Matched case-control data with a misclassified exposure: what can be done with instrumental variables?

Matched case-control studies are used for finding the association between a disease and an exposure after controlling the effect of important confounding variables. It is a known fact that the disease-exposure association parameter estimators are biased when the exposure is misclassified, and a matched case-control study is of no exception. Any bias correction method relies on validation data that contain the true exposure and the misclassified exposure value, and in turn the validation data help to estimate the misclassification probabilities. The question is what we can do when there are no validation data and no prior knowledge on the misclassification probabilities, but some instrumental variables are observed. To answer this unexplored and unanswered question, we propose two methods of reducing the exposure misclassification bias in the analysis of a matched case-control data when instrumental variables are measured for each subject of the study. The significance of these approaches is that the proposed methods are designed to work without any validation data that often are not available when the true exposure is impossible or too costly to measure. A simulation study explores different types of instrumental variable scenarios and investigates when the proposed methods work, and how much bias can be reduced. For the purpose of illustration, we apply the methods to a nested case-control data sampled from the 1989 US birth registry.