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Table 3 Effect modification of the risk difference by group

From: Bias magnification in ecologic studies: a methodological investigation

  Group 0 Group 1 Crude
  expose unexpose sum expose unexpose sum expose unexpose sum
case 20 10 30 48 12 60 68 22 90
noncase 80 90 170 32 108 140 112 198 310
total 100 100 200 80 120 200 180 220 400
risk 0.2 0.1   0.6 0.1   0.378 0.1  
RD 0.1    0.5    0.278   
X i 0.5    0.4      
Y i 0.15    0.3      
n i 200    200      
  1. The background risks in each group are the same but the risk differences vary. The crude individual-level risk difference lies between the two extremes, as it must when exposure is binary. The ecologic estimate of the risk difference, (Y 1-Y 0)/(X 1-X 0)= -1.5, is extremely biased. RD = risk difference; X i and Y i are the average exposure and average risk in group i; n i = size of group i.