Infrequent fliers and cancer

Fun with correlational studies: How often should you fly in order to minimize your risk of developing cancer? Clearly flying very frequently is not a good idea since the risk of certain cancers is increased in airline flight crew. This makes perfect sense since airplanes fly at high altitude where there is greater exposure to cosmic radiation, and we all know that radiation exposure increases your risk of developing cancer.
There is, however a contradictory correlation, that people living at higher altitudes experience lower rates of cancer. This was a surprising finding which led to the hypothesis that the thinner air at higher altitudes offered some protection, perhaps having something to do with oxygen free radicals. This seems unlikely to me since, at altitudes that people inhabit there is no change in air composition with altitude. The air is thinner but the relative amount of oxygen does not change. Since we know that intermediate radiation doses can be protective for certain cancers, would it not make sense that the higher doses of radiation at higher altitudes be protective?
I suggest that a devious airline (with no respect for privacy) and an American health insurance company (which has little respect for anything but money) join forces and use frequent flier miles and see if there is an amount of flying that protects against some types of cancer.