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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.