Full-likelihood approaches to misclassification of a binary exposure in matched case-control studies

We consider analysis of matched case-control studies where a binary exposure is potentially misclassified, and there may be a variety of matching ratios. The parameter of interest is the ratio of odds of case exposure to control exposure. By extending the conditional model for perfectly classified data via a random effects or Bayesian formulation, we obtain estimates and confidence intervals for the misclassified case which reduce back to standard analytic forms as the error probabilities reduce to zero. Several examples are given, highlighting different analytic phenomena. In a simulation study, using mixed matching ratios, the coverage of the intervals are found to be good, although point estimates are slightly biased on the log scale. Extensions of the basic model are given allowing for uncertainty in the knowledge of misclassification rates, and the inclusion of prior information about the parameter of interest.