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Table 2 Confounding by group

From: Bias magnification in ecologic studies: a methodological investigation

  Group 0 Group 1 Crude
  expose unexposed sum expose unexpose sum expose unexpose sum
case 16 12 28 48 24 72 64 36 100
noncase 24 48 72 12 16 28 36 64 100
total 40 60 100 60 40 100 100 100 200
risk 0.40 0.20   0.80 0.60   0.64 0.36  
RD 0.20    0.20    0.28   
X i 0.40    0.60      
Y i 0.28    0.72      
n i 100    100      
  1. Since background risks and exposure distributions differ between the two groups, the crude individual-level estimate of the risk difference is confounded. The ecologic estimate of the risk difference, (Y 1-Y 0)/(X 1-X 0) = 2.2, is much more confounded. RD = risk difference; X i and Y i are the average exposure and average risk in group i; n i = size of group i.