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The individual analysis of alcohol yields a rate ratio of 5 independent of the level of smoking, but the ecological analysis produces an attenuated effect. Adjustments for smoking reduces the effect even further, thus producing more bias.

Ecological level Analysis                                       Ecological regression rate 6.8 + 5 * % alcohol
% smokers            0.5            0.4           0.36       Estimated ecological rate ratio = 1+(5/6,8) = 1.73
% alcohol               0.4            0.4           0.49      rate = 29 + 7 * % alcohol + 76 * % smoking
Cancer rate           8.6            8.9            9.2        Estimated ecological rate ratio = 1.2 (evaluated at mean smoking of  0.42)
                                                       From Greenland and Morgenstern, Int J Epidem 1989; 18: 269-74