Effect Measure has an interesting entry on cancer deaths (down) and incidence (up), which got me theorizing...
So cancer is a mess - there are multiple causes - smoking, diet, heredity, chemicals, viruses and radiation.
Treatment has improved, and some environmental insults have been reduced - like smoking - so one would expect to see improvement, on the other hand people live longer and the population is older on average (in the developed world), viruses are more widespread and some environmental insults are increasing.
So... bear with me.
If I recall correctly, mostly from having lunch with cancer types at College on a regular basis (and what source of information could be more rigorous than my half-remembered casual lunch conversations), a key underlying assumption is that all other things being equal, the probability of a cell becoming cancerous is just some small random number per unit time, where the amplitude of the probability is partly a function of heredity and co-factors, and partly a function of the external insults.
The net probability comes essentially from the product of a number of independent events each with a low probability of occuring. (I oversimplify, there is covariance of the events, they are only approximately independent in general).
There are a lot of cells. Live long enough you run out of luck.
So, ought that then not mean that if you have more cells you have a higher probability of getting cancer?
And people are getting bigger (not just fatter, bigger).
The number of cells ought to scale roughly as the cube of the height of a person, so as people get bigger on average, and get bigger earlier (kids are bigger at some fixed age, better diets etc, I believe) the chance of getting cancer, all other things being equal, ought to be higher.
Clearly this could be seen trivially in cancer incidence data as a function of time or population, for which the other confounding factors have been controlled.
So I ought to be able to look it up, but if I did that I'd write a letter to Nature or something, not blog it.
(ok, I googled, getting well enough controlled data and the population height data for the same population looks to be non-trivial, so seriously, Nature letter...).
I anticipate a rush to stop kids from eating vegetables or getting good sleep, and future genetic engineering for shortness - 150cm mean adult height ought to be adequate...
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Doesn't smoking stunt one's growth, too? That would help reduce your risk.
told you there were covariances...
so smoke 'em while you're young and then quit?
well, except for the "kissing a smoker is like licking a stale ashtray" effect, worked for me.
There is some association between obesity and cancer incidence, in adults at least. While the number of cells may be greater in overweight people (its not strictly proportional to weight however as a lot of the weight will be in fat cells which are simply bigger in obese individuals) dont forget that a lot of the reason that people are obese is down to things like poor diet and lack of exercise - factors also associated with an increased risk of cancer. Theres been some interesting experiments done with rats where they were kept on an extremely calorie poor diet with the result that they had much lower cancer incidence and lived a lot longer. Unfortunately the corresponding diet for humans would not be seen as acceptable due to its extreme austerity.
yeah, that is why extracting this info from data is non-trivial;
you'd need cancer incidence data controlled for major factors like smoking, and then both the height and something like a BMI index to control for weight due to fat as opposed to being bigger.
Doable, but not in 15 minutes for a blog entry.
OK, didn't see this post, so I didn't answer you properly on Effect Measure. My apologies (and thanks for the link, BTW!). The data are hard to interpret, but the usual view is that very little cancer (estimates are usually 10 - 30%) is from spontaneous mutations in the absence of external drivers. This is based largely on migrant studies, where groups that share genetic endowments (e.g., Japanese) are compared as they change cancer risks as they change environments (which includes diet, lifestyle as well as air, water, food, etc.), say stomach cancer from Japan to Hawaii to California. The classic observation is that cancer risks adjust after a suitable delay to the cancer risks of the environment where the migrant is living. In your example, then only a minority of cancers would be involved in this spontaneous change of phenotype. Now the correlations you are ignoring are most pertinent to the external drivers, since they affect all the cells, not just random ones. So your question raises a theoretical possibility that might even have some effect but it would be in the higher order terms (since I'm talking to a physicist I'll use Taylor series language :)).
It seems to me that the immune surveillance cells in the body would scale up according to lean body mass, so there wouldn't be much of a differnce. The obesity factor seen in a number of cancers is probably attributed to increased levels of hormones produced by adipocytes and may also be partially due to an increased level of certain fatty acids which seem to act as cancer promoters.
Well, actually, the size effect ought to be first order and strong: that is to say, if you hold all other variables constant, the incidence ought to scale linearly with fractional change in height and with a proportionality of ~ 3.
That is to say - two identical populations, but one 10% taller, the taller ought to have 30% higher incidence.
This must be true if to first order the probability of a cell becoming cancerous is small per unit time, and the aggregate probability is from independent cumulative events - ie it is linear in the causative factors and not strongly covariant for different causative factors.
So, we could invert the argument and say that if cancer incidence does not scale linearly with number of cells in the individual, then the causal mechanism must not be due to independent events.
This is not sensitive to change in environmental insults, or internal correction mechanisms, as long as the probability of an error leading to cancer is independent for each cell.
Level of obesity at fixed size would be orthogonal effect, since it changes mass without changing cell count proportionally.
So the simple prediction is cancer incidence should scale linearly with mean height, and the delta incidence ~ 3 times delta height
Steinn: Actually metabolic activity (the relevant physiological category) scales with an exponent of about .75 with weight. It should be .67 to account for the fact that surface area goes up with the square while weight goes up with the cube but that's not the way it seems to be. There are various explanations offered for this (which I can't recall at the moment, just like a lot of other things, like the names of people I've known for 30 years, etc.). Also height is not just a linear factor since it is usually a function of bone length, not just piling cells on top of each other. Same number of cells stretched out over a longer frame (at least that's my understanding of it and I've not been able to find something different). So it is some extra ostecytes, not new cells across the board proportionally.
Your inverted argument suggests what we already know, that the probability of a cell becoming cancerous is not independent of everything else going on in the organism.
The 3/4 law for metabolic activity (Kleiber's Law) is a standard example in physics classes of scale invariance or "power-law" dependance of interesting things.
At some basic level, is all other factors are constant, then the cancer incidence per person per unit time ought to depend linearly on the total number of cells, because the approximation that the error-chain that leads to cells becoming cancerous has small probability per cell per unit time, and that each even is independent, are reasonable assumptions.
For this to fail grossly, you would have to have cells that become pre-cancerous signal other cells and make the differently likely to become pre-cancerous or cancerous.
External events that affect many cells (including internal body factors that are not local to some specific clump of cells, like hormonal levels etc) are orthogonal to this effect.
What is worrying, is that if there is intracell signaling and things are not independent, then the basic model for cancer vulnerability to environmental insults is wrong, the effects of exposure at low levels of exposure would not be linear and the extrapolations would be completely wrong - not in general the effect would be worse than linear, ie cells could well be more vulnerable to cancer if there is intracellular signaling.
The simple thing would be to find a data set for homogenous population (non-smokers all in same environment with similar economic conditions - maybe small town Mormon communities) and cut the sample for adults (say age 30-50) by height, and see if the incidence is different for short people or tall people.
If it could be corrected for obesity (eg only people with BMI less than some value) than it would be even better.
Trivial to do, if the data is there.