Table 4.

Non-differential exposure misclassification in a 2 × 2 table

	Correct			Misclassified
	expose	unexpose	sum	expose	unexpose	sum
Case	a i	b i	ai+bi	sai + (1-t)bi	(1-s)ai+tbi	ai+bi
noncase	c i	d i	ci+di	sci + (1-t)di	(1-s)ci+tdi	ci+di
Total	ai+ci	bi+di	n i	s(ai+ci) + (1-t)(bi+di)	(1-s)(ai+ci) + t(bi+di)	n i
X i	(ai+ci)/ni			s(ai+ci)/ni + (1-t)(bi+di)/ni
Y i	(ai+bi)/ni			(ai+bi)/ni

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.