Are being big and old risk factors for cancer or not?

I don’t like the traditional explanation for why we don’t all get cancer.

I understand it. The traditional explanation is that there’s a variety of checks in our DNA to prevent cancer from happening, as well as a robust immune response when it does happen. Anyone who gets cancer had to have cells that bypassed the checks, evaded the immune system, and overcame the metalevel control of DNA that doesn’t allow cells to bypass checks in the first place.

I don’t like this explanation because it doesn’t adequately explain, to me, why both older individuals and bigger individuals are more likely to get cancer than younger or smaller individuals within a species, but not across species [1]. Why is a 70 year old human more likely to get cancer this year than a 10 year old human, but a 10 year old human is less likely to get cancer than a 3 year old mouse? Why is a 7 foot human more likely to get cancer than a 6 foot human, but a 6 foot human is more likely to get cancer than a 10 foot elephant?

In order to explain these facts, we end up having to add fiddly little details to our explanations, trying to discuss how aging makes DNA replication more error prone and thus more likely to have the sort of mutations that allows cells to bypass checks, but that clock ticks faster in mice than in humans. Or we have to talk about species specific cancer adaptations, and say some of them are more effective than others, but then all else being equal, size makes cancer worse.

To me, it smacks of epicycles: little features we have to add to models to incorporate all the facts we know, until our beautiful, concise model becomes a bloated mess. It seems…sloppy. I wonder if there will be a Newtonian model of cancer to come along to replace our Ptolemaic one, and show us exactly where we’re going wrong [2]. 

[1] It’s difficult to get these numbers for all species, but we can at least say

a) Older humans are more likely to get cancer in a given year than younger humans.

b) Taller humans are more likely to get cancer than shorter humans.

c) Bigger dogs are more likely to get cancer than smaller dogs.

d) Older dogs are more likely to get cancer than younger dogs.

But

a) There’s no relation between animal size or lifespan and relative risk of cancer.

b) Whales and elephants don’t get cancer very often, but are big and live a long time.

c) Mice do get cancer relatively frequently, but are small and live a short time.

[2] Hopefully this will also incorporate the weird relationship between animal size and lifespan, namely that bigger animals tend to live longer when comparing across species, but live a shorter amount of time when comparing within species. I wrote a whole blog post about this paradox, in which I suggested that the answer was the immune system. That might be an answer here, too.