Is the median the message?

Stephen Jay Gould and Cancer Survival

Thomas Eakins, The Agnew Clinic (1889).

How should one respond to a terminal prognosis? In July 1982, a doctor diagnosed Harvard paleontologist Stephen Jay Gould with peritoneal mesothelioma, a lethal cancer. Gould asked his doctor what he should read about his condition; she deflected his question. So he went to the Harvard Medical School library and searched the literature. In an essay titled, The median is not the message, Gould wrote that,

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.

Gould was a force of nature. He staked out controversial positions on several topics in evolutionary biology. He was also the most widely read science essayist of his era, publishing hundreds of columns, including The median is not the message. That essay continues to influence how people communicate and understand cancer prognoses. 

Gould argued that if a doctor gives you a single number as a prognosis, you shouldn’t believe it. The graph below illustrates the kinds of data sets that physicians rely on to make prognoses.

Doctors use graphs like this to summarize data on large samples of patients with a disease. The horizontal axis is the number of months patients survived following their cancer diagnoses. The vertical axis is the probability density of dying after that number of months. OK, so how would you summarize this information in a single number? One common way is the median, eight months in these data. The median is that time such that half of the patients survived for fewer months, and half survived longer. If a patient asks, “how long will I live?”; the median survival time is a reasonable answer.

So what was Gould’s problem with the median? He correctly argued that the median captures just one fact about the random distribution of cancer survival times: how long the ‘middle’ patient lived. But you are unlikely to live that many months. If you look at the data, the more important message is that survival times are highly variable; you could die almost as soon as you were diagnosed. But you could also live for years.

Moreover, Gould strongly believed that a hopeful attitude would help him survive longer. 

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 socio­economic 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. 

I knew Gould. I took his course as an undergraduate. Later, as a junior professor, I worked with Gould on science policy as part of the American Association for the Advancement of Science. He was utterly personable, ready to debate anything, and seemed to enjoy every aspect of his busy life. If a hopeful attitude could cure cancer, Gould would be a survivor. And in fact, Gould lived for 20 years past his diagnosis, dying in 2002 not from mesothelioma but from a different cancer, metastatic adenocarcinoma.

Stephen Jay Gould (1941-2002)

Did Gould’s hope extend his life? This was an exciting idea that was widely believed in the 1980s. Evidence was beginning to emerge that connections between the body and the mind can affect the occurrence and course of some diseases. For example, exposure to stress can increase your risk of contracting at least some infectious diseases. However, the evidence about whether your attitude can affect your health is mixed. The current view of the American Cancer Society is that

Studies have shown that keeping a positive attitude does not change the course of a person’s cancer. 

If the ACS is correct, Gould survived because… well, who knows? But not because he had the right attitude. 

But even if it is true that your attitude will not influence the outcome of your disease, what’s the harm in a positive attitude? None, and yes, I hope to survive cancer. However, I don’t want the kind of hope that is just despair in disguise, the lamentation that “my only hope is X,” where X is some yet-more-exotic treatment than the one that failed last time. The hope that I want affirms the life I have, however many months it lasts. 

Steve had that kind of hope.