Earlier quoted context omitted.
"when we smash together Muons and nucleons that there is a certain chance that we will produce Kaons." I don't think that is a fair comparison. My description had much more content than this, it was a high level overview of the proposed process. In contrast, your example does not explain anything.
> Every time a cell divides there is some chance of a genetic error occurring. > Activities that damage tissue, etc and necessitate cell division to replenish the cells will contain cells with more errors. I don't see how your explanation could enable anything but a statistical model. The underlying processes I'm talking about would be molecular interactions modeled through the domain of theoretical chemistry or even…
First, I wouldn't call Armitage and Doll a "statistical model", it is more a "rational model" derived from first principle considerations. "Statistical models" are stuff like linear regressions, at least to me.
Second, my explanation is useful in that if it is correct, we would need a certain combination of division and error rates to explain age-specific incidence curves. So, within the context of the model (which is commonly accepted), we can put upper lower bounds on these values from epidemiological data.
See for example my earlier discussion on this site[1]. Even if you disagree with my conclusions (somatic mutation can't do it... something is up and hundreds of billions to trillions of $ have been wasted barking up the somatic mutation tree), or find a mistake, that is still what it can be used for: