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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.