The Median isn't the message

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Regular Member

Date Joined Jun 2007
Total Posts : 75
   Posted 7/9/2008 6:12 AM (GMT -7)   
Steve Tucker (PCa specialist in Singapore) posted an interesting article on cancer and statistics on the hrpca web-site. I thought that some of the members would be interested to read it.

The Median Isn't the Message by Stephen Jay Gould

My life has recently intersected, in a most personal way, two of Mark Twain's famous
quips. One I shall defer to the end of this essay. The other (sometimes attributed to
Disraeli), identifies three species of mendacity, each worse than the one before - lies,
darned lies, and statistics.

Consider the standard example of stretching the truth with numbers - a case quite relevant to
my story. Statistics recognizes different measures of an "average," or central tendency. The
mean is our usual concept of an overall average - add up the items and divide them by the
number of sharers (100 candy bars collected for five kids next Halloween will yield 20 for
each in a just world). The median, a different measure of central tendency, is the half-way
point. If I line up five kids by height, the median child is shorter than two and taller than the
other two (who might have trouble getting their mean share of the candy). A politician in
power might say with pride, "The mean income of our citizens is $15,000 per year." The
leader of the opposition might retort, "But half our citizens make less than $10,000 per
year." Both are right, but neither cites a statistic with impassive objectivity. The first invokes
a mean, the second a median. (Means are higher than medians in such cases because one
millionaire may outweigh hundreds of poor people in setting a mean; but he can balance
only one mendicant in calculating a median).

The larger issue that creates a common distrust or contempt for statistics is more troubling.
Many people make an unfortunate and invalid separation between heart and mind, or feeling
and intellect. In some contemporary traditions, abetted by attitudes stereotypically centered
on Southern California, feelings are exalted as more "real" and the only proper basis for
action - if it feels good, do it - while intellect gets short shrift as a hang-up of outmoded
elitism. Statistics, in this absurd dichotomy, often become the symbol of the enemy. As
Hilaire Belloc wrote, "Statistics are the triumph of the quantitative method, and the
quantitative method is the victory of sterility and death."

This is a personal story of statistics, properly interpreted, as profoundly nurturant and life-
giving. It declares holy war on the downgrading of intellect by telling a small story about the
utility of dry, academic knowledge about science. Heart and head are focal points of one
body, one personality.

In July 1982, I learned that I was suffering from abdominal mesothelioma, a rare and
serious cancer usually associated with exposure to asbestos. When I revived after surgery, I
asked my first question of my doctor and chemotherapist: "What is the best technical
literature about mesothelioma?" She replied, with a touch of diplomacy (the only departure
she has ever made from direct frankness), that the medical literature contained nothing really
worth reading.

Of course, trying to keep an intellectual away from literature works about as well as
recommending chastity to Homo sapiens, the sexiest primate of all. As soon as I could
walk, I made a beeline for Harvard's Countway medical library and punched mesothelioma
into the computer's bibliographic search program. An hour later, surrounded by the latest
literature on abdominal mesothelioma, I realized with a gulp why my doctor had offered that
humane advice. The literature couldn't have been more brutally clear: mesothelioma is
incurable, with a median mortality of only eight months after discovery. I sat stunned for
about fifteen minutes, then smiled and said to myself: so that's why they didn't give me
anything to read. Then my mind started to work again, thank goodness.

If a little learning could ever be a dangerous thing, I had encountered a classic example.
Attitude clearly matters in fighting cancer. We don't know why (from my old-style
materialistic perspective, I suspect that mental states feed back upon the immune system).
But match people with the same cancer for age, class, health, socioeconomic status, and, in
general, those with positive attitudes, with a strong will and purpose for living, with
commitment to struggle, with an active response to aiding their own treatment and not just a
passive acceptance of anything doctors say, tend to live longer. A few months later I asked
Sir Peter Medawar, my personal scientific guru and a Nobelist in immunology, what the
best prescription for success against cancer might be. "A sanguine personality," he replied.
Fortunately (since one can't reconstruct oneself at short notice and for a definite purpose), I
am, if anything, even-tempered and confident in just this manner.

Hence the dilemma for humane doctors: since attitude matters so critically, should such a
sombre conclusion be advertised, especially since few people have sufficient understanding
of statistics to evaluate what the statements really mean? From years of experience with the
small-scale evolution of Bahamian land snails treated quantitatively, I have developed this
technical knowledge - and I am convinced that it played a major role in saving my life.
Knowledge is indeed power, in Bacon's proverb.

The problem may be briefly stated: What does "median mortality of eight months" signify
in our vernacular? I suspect that most people, without training in statistics, would read such
a statement as "I will probably be dead in eight months" - the very conclusion that must be
avoided, since it isn't so, and since attitude matters so much.

I was not, of course, overjoyed, but I didn't read the statement in this vernacular way either.
My technical training enjoined a different perspective on "eight months median mortality."
The point is a subtle one, but profound - for it embodies the distinctive way of thinking in
my own field of evolutionary biology and natural history.

We still carry the historical baggage of a Platonic heritage that seeks sharp essences and
definite boundaries. (Thus we hope to find an unambiguous "beginning of life" or
"definition of death," although nature often comes to us as irreducible continua.) This
Platonic heritage, with its emphasis in clear distinctions and separated immutable entities,
leads us to view statistical measures of central tendency wrongly, indeed opposite to the
appropriate interpretation in our actual world of variation, shadings, and continua. In short,
we view means and medians as the hard "realities," and the variation that permits their
calculation as a set of transient and imperfect measurements of this hidden essence. If the
median is the reality and variation around the median just a device for its calculation, the "I
will probably be dead in eight months" may pass as a reasonable interpretation.

But all evolutionary biologists know that variation itself is nature's only irreducible essence.
Variation is the hard reality, not a set of imperfect measures for a central tendency. Means
and medians are the abstractions. Therefore, I looked at the mesothelioma statistics quite
differently - and not only because I am an optimist who tends to see the doughnut instead of
the hole, but primarily because I know that variation itself is the reality. I had to place myself
amidst the variation.

When I learned about the eight-month median, my first intellectual reaction was: fine, half
the people will live longer; now what are my chances of being in that half. I read for a
furious and nervous hour and concluded, with relief: darned good. I possessed every one
of the characteristics conferring a probability of longer life: I was young; my disease had
been recognized in a relatively early stage; I would receive the nation's best medical
treatment; I had the world to live for; I knew how to read the data properly and not despair.

Another technical point then added even more solace. I immediately recognized that the
distribution of variation about the eight-month median would almost surely be what
statisticians call "right skewed." (In a symmetrical distribution, the profile of variation to the
left of the central tendency is a mirror image of variation to the right. In skewed
distributions, variation to one side of the central tendency is more stretched out - left skewed
if extended to the left, right skewed if stretched out to the right.) The distribution of variation
had to be right skewed, I reasoned. After all, the left of the distribution contains an
irrevocable lower boundary of zero (since mesothelioma can only be identified at death or
before). Thus, there isn't much room for the distribution's lower (or left) half - it must be
scrunched up between zero and eight months. But the upper (or right) half can extend out
for years and years, even if nobody ultimately survives. The distribution must be right
skewed, and I needed to know how long the extended tail ran - for I had already concluded
that my favorable profile made me a good candidate for that part of the curve.

The distribution was indeed, strongly right skewed, with a long tail (however small) that
extended for several years above the eight month median. I saw no reason why I shouldn't
be in that small tail, and I breathed a very long sigh of relief. My technical knowledge had
helped. I had read the graph correctly. I had asked the right question and found the answers.
I had obtained, in all probability, the most precious of all possible gifts in the circumstances
- substantial time. I didn't have to stop and immediately follow Isaiah's injunction to
Hezekiah - set thine house in order for thou shalt die, and not live. I would have time to
think, to plan, and to fight.

One final point about statistical distributions. They apply only to a prescribed set of
circumstances - in this case to survival with mesothelioma under conventional modes of
treatment. If circumstances change, the distribution may alter. I was placed on an
experimental protocol of treatment and, if fortune holds, will be in the first cohort of a new
distribution with high median and a right tail extending to death by natural causes at
advanced old age.

It has become, in my view, a bit too trendy to regard the acceptance of death as something
tantamount to intrinsic dignity. Of course I agree with the preacher of Ecclesiastes that there
is a time to love and a time to die - and when my skein runs out I hope to face the end
calmly and in my own way. For most situations, however, I prefer the more martial view that
death is the ultimate enemy - and I find nothing reproachable in those who rage mightily
against the dying of the light.

The swords of battle are numerous, and none more effective than humor. My death was
announced at a meeting of my colleagues in Scotland, and I almost experienced the
delicious pleasure of reading my obituary penned by one of my best friends (the so-and-so
got suspicious and checked; he too is a statistician, and didn't expect to find me so far out
on the right tail). Still, the incident provided my first good laugh after the diagnosis. Just
think, I almost got to repeat Mark Twain's most famous line of all: the reports of my death
are greatly exaggerated.
Dutchy's husband
Diagnosis: 7/6: PSA 1,946, multiple bone metastases in thoracic, lumbar spine, pelvis, bilateral ribs and proximal left tibia, 2 weeks Casodex (50 mg)

Treatment: 3 monthly Lupron injection (22.5 mg) + Zometa (4 mg IV). Added daily Casodex (50 mg) in September 2007.

25/06: PSA 407
20/08: PSA 3,7
29/09: PSA 0.7
14/10: PSA 0.17
18/12: PSA < 0.003
15/03: PSA <0.003
15/05: PSA <0.003

May 2008: diagnosed with advanced colon cancer

Roger G
Regular Member

Date Joined Apr 2008
Total Posts : 150
   Posted 7/9/2008 8:48 AM (GMT -7)   

Wow... I really have a bad headache now. Did I mention I really hate stats :)
Age: 43 (2008)
DRE Small Ridge on prostate, PSA 1.5
07/2007: Diagnosed cancer, T2c, Gleason 3+4=7
09/2007: Laparoscopic prostectomy @ Hamilton General, 4 hrs.
              Both nerve bundles spared
              Pathology Report: Tumor confined w/in prostate
              T2c, Gleason is 3+3=6
              Went home with JP drain
10/2007: Made return trip to hospital.  All urine was comming out JP drain.
10/2007: Catheter removed. Next to no leakage
11/2007: 1st PSA <.003 :)
              ED: Started Viagra, no response yet.
12/2007: Had confidence to go padless!!!!!
12/2007: ED:  Stopped Viagra as it's causing hemroid problems.
01/2008: 2nd PSA <.003 :)
              ED: next to no response.
04/2008: 3nd PSA <.003 :)
              ED: next to no response.  Changed the Viagra prescription.

New Member

Date Joined Jun 2008
Total Posts : 4
   Posted 7/9/2008 9:28 AM (GMT -7)   

Thanks so much, Dutchy, for posting this piece by one of my favorite writers.  Here's a summary of his article that might be easier to understand:

"In July of 1982, Gould was diagnosed with peritoneal mesothelioma, a highly deadly form of cancer affecting the abdominal lining and frequently found in people who have been exposed to asbestos. After a difficult two-year recovery, Gould published a column for Discover magazine, titled "The Median Isn't the Message," which discusses his reaction to discovering that mesothelioma patients had a median lifespan of only eight months after diagnosis.[6] He then describes the true significance behind this number, and his relief upon realizing that statistical averages are just useful abstractions, and do not encompass the full range of variation. The median is the halfway point, which means that 50% of patients will die before 8 months, but the other half will live longer, potentially much longer. He then needed to find out where his personal characteristics placed him within this range. Considering the cancer was caught early, the fact he was young, optimistic, and had the best treatments available, Gould figured that he should be in the favorable half of the upper statistical range. After an experimental treatment of radiation, chemotherapy, and surgery, Gould made a full recovery, and his column became a source of comfort for many cancer patients." 

Gould in fact lived twenty years, not eight months, before his cancer took him.  He became something of a mix between a rock star and a guru at Harvard because of his status as one of the great scientists of our time and his exuberance for life.  He believed it was his positive attitude that kept him alive so long, and also allowed him to die with acceptance and a love of life right up to the last minute.

Three books have become very helpful to me as I face my own much more encouraging diagnosis:  Surviving Prostate Cancer is already well-known here for its easy to understand explanations of this complicated disease.  At the heart of Dr. Walsh's message is one of great optimism. 

Bill Moyer's Healing and the Mind documents the great successes many physicians are finding in treating a variety of illnesses with a combination of traditional medicine with nontradional methods such as diet, exercise, and meditation (although "non-traditional might not be the best term since these practices have been with us for thousands of years!).  And Jon Kabat-Zinn's Full Catastrope Living is a handbook for "using the wisdom of your body and mind to face stress, pain, and illness."  Kabat-Zinn is a doctor at the Harvard Medical School and for many years has run classes that help patients live longer and live better, even in the face of the worst possible medical conditions. 

Over the last few years, I've been moving steadily to turn around some of the bad habits that were destroying my health and quality of life.  I've quit drinking and smoking, to name the two most important ones.  Now that I'm facing cancer, I'm using these three books not just to help me get better physically but to grow emotionally and spiritually as well. 

A fuller biography of Gould can be found at

Best to all,


Doting Daughter
Veteran Member

Date Joined Aug 2007
Total Posts : 1064
   Posted 7/9/2008 9:32 AM (GMT -7)   
Thanks to you both for sharing!
Father's Age 62 (now 63)
Original Gleason 3+4=7, Post-Op Gleason- 4+3=7,
DaVinci Surgery Aug 31, 2007
Focally Positive Right Margin, One positive node. T3a N1 M0.
Bone Scan/CT Negative (Sept. 10, 2007)
Oct. 17 PSA 0.07
Nov. 13 PSA 0.05
Casodex adm. Nov 07, Lupron beg. Dec 03, 2007 2 yrs
Radiation March 03-April 22, 2008- 8 weeks 5x a week
July 3, 08 PSA .02
Praying for a cured dad.

Co-Moderator Prostate Cancer Forum

Roger G
Regular Member

Date Joined Apr 2008
Total Posts : 150
   Posted 7/9/2008 2:35 PM (GMT -7)   

Thank your the Coles note version. The only thing the auther left out was the mode. Great article btw.
Age: 43 (2008)
DRE Small Ridge on prostate, PSA 1.5
07/2007: Diagnosed cancer, T2c, Gleason 3+4=7
09/2007: Laparoscopic prostectomy @ Hamilton General, 4 hrs.
              Both nerve bundles spared
              Pathology Report: Tumor confined w/in prostate
              T2c, Gleason is 3+3=6
              Went home with JP drain
10/2007: Made return trip to hospital.  All urine was comming out JP drain.
10/2007: Catheter removed. Next to no leakage
11/2007: 1st PSA <.003 :)
              ED: Started Viagra, no response yet.
12/2007: Had confidence to go padless!!!!!
12/2007: ED:  Stopped Viagra as it's causing hemroid problems.
01/2008: 2nd PSA <.003 :)
              ED: next to no response.
04/2008: 3nd PSA <.003 :)
              ED: next to no response.  Changed the Viagra prescription.

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