Test of the linear-no threshold theory: rationale for procedures.

A tightly reasoned justification is presented for the procedures used in our test of the linear-no threshold theory of radiation carcinogenesis by comparing lung cancer rates with average radon exposure in U.S. counties. A key point is its dependence on ecological variables rather than on characteristics of individuals and the principal problems involve treatment of potential confounding factors (CF). The method of stratification is introduced and shown to be preferable to multiple regression for evaluating effects of confounding. Utilizing numerous available CF reduces the problem of representing a complex confounding relationship by the average value of a single CF. The requirements on a CF for affecting the results are quantified in terms of its correlations with lung cancer rates and radon levels and it is shown that the existence of an unknown confounder satisfying these requirements is highly implausible. Effects of combinations of confounding factors are treated and shown not to be important. The problem of confounding factors on the level of individuals is resolved. Consideration of plausibility of correlations is used in several applications, including treatments of uncertainty in smoking prevalence, within county differences in radon exposure between smokers and non-smokers, variations in intensity of smoking, differences between measured radon levels and actual exposures, etc. Examples are presented for all applications. The differences between our study and case-control studies, and the advantages of each for testing the linear-no threshold theory, are discussed.