The potential for bias in Cohen's ecological analysis of lung cancer and residential radon.

Cohen's ecological analysis of US lung cancer mortality rates and mean county radon concentration shows decreasing mortality rates with increasing radon concentration (Cohen 1995 Health Phys. 68 157-74). The results prompted his rejection of the linear-no-threshold (LNT) model for radon and lung cancer. Although several authors have demonstrated that risk patterns in ecological analyses provide no inferential value for assessment of risk to individuals, Cohen advances two arguments in a recent response to Darby and Doll (2000 J. Radiol. Prot. 20 221-2) who suggest Cohen's results are and will always be burdened by the ecological fallacy. Cohen asserts that the ecological fallacy does not apply when testing the LNT model, for which average exposure determines average risk, and that the influence of confounding factors is obviated by the use of large numbers of stratification variables. These assertions are erroneous. Average dose determines average risk only for models which are linear in all covariates, in which case ecological analyses are valid. However, lung cancer risk and radon exposure, while linear in the relative risk, are not linearly related to the scale of absolute risk, and thus Cohen's rejection of the LNT model is based on a false premise of linearity. In addition, it is demonstrated that the deleterious association for radon and lung cancer observed in residential and miner studies is consistent with negative trends from ecological studies, of the type described by Cohen.