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Table 5 Effect of non-differential exposure misclassification on individual and ecologic studies

From: Bias magnification in ecologic studies: a methodological investigation

  Group 0 Group 1 Crude
Correct          
  expose unexpose sum expose unexpose sum expose unexpose sum
cases 160 80 240 720 10 730 880 90 970
noncases 40 720 760 180 90 270 220 810 1030
total 200 800 1000 900 100 1000 1100 900 2000
risk 0.8 0.1   0.8 0.1   0.8 0.1  
RD 0.7    0.7    0.7   
X i 0.20    0.90      
Y i 0.24    0.73      
Misclassify          
  expose unexpose sum expose unexpose sum expose unexpose sum
cases 144 96 240 578 152 730 722 248 970
noncases 176 584 760 162 108 270 338 692 1030
total 320 680 1000 740 260 1000 1060 940 2000
risk 0.45 0.14   0.78 0.58   0.68 0.26  
RD 0.31    0.20    0.42   
X i 0.32    0.74      
Y i 0.24    0.73      
  1. The data are misclassified assuming the same sensitivity and specificity in each group, both equal to 0.8. Since there are no other sources of bias in this example, the crude individual and ecologic estimates of the RD are identical (0.7) for the correct data. For the misclassified data, the crude individual level estimate of the RD (0.42) is biased toward the null while the ecologic estimate (1.17) is biased away from the null. RD = risk difference; X i and Y i are the average exposure and average risk in group i.