Bayesian variable selection for logistic regression with a differentially misclassified binary covariate

A Bayesian approach for variable selection is developed for use in models with a misclassified binary predictor variable. We define the main outcome model containing the latent predictor, the measurement model associated with the prevalence of the predictor, and the sensitivity and specificity models of the fallible classifier conditioned on the true value of the predictor. We use binary indicator variables to execute the Gibbs sampler-based variable selection process, and we identify the highest posterior probability model given the data. We demonstrate the performance of the procedure in several simulation studies, and we utilize the selection method to optimize model performance in two datasets.