Reply to `Explaining the lung cancer versus radon exposure data for USA counties'

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Abstract
Professor Cohen states in his letter that his analysis `encompasses all of the Doll suggestions'. It is, however, logically impossible for it to have done so using data at the level of counties. This is because the effect of cigarette smoking on the relationship between residential radon and individual lung cancer risk will be determined by the relationship between smoking status and lung cancer among the individuals within each county. Unless smoking is irrelevant to lung cancer risk (which we know to be untrue) or smoking status and residential radon are uncorrelated within each county (which seems unlikely), the relationship between residential radon and lung cancer at the county level will differ from that at the level of the individual in a way that cannot be overcome by including corrections for smoking habits at the county level, even if these corrections correctly represent the smoking habits of the individuals within each county. The difference in the relationship between a risk factor and a disease rate at the level of the individual and at an area level is the ecologic fallacy and is described in detail by Greenland and Robins (1994) and Morgenstern (1998). Lubin (1998) has also demonstrated that biases caused by the ecologic fallacy can be of any magnitude from minus infinity to plus infinity. In two recent studies (Lagarde and Pershagen 1999, Darby et al 2000), parallel individual and ecological analyses have been carried out of identical data from case-control studies of residential radon (Peshagen et al 1994, Darby et al 1998). These analyses have shown that, in addition to any bias caused by the ecological fallacy, ecological studies of residential radon and lung cancer are also prone to biases caused by determinants of lung cancer risk that vary at the level of the ecological unit concerned. In these two examples, the additional variables were latitude and urban/rural status respectively. The explanation of these variables is not yet well understood and they may well be, in part, surrogate measures for some aspects of the subjects' smoking history not accounted for by the measures of smoking status that have been derived from the individual questionnaire data and used in the analysis of the data for individuals. They had only a minor effect on analysis at this level but a substantial effect on the ecological analyses. The presence of these variables is further evidence of the pitfalls of ecological studies.