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The constant rate ratio for smoking (=10) in the 3 regions implies that there is no confounding by smoking. The rate ratio for radon is 2 in each region. The ecological regression, without smoking, shows an inverse effect, even though the individual analysis showed a positive effect. Controlling for smoking does not alter this negative effect.

Ecological level Analysis                                    Ecological regression rate 84-59 * % high radon
% smokers             0.5             0.4          0.3       Estimated ecological rate ratio = 1+(-59/84)=.30
% high radon          0.26           0.35        0.5      rate = 29 + 7 * % high radon + 76 * % smoking
Cancer rate            69.3           62.1        55.5    Estimated ecological rate ratio = 1.1 (mean smoking for prevalence = 0.4)