On the discrepancy between epidemiologic studies in individuals of lung cancer and residential radon and Cohen's ecologic regression.

There is still substantial confusion in the radiation effects community about the inherent limitations of ecologic analysis. As a result, inordinate attention has been given to the discrepant results of Cohen, in which a negative estimate is observed for the regression of county mortality rates for lung cancer on estimated county radon levels. This paper demonstrates that Cohen's ecologic analysis cannot produce valid inference on the exposure-response relationship for individuals unless lung cancer risk factors (smoking, age, occupation, etc.) for individuals are statistically uncorrelated with indoor radon level within counties or unless risk effects for radon and other factors are additive. Both of these assumptions are contradicted in the literature. Thus, contrary to common assumption, when a linear no-threshold model is the true model for radon risk for individuals, higher average radon concentration for a county does not necessarily imply a higher lung cancer rate for the county. In addition, valid inference from county-level ecologic analysis and the elimination of the ecologic bias cannot be achieved with the addition of county-wide summary variables (including "stratification" variables) to the regression equation. Using hypothetical data for smoking and radon and assuming a true positive association for radon and lung cancer for individuals, the analysis demonstrates that a negative county-level ecologic regression can be induced when correlation coefficients for smoking and radon within county are in the range -0.05 to 0.05. Since adverse effects for radon at low exposures are supported by analysis of miner data (all data and data restricted only to low cumulative exposures), a meta-analysis of indoor radon studies, and molecular and cellular studies, and since ecologic regressions are burdened by severe limitations, the negative results from Cohen's analysis are most likely due to bias and should be rejected.