Staying Positive

What follows is a rather wordy discourse that explains why Heather and I are staying positive.

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, 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:  ****ed  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.