-of-life added to the life table has to shift from younger to older ages. As we both know by now, it's far more difficult to extend the life of an adult than an infant, at least in the absence of escape velocity. In Robin's paper he suggested that death rates are declining exponentially. This would mean that over given fixed periods of time, the rate of decline is accelerating much like the risk of death accelerates exponentially as a function of age. This has not occurred in humans, or any other species for that matter. In fact, to the contrary, death rates have stagnated among older women in the U.S. for most of the last quarter century, and we're not quite sure why. With regard to Jim's "best practice" life expectancy, this trend does not exist anywhere in the real world for any country -- it is a composite figure as you know based on data from a large number of countries. In my talk at Oxford I'm going to show what happens when you use this methodology to project height and weight for the U.S. population -- the result is quite interesting.
S. Jay Olshansky

[ag24]

Hi Jay - I wondered whether you might be meaning something different by "declining exponentially" than I did. I (and I think Robin) meant declining by a constant factor per unit time -- indeed very much as the risk of death accelerates exponentially as a function of age, but with the arrow of time reversed.

> height and weight for the U.S. population

Oh dear. I hope you will resist the temptation to use pictures this time...

[sjayo]

Aubrey: Of course I can't resist the opportunity. I've estimated that about the time we run one mile instantaneously (using best practice linear extrapolation of running times), which will be in the year 2580, males will be 7 1/2 feet tall and weigh about 530 pounds. My pictures are drawings of giants of the future compared to just plain old obese today.
S. Jay Olshansky

[robinhanson]

S. Jay Olshansky, was the quote I supplied clear enough for you?

[sjayo]

Robin: I don't think you're interpreting the quote correctly. Here is the quote that apparently led you to believe death rates were declining at an exponentially increasing rate:

"...forecast of k changes linearly and each forecasted death rate changes at a constant exponential rate"

This is not a statement that historical trends in age-specific death rates declined at an exponentially increasing rate -- that would mean that over fixed periods of time the rate of decline accelerated exponentially. Do you understand what that would mean? If not, read 3 posts up -- I explained it there. That's not what happened. Besides, they're talking about a "forecasted" death rate, not an observation of the past, which of course is what you were commenting on. So no, although I liked your article in general, your comment that death rates declined exponentially is still as incorrect today as it was on 26 August when I first pointed it out. Is that clear enough?
S. Jay Olshansky

Edited by sjayo, 29 August 2005 - 03:25 PM.

[robinhanson]

S. Jay Olshansky, you excerpted one sentence (lines 4-6) from the 12 line quite I showed, and complain it is only about forecasts, not about the past. But the very next sentence (lines 6-8) says

Figure 2 shows past values of k for the U.S.
from 1900 to 1989 and their forecasts from 1990 to 2065. Note that the
estimated values of k over the base period change in a linear fashion.

In the past k has been linear, and that is why they forecast a future linear k. Hence log mortality rate is linear in time, and so mortality rate is exponential in time.

[sjayo]

Robin: I figured it would be simpler if I just asked Ron Lee to explain this. Here is his response. As you will see, he intended to use the phrase exponential rate of decline to mean a constant proportional rate of decline in death rates -- not an actual exponential rate of decline, which of course the data do not indicate as Ron notes in his last sentence. No worries though, even Ron acknowledged the ambiguity of the phrase.
S. Jay Olshansky

The phrase "rate of decline of death rates" is ambiguous. It could mean
the change over time in the death rate, say m(x,t)-m(x,t-1), which I would
call the arithmetic rate of decline. Or it could mean the exponential or
proportional rate of decline, ln[m(x,t)] - ln[m(x,t-1)]. So opportunities
for misunderstanding abound. What I surely meant was that the exponential
or proportional rate of decline was constant. IN general, if mortality is
declining and the exponential rate of decline is constant, then the
arithmetic rate of decline will be decreasing over time.

[jaydfox]

Heh, mortality rates have fallen at an exponential rate. But, consider the implication of such a statement. People normally think of exponential in terms of things getting bigger and bigger, or faster and faster, of accelerating.

For example, if the mortality rate fell by 2% in the 1950's, and then by a further 3% in 1960's, and then by a further 4.5% in the 1970's, and then by a further 6.8% in the 1980's, and then by a further 10.1% in the 1990's, etc. That would be what is "implied" by exponential.

But what is actually the fact of the matter, is that a mortality rate that declines at a constant, say 5%, relative rate (relative to its previous value) is exponential, but on the "tail" or "decelerating" side of the curve, not the "exploding" or "accelerating" side of the curve.

For example, a mortality rate (for some unspecified mortality class) of 0.50000 in the 1950's, which reduced to 0.47500 in the 1960's, which reduced to 0.45125 in the 1970's, which reduced to 0.42869 in the 1980's, which reduced to 0.40725 in the 1990's, is declining exponentially (on a linear scale: on a logarithmic scale, it's declining linearly). But consider, on a linear, absolute scale, the decline is actually decelerating (since otherwise it could reach zero and overshoot the mark into negative territory, which I guess would involve zombies rising from the dead!).

So rather than get worked up about this, let's just recognize that this was a simple misinterpretation by several parties on what "exponential" implied and/or meant. In such cases, one should be clear and provide explanation, or avoid the term altogether. Even though the use of the word "exponential" was technically correct, in declaring a linearly decelerating drop in mortality rates (i.e. the "tail" side of an exponential curve, like that used in half-life studies), it was rather implicitly saying that the rates were accelerating in some meaningful way. "Exponential" is a very charged word. Let's just stick with decreasing at a near-constant relative rate (or percentage rate, where the percentage implies it's relative) per time.

[Mind]

Mark, I think your contrast between less advanced societies and the U.S. has more to do with diet than technology. I think it is unquestionable that technologically advanced societes are better at correctly diagnosing disease and other ailments. We are also better at "patching things up" because we have good precision tools. The hunter-gatherer and agrarian societies you are referring to exercise more and eat better, and I think that explains the difference in life expectancy. Like dukenukem says "Americans are on a death diet".

[sjayo]

Yes Jaydfox, the word exponential is often misused, and as Ron Lee indicates, even he suggests that in his own writing it can have an ambiguous meaning. That is why I was pointing out what it doesn't mean when referring to declines in death rates for the U.S. population. This was actually a minor point relative to the suggestion that death rates declined more rapidly in the latter part of the century relative to the beginning of the century, or that life expectancy is influenced by the age distribution of the population. In spite of these issues, the overall content of the article was excellent. End of discussion as far as I'm concerned.
S. Jay Olshansky