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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