When exposure to a carcinogenic substance is suspected, the cause/effect relationship on any given case can never be ascertained. Lung cancer occurs spontaneously, and there is no difference between a "natural" cancer and another one caused by radon (or smoking). Furthermore, it takes years for a cancer to develop, so that determining the past exposure of a case is usually very approximative. The health effect of radon can only be demonstrated through theory and statistical observation.
The study design for epidemiological methods may be of three kinds:
* The best proofs come from observations of cohorts (predetermined populations with known exposures and exhaustive follow-up), such as those on miners, or on Hiroshima and Nagasaki survivors. Such studies are efficient, but very costly when the population needs to be a large one. Such studies can only be used when the effect is strong enough, hence, for high exposures.
* Alternate proofs are case-control studies (the environment factors of a "case" population is individually determined, and compared to that of a "control″ population, to see what the difference might have been, and which factors may be significant), like the ones that have been used to demonstrate the link between lung cancer and smoking. Such studies can identify key factors when the signal/noise ratio is strong enough, but are very sensitive to selection bias, and prone to the existence of confounding factors.
* Lastly, ecological studies may be used (where the global environment variables and their global effect on two different populations are compared). Such studies are "cheap and dirty": they can be easily conducted on very large populations (the whole USA, in Dr Cohen's study), but are prone to the existence of confounding factors, and exposed to the ecological fallacy problem.
Furthermore, theory and observation must confirm each other for a relationship to be accepted as fully proven. Even when a statistical link between factor and effect appears significant, it must be backed by a theoretical explanation; and a theory is not accepted as factual unless confirmed by observations.