# Hope, Statistics and Cancer

by Saurabh Jha

Stephen J. Gould

When diagnosed with abdominal mesothelioma, a rare cancer with a blighted future, evolutionary biologist and writer, Stephen Jay Gould, turned his attention to the statistics; specifically, the central tendency of survival with the tumor. The central tendency – mean (average), median and mode – project like skyscrapers in a populated city and are the summary statements of a statistical distribution.

The “average” is both meaningful and meaningless – you could say that the average utility of average is zero. Consider a gamble – fair coin toss where you get \$50 if it lands heads and lose \$50 if it lands tails. The average (net) gains of this coin toss, if the coin is thrown hundreds of time, is zero. But no one gets nothing – you either get \$50 or lose \$50. The average is twice wrong – it over estimates for some and under estimates for others. Yet the average of this gamble has important information. It helps you decide if you could profit from making people play this gamble – you wouldn’t profit unless you charged a small fee to play the gamble.

The median is the mid-point of a distribution. Gould’s cancer had a median survival of eight months. This means that half (unlucky half) lived fewer than eight months and half (lucky half) lived more than eight months with this tumor. The mean is affected by outliers but the median is not – billionaires of Mumbai raise the average, not median, income of the city. That is skewness of a distribution affects the mean, not the median. Put another way, the median (Mumbai’s slums) conceals the skewness (Bollywood).

Gould, describing in his classic essay “The median is not the message,” ignored the median but looked at the skewness, which was right-sided – some who lucked out with survival lucked out big. Gould was initially despondent when he saw that the median survival of his cancer was only eight months. Gould was naturally disposed to optimism. He was dealt a rough hand but was not going down without a fight. His optimism, and fight, increased as he unraveled the distribution – first with the hope that he could be in the lucky half of the distribution, then with the hope that he could be one of the outliers in that skewed distribution, then with the hope that the treatment that he was being given, an experimental cocktail, could make him an outlier.

Gould lived twenty years after his diagnosis, perhaps, in part, because of his optimism, although there’s no way of knowing for sure that optimism helped. There’s no way Gould knew for sure that he would be an outlier. He did not choose to be in the long positive tail – he hoped he was. He could, quite easily, have settled his affairs, written his will, and traveled the world believing he had only 8 months to live. For every optimistic Gould who lives twenty years with mesothelioma there may be ten optimistic Goulds who live only two months.

Gould’s story is at the heart of the tension within evidence-based medicine (EBM) and end of life medical costs. EBM is driven by central tendency, the average, amongst others. But it is individuals who vary who build averages. Variation is a fact of life. Gray is the only truth. Variation is our half-truth – half remains concealed because whilst we know that we’re part of the variation we don’t know where exactly we’re placed, we don’t know which shade of gray we belong to.

Cancers vary in prognosis. Cancers vary in their response to treatment. This begs the question: in the absence of perfect information, what should the oncologist tell the patient? Should the oncologist reveal the median survival only? If so, why? What normative ethics say only the central tendencies of a distribution be discussed? Should the oncologist give a whiff of hope that the patient could be an outlier? Should the oncologist mention the short left, not long right, tail, stress the imminence of death, so that the patient can exit the planet with grace? What is the truth – the median, long tail of optimism or short tail of pessimism? If all three are truths which truth should be mentioned first and which truth should be mentioned last?

The easy answer is that it depends on the patient. That answer is simplistic, and a cop out. My friend, an oncologist, tells me that patients seek him for hope. He gives them hope and is unapologetic about doing so. Some might say that he gives his patients false hope – but that accusation assumes a numerical probability of death, a threshold or a range, which neatly separates false from true hope, hype from reality. There is no such number and even if it existed it’d be nearly impossible to give each individual their unique threshold of true vs. false hope, as the question will once again arise – what if I am the lucky outlier?

My friend put it pithily. “I’m not a fucking funeral director. I’m an oncologist.” Patients see him for possibilities, not limitations. Like Gould, his patients wonder if there are outliers (there often are) in the survival distribution of their cancer, and if they could be an outlier. He blasts his patients with chemotherapy and if there are new ones, he tries them out as well. There are no short cuts with hope. When he suspects a complication of cancer, such as a clot in the lungs, he goes after it with hammer and tongs. Because there’s no retreating from hope.

Hope and over treatment are a dialectic – a marriage of inconvenience. Hope is a state of mind, a culture of expectation, will of the people, which can’t be switched off by pressing a button. The most powerful driver of medical costs in the US is not the incentive structure. It is not doctors’ fear of being sued. The most powerful driver of medical costs is hope.

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