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Table 4 Non-differential exposure misclassification in a 2 × 2 table

From: Bias magnification in ecologic studies: a methodological investigation

 

Correct

Misclassified

 

expose

unexpose

sum

expose

unexpose

sum

Case

a i

b i

a i +b i

sa i + (1-t)b i

(1-s)a i +tb i

a i +b i

noncase

c i

d i

c i +d i

sc i + (1-t)d i

(1-s)c i +td i

c i +d i

Total

a i +c i

b i +d i

n i

s(a i +c i ) + (1-t)(b i +d i )

(1-s)(a i +c i ) + t(b i +d i )

n i

X i

(a i +c i )/n i

  

s(a i +c i )/n i + (1-t)(b i +d i )/n i

  

Y i

(a i +b i )/n i

  

(a i +b i )/n i

  
  1. Assume that the proportion of people misclassified does not depend on disease status. Sensitivity s is the fraction of exposed people classified as exposed; specificity t is the fraction of unexposed people classified as unexposed. On the group level, the average risk remains the same but the average exposure changes. X i and Y i are the average exposure and average risk in the group; n i = size of the group.
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Environmental Health

ISSN: 1476-069X