# Cancer and luck

Two years ago, Cristian Tomasetti and Bert Vogelstein, working at the Sidney Kimmel Cancer Center of Johns Hopkins, explained why cancer occurs more in some tissues than others. Their answer is summarized in the wonderful graph left (click to enlarge). The difference is largely a matter of how often stem cells have to divide in order to maintain the tissue concerned. More frequent division increases the risk for random mutation. Note both axes of that graph are logarithmic! So the lifetime risk of osteosarcoma is about 100 times less than the risk of colorectal cancer.

That variation puts a focus on the role of luck in cancer development: *“These results suggest that only a third of the variation in cancer risk among tissues is attributable to environmental factors or inherited predispositions.”* Seemingly because of that, their paper generated some flurry in both the popular and professional press. I suspect a large part of that was caused by the fact that most people are not comfortable working with statistics, and don’t understand there are shifts in probability moving from variation in tissue to variation in population, and from chance of a cancer-related mutation to chance of cancer.

Cancers rarely are caused by a single mutation. Cancer development depends on a cell line experiencing a sequence of mutations that produces a wrong combination in some cell, without first being repaired or producing a combination that ends the line. The cancerous line then has to slip past the immune system. That makes cancer development an example of a stochastic process. The probability of some final result is *not* the same as the probability of particular causal events along the way.

This month, the same two authors published another paper diving deeper into that relationship. What they found is exactly what one should expect from this kind of stochastic process and from known biology:

*Most mutations leading to cancer are random.*From 32 cancer types in the United Kingdom, they calculated that 29% of cancer mutations have environmental cause (E), 5% are inherited (H), and 66% are random (R).*Environmental and lifestyle influence are important nonetheless.*Their model “is compatible with the estimate that 42% of these cancers are preventable by avoiding known risk factors.”

If you think there is some contradiction between 66% of cancer mutations being random in a set of cancers, and 42% of those same cancers being preventable, you are not yet understanding how stochastic processes work.

An implication of all this is that most cancers will have some random mutations as part of its causal history. Here is a simple probability exercise: if a cancer was caused by 3 mutations, and assuming the mutation probabilities above, and assuming independence between those mutations, what is the probability that at least one of the cancer’s mutations was random? What is the probability that at least one is environmental? (Answer: 1 – (1-0.66)^3, or 96% chance of at least one random mutation. 1 – (1-0.29)^3, or 64% chance of at least one environmental mutation.) Of course, mutations are not independent, since they affect the cell’s development and reproduction. That exercise is not intended as a substantive model, but to remind how probability works with combinations. The linked report presents some other examples. Lung cancer is interesting, since for it the environmental factors dominate: *“Even though 89% of lung adenocarcinomas are preventable by eliminating E factors, we calculate that 35% of total driver gene mutations are .. due to R.”*

Importantly, the fraction of mutations that are inherited, environmental, or random depends on type of tissue, on the type of cancer, on the population, and on the environment. The numbers given above are not a law for humanity, but the result for “32 cancer types in the United Kingdom.” At the present time. If the UK decides to allow its industry to generate more air and water pollution, the fraction of environmental mutations will increase. If it manages to decrease the number of people who smoke, that fraction will decrease.

Stochastic processes are a subtle notion. Many scientists stumble using them. I don’t hold out much hope for most journalists. I found out about these papers through an article in the popular press that made a mess of things, confusing the fraction of cancer *mutations* with the fraction of cancers, and calling mutations “alarming.”

The results in these two papers are interesting, but not surprising. They confirm the current model of cancer development, including how cancers evolve resistance to chemotherapy. They corroborate why cancer is a disease of aging, why it has a higher incidence in tall people than short people, and why lifestyle influences are important, and why the disease still is unpredictable despite all that.

They do not change practical thinking. Do what doctors recommend: Don’t smoke. Don’t drink too much. Exercise. Eat your vegetables. This research does *not* gainsay any of that, nor the epidemiological evidence related to it. Nor will this research change cancer diagnosis or treatment any time soon.

It is nice research because it gives a clearer picture of cancer etiology, and starts to put some numbers around the conceptual stochastic model. As these mathematical models get sharper, they will shape more practical research down the line, focusing efforts better on where gains can be made, and improving the testing of various hypotheses and treatments.

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