Inference for case-control studies when exposure status is both informatively missing and misclassified

In case-control studies, it is common for a categorical exposure variable to be misclassified. It is also common for exposure status to be informatively missing for some individuals, in that the probability of missingness may be related to exposure. Procedures for addressing the bias due to misclassification via validation data have been extensively studied, and related methods have been proposed for dealing with informative missingness based on supplemental sampling of some of those with missing data. In this paper, we introduce study designs and analytic procedures for dealing with both problems simultaneously in a 2x2 analysis. Results based on convergence in probability illustrate that the combined effects of missingness and misclassification, even when the latter is non-differential, can lead to naïve exposure odds ratio estimates that are inflated or on the wrong side of the null. The motivating example comes from a case-control study of the association between low birth weight and the diagnosis of breast cancer later in life, where self-reported birth weight for some women is supplemented by accurate information from birth certificates.