ABSTRACT
In Example C of Chapter 3 we considered the problem of inferring the association between a binary X and a binary Y , when the available data are observations of (X∗,Y ) rather than (X ,Y ). Recall that in this context X∗, which is also binary, is regarded as a “noisy surrogate” for X . Moreover, the quality of the surrogate is quantified by its sensitivity, Pr(X∗ = 1|X = 1), and specificity, Pr(X∗= 0|X = 0). Also recall that the assumption of nondifferential misclassification may be warranted, whereby conditional independence between X∗ and Y given X is assumed. Often in a biostatistical context, X indicates absence or presence of an exposure and Y indicates disease status. Then nondifferentiality corresponds to the imperfect measurement of exposure being completely blind to disease status.
