Luck and Cancer

I was on Radio 4 PM (starting at 37:09) and BBC News Channel yesterday discussing the study published in Science " Variation in cancer risk among tissues can be explained by the number of stem cell divisions ". This had been reported by much of the press as showing that “the majority of cancer cases are down to sheer bad luck”. But the study made no such claim, and so how did these headlines come about?

The main findings are shown in the summary figure from Science's News section, reproduced in a slightly edited form below.

Figure from Science: blue dots added by me indicating the types the authors claim form a 'cluster'. The headline underneath is Science's own, and is misleading in that it takes an analysis of aggregate risks in populations and applies it to individuals.

This shows that organs with a large number of lifetime stem-cell divisions have higher incidences of cancer, which is hardly very surprising. The correlation is 0.81, which is squared to produce an $R^2$ of 0.65, which they interpret as meaning around two-thirds of the variation in incidence rates is explained by chance mutations of stem-cells. The authors conclude in their abstract that “only a third of the variation in cancer risk among tissues is attributable to environmental factors or inherited predispositions”, which may be a fairly reasonable statement to make about population rates in different tissues, but of course says nothing about variation in risks between individuals, and certainly does not say that two-thirds of cases are just luck.

But you can see how this mistake happens. For example, Reuters report the findings as “two-thirds of cancer incidence of various types can be blamed on random mutations”, which is reasonable, but the sub-editor then produces the headline “Biological bad luck blamed in two-thirds of cancer cases”. But this misinterpretation is perhaps hardly surprising as Science itself writes on its main web-site “Analysis linking number of stem cell divisions to different cancer risks suggests most cancer cases can’t be prevented”. If feeling generous, this could be interpreted as reporters ‘simplifying’ the language, and so getting it wrong.

But the authors themselves cannot escape blame. They proceeded to use some over-elaborate cluster analyses to claim that the points fell into two groups: 9 cancers that had a higher incidence than expected due to the random mutations [which I have marked as blue in the Figure above], and the remainder (22) whose incidence were explainable by chance alone. But this separation into two groups seems fairly arbitrary: can you see two natural clusters in the Figure? No, neither can I.

And even if the cluster analysis were OK, the authors only selected cancers for which stem cell divisions could be estimated, and did not include common cancers such as breast and prostate, and yet broke osteosarcoma down into five categories. So any claim about proportions of cancer-types is misleading. But whether the ‘two-thirds’ came from the $R^2$, or the 22/31 cancer types that were 'just luck', journalists almost universally interpreted this as ‘the majority of cancer cases”, which had never been claimed by the authors.

Overall, any blame for inappropriate reporting does not lie only with the media. It also lies with the scientists and the way the journal reported the study: see the recent study that showed in detail the inappropriate coverage stemming from press releases.

In the end it is perhaps not worth making much fuss about, as -

• It’s already recognised that the majority of cancers are not preventable by lifestyle changes: Cancer Research UK’s analysis said around 40% might be preventable, which means 60% are not
• To quote Sir Richard Doll, "whether an exposed subject does or does not develop a cancer is largely a matter of luck".

So the basic messages that were reported were perhaps rather accurate, even if they were not justified by the study itself.

NB See also Plumbum's fine blog on this, which has further links to other commentaries.

PS [added 3rd Jan] It is important, but tricky, to distinguish the study's concern with the role of random mutations in population cancer incidence in different tissues, from the role of luck in an individual getting cancer. The media have (incorrectly) generally written the story as if it concerned the latter. One way of seeing that the analysis in the Science paper does not address the role of 'luck' in the individual case is to think of what they might have said had their correlation been zero. Would this have meant that there was no "luck" in who got cancer? Obviously not. See George Davey-Smith's 2011 lecture for a lot more on this.

PPS [added 4th Jan] To elaborate on Doll's idea that getting cancer is "largely a matter of luck": risk factors such as smoking can increase an individual's risk, but whether one actually gets a cancer is still a matter of unpredictable chance. On PM I used my usual analogy of a lottery: there are tickets in a bucket marked cancers of different types, and a lot of blank tickets (and some marked 'run over by bus' etc). Smoking means you might get 20 times as many 'lung-cancer' tickets, but you still may be lucky and not draw one: many smokers don't get lung cancer. So chance plays a very strong role, even in so-called preventable cancers. This leads to the apparently paradoxical observation that most lung cancers are 'caused' by smoking, while all lung cancers are also a matter of bad luck. As pointed out by George Davey-Smith, it is not an either/or argument.