Many publications have claimed that increased residential radon levels increase lung cancer risk. However, there is a major problem with such publications.
When publications have compared the lung cancer rates between residences with different residential radon levels, a reduction of lung cancer with increasing residential radon level has been reported in case-control studies (Thompson, 2011) and ecological studies (Cohen, 1995) (see Figure below) and (Denton & Namazi, 2013).

Though several authors have criticized Cohen's study, he has thoroughly rebutted those criticisms, and his study has never been refuted, continuing to provide support for the science that higher levels of residential radon reduce lung cancer risk.
A recent ecological study (Simeonov & Himmelstein, 2015), which examined lung cancer incidence in the counties of the USA, and considered a large number of demographic variables, concluded that lung cancer risk increases with smoking prevalence. It also concluded that lung cancer incidence decreases with elevation, and that this correlation can explain the observed negative correlation between radon levels and lung cancer incidence in the counties of the USA. Let us examine if this explanation is valid.
Using the data tabulated in the publication (Simeonov & Himmelstein, 2015) available at: https://dfzljdn9uc3pi.cloudfront.net/2015/705/1/county-data.txt, and considering the counties within a narrow range of values for elevation and smoking prevalence, a scatter-plot has been generated between residential radon levels and lung cancer rates, and it shows a negative slope indicating reduction of lung cancers with increasing residential radon levels (see graph below).
Confounding by smoking prevalence or by elevation would not be able to explain this negative slope, as the data include only a narrow range of smoking prevalence and elevation. Hence, the explanation given by Simeonov & Himmelstein stating that confounding by elevation can explain the observed negative correlation between radon level and lung cancer rate is not valid.
A study of lung cancer in women who predominantly never smoked has shown evidence for a U-shaped dose-response that is consistent with radiation hormesis and inconsistent with the LNT model (Bogen & Cullen, 2002).
All these data are consistent with radiation hormesis and inconsistent with the LNT model.
References
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Bogen, K. T. & Cullen, J. (2002) Residential Radon in U.S. Counties V Lung Cancer in Women Who Predominantly Never Smoked. Environmental Geochemistry and Health, 24(3), 229-247. http://dx.doi.org/10.1023/A:1016051322603
Cohen, B. L. (1995) Test of the linear-no threshold theory of radiation carcinogenesis for inhaled radon decay products. Health Phys, 68(2), 157-74. http://www.ncbi.nlm.nih.gov/pubmed/7814250
Denton, G. R. W. & Namazi, S. (2013) Indoor Radon Levels and Lung Cancer Incidence on Guam. Procedia Environmental Sciences, 18(0), 157-166. http://www.sciencedirect.com/science/article/pii/S1878029613001539
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