Medical Brief:The Median Isn’t the Message

The “Median Isn’t the Message” is an essay written by Stephen J. Gould in 1991 as part of his book Bully for Brontosaurus: Reflections in Natural History. The essay has been reprinted many times for many different audiences. In 2013 it was reprinted in the American Medical Association Journal of Ethics. I believe that Stephen J. Gould’s message is as relevant today as it was when he originally wrote it. I thought this essay so important and so well written, that it was required reading for every one of my residents over the past 20 years.

Here is a link to the complete essay:

If you haven’t read it yet, I highly recommend it but recognizing people’s busy schedules, I’ve created a summary below.

  • Statistics are important but they need to be understood or they can be used improperly to convey half-truths and even mis-truths
  • In 1982 Stephen J. Gould learned that he had abdominal mesothelioma, a rare and fatal cancer usually associated with exposure to asbestos. His oncologist told him there was nothing worth reading in the medical literature about this disease
  • In Gould’s own words: “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”
  • So of course he read everything at Harvard’s medical library and the literature was brutally clear: mesothelioma is incurable with a median mortality of 8 months after discovery
  • And here in his own words is Stephen J. Gould’s response to learning this: “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, and socio-economic status, and, in general, those with positive attitudes, with a strong will and purpose for living, with commitment to struggle, and with an active response to aiding their own treatment and not just a passive acceptance of anything doctors say tend to live longer.”
  • And this was not only his perception- as he asked Nobel Laureate in immunology,  Sir Peter Medawar, what factor influences a successful fight against cancer and the response was “A sanguine personality”
  • Since attitude matters, Gould, being the intellectual he was, opined about how humane doctors should communicate with their patients. Again in Gould’s own words “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, both because this formulation is false, and because attitude matters so much.”
  • Because of Gould’s understanding of statistics he understood what the median mortality of eight months meant and importantly what it did not mean. As an evolutionary biologist, Gould was not only familiar with but comfortable with the fact that variation is “nature’s only irreducible essence”; it’s “hard reality”.
  • Medians and means are abstractions of reality
  • Gould therefore looked at the mesothelioma statistics quite differently--because not only was he an optimist, but because of his understanding of nature, statistics and essence of variation in processes of life
  • If the median is 8 months, half of the people will live shorter than 8 months and half the people will live longer.  Because he was young, the disease was recognized at a relatively early stage, Gould  was able to get excellent medical care and he had a strong will to live, he believed his chances were good that he would live longer than 8 months, so he did not despair.
  • Again, given his keen understanding of science and statistics, he recognized that the distribution of variation around the 8-month median would be “right skewed”. Because of this, he wanted to know how long the right-sided tail of the survival curve was. Even though the tail was small, there was an extended tail when Gould evaluated the data.
  • Gould wound up receiving an experimental protocol that he chose, in large part because of his understanding of the data. He did not die within 8 months of diagnosis. In fact, he lived on for 20 years.
  • Stephen J Gould  died in 2002 of lung cancer, unrelated to his abdominal mesothelioma, a diagnosis he received 20 years earlier.

As doctors, we all know the definition of “median” and understand the concept of tails in statistics (both long ones and thin ones). Yet, we often fall into the trap of telling pet parents median survival times (MSTs) without providing additional context. We know some dogs do end up living much longer than MSTs would suggest and we know some dogs end up living less time. Providing this perspective to pet parents might help set expectations and assist in making care decisions that are based upon the full range of information that is available rather than on a single data point.