Luck and Cancer

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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 -

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.


Surely something is lacking. Suppose half the population regularly doses themselves with some chemical. Let's say a small molecule that can easily diffuse throughout nearly all tissues, and which strongly increases the rate of mutation (per stem cell division), but by the same amount in every tissue. This paper would place such increased cases within the "bad luck" category, though they are lifestyle-induced. Correlation with the number of stem cell divisions does not imply lack of environmental influence. Not to mention that, when it comes to cancers, not all mutations are equal.

Apologies for this pickiness but I decided to check: ""To quote Sir Richard Doll, "whether an exposed subject does or does not develop a cancer is largely a matter of luck" "" First, his biog on Wikipedia ( opening paras seems to contradict this notion by saying he showed: "prove that smoking caused lung cancer and increased the risk of heart disease" Second I could not find the quote buried in the article linked to under his name and finally I checked Google: ""No results found for Sir Richard Doll, "whether an exposed subject does or does not develop a cancer is largely a matter of luck"."" I spent a little bit of time reading: The age distribution of cancer and a multi-stage theory of carcinogenosis co-authored by Doll as I did the Comment section in yesterday's Guardian. It strikes me that it is "worth making much fuss about" how can a basic message be accurate if "not justified by the study itself" and going against common knowledge for a substantial set of cancers. Just one example my father (an internet luddite) related to me about asbestosis sufferers: The asbestos factory workers could not be interviewed for his study since none had made it to retirement age. Now I appreciate that cancer covers a multitude of sins and that to quote the Guardian (pg 32, 3/1/15): "we need courage and grace" [apologies again as my post maybe not exemplify the latter] but I do wonder what agenda the previous part of the headline "There are no human actions to blame for most cancers" was playing to. HNY

Sorry, I linked to the main Doll paper rather than his commentary where he uses this quote - thanks for pointing this out and I have corrected the link. I hope my PPS has made it a bit clearer that there is no contradiction between saying that smoking/asbestos etc massively increases your risk of cancer, while also saying there is a strong role of luck in whether you actually get it or not.

Thanks for the update and PPS which I appreciate for its metaphor, but I still beg to differ overall as I feel at some point (I think ours is a % number debate combined with population focus) luck will largely become irrelevant: that is when your bucket is stuffed full of tickets due to a person's various excesses. An interesting experiment (maybe akin to Doll's paper) is to ascertain the comparable rate of demise of those patients outside hospitals in wheelchairs and with drips smoking in the freezing cold. Putting it down to luck absolves people from their communal responsibilities.

Among the cancers which may not be preventable by lifestyle changes, many of them could involve some genetic inheritance, which may not distinguish between tissues. Therefore, although cancer is certainly a question of bad luck, the conclusions of the paper are exaggerated.

Among the cancers which may not involve genetic inheritance, many of them may be preventable by lifestyle changes, which may not distinguish between tissues. (Apologies to Daniel Dorcos.) At very least, such possibility is entirely compatible with the evidence of this paper. The PS added 3rd Jan is helpful, and I plead guilty earlier to not distinguishing clearly between the role of luck in an individual getting cancer and the role of luck in which tissue gets the cancer. I have read and reread the abstract of this paper many times, and I still believe that I merely follow the authors in so doing. Their critical sentence is "The majority is due to “bad luck,” that is, random mutations arising during DNA replication in normal, noncancerous stem cells". Whether or not intended by the authors, this sentence is going to be understood as meaning a minimum and unavoidable background rate of random mutation during cell division regardless of environment or genetics. That would be unjustified. We could be exposing ourselves to agents and behaviours that multiply the random mutation rate (and cancer incidence) hundredfold in all tissues, and the relationships reported in this paper would be the same. As is the possibility with genetic dispositions to mutation that do not distinguish between tissues.

@ normanfry. I fully agree with you. What I mean is that the Cancer Research UK's analysis percentage (60%) of cancers unrelated to lifestyle does not correspond to the "bad luck" percentage according to the Science paper, because an incalculable proportion of these cancers are influenced by the inherited genetic background. It is likely that with the "best" lifestyle and the "best" genetic inheritance, cancer incidence might be reduced by more than half.

Follow Daniel's link for an excellent contribution from Steven Pelech.

1. The correlation reported For ERS and total cell divisions of 0.81 is highly significant by test. Does the essentially zero slope of the regression curve affect the significance of the conclusions made? 2. Armitage and Doll reported decades ago that the risk of several cancer types are similar and increases with about the sixth power of age. In addition, it seems clear that the rate of cell division may be rapid in infancy and during early growth, slowing dramatically as we age. Doesn't the nonlinear nature of the two variables complicate the inferences that can be made from this model? 3. Wouldn't the adjusted ERS analysis in the supplemental report be more informative if performed with regression analysis? Dichotomization of data is generally thought to reduce the power of inference but Tomasetti and Vogelstein do not address this issue. Is anyone bothered by the dichotomization of the data?

The fact that the paper was published in science is – at least to me – not automatically a synonym of quality of truth or of correct thinking in science. Cancer is triggered in (1) 5-10% by mutations (2) 15% by infections and (3) 80% are sporadic, meaning unknown cause. This alone reveals that the authors made a huge mistake: taking the basis of some 5% of cancers for the majority of cancers. The authors may take into account the primary publications of somatic mutation theory by Theodor Boveri (1914), Karl-Heinrich Bauer and Carl Nordling (1953) instead of celebrating an opinion from some 100 years ago although it mutated to a dogma within the last some three decades. It is further quite interesting that none of the advocates of the somatic mutation theory as the authors as well as Knudson and others cited one paper of the original literature, as named above. The readers may judge it by themselves – why? Mathematically, the bad luck paper is an untenable statistic as it is based on the origin of 5% of cancers (somatic mutation theory) transformed wrongly by the authors to the mass of cancers (some 80% of sporadic cancers) and by this confounds cancer biology with lack of knowledge adequacy. Someone may be interested in necessary critical thinking for making progress in understanding carcinogenesis for improving cancer diagnosis and treatment: Plausible Cancer Hypothesis for the Origin for the Mass of Cancers “Epistemology of the Origin of Cancer: a new paradigm” Article in EpochTimes by James Grundvig: “A New Understanding of the cause of Cancer” Biochemistry / Physiology of Microenvironment, Carcinogenesis and Anticancer Treatment “Cell-Cell Communication in the Tumor Microenvironment, Carcinogenesis, and Anticancer Treatment” Necessary New Goal-Orientated Anticancer Strategy “Imagine A World Without Cancer”: