Correcting for Misclassification in Two-Way Tables and Matched-Pair Studies

Barron has presented a matrix formula that allows correction for nondifferential misclassification in two-by-two tables. We show how extensions of his result can be applied to situations involving differential misclassification, matched data, and arbitrary two-way tables. We also discuss some important limitations in the application of algebraic corrections for misclassification. In particular, we show that study misclassification rates need not reflect population misclassification rates if the distribution of the misclassified variable is determined by aspects of the study design.