Analysis of matched case-control data in presence of nonignorable missing exposure

The present article deals with informative missing (IM) exposure data in matched case-control studies. When the missingness mechanism depends on the unobserved exposure values, modeling the missing data mechanism is inevitable. Therefore, a full likelihood-based approach for handling IM data has been proposed by positing a model for selection probability, and a parametric model for the partially missing exposure variable among the control population along with a disease risk model. We develop an EM algorithm to estimate the model parameters. Three special cases: (a) binary exposure variable, (b) normally distributed exposure variable, and (c) lognormally distributed exposure variable are discussed in detail. The method is illustrated by analyzing a real matched case-control data with missing exposure variable. The performance of the proposed method is evaluated through simulation studies, and the robustness of the proposed method for violation of different types of model assumptions has been considered.