A Bayesian semiparametric model for case-control studies with errors in variables

We develop a model and a numerical estimation scheme for a Bayesian approach to inference in case-control studies with errors in covariables. The model proposed in this paper is based on a nonparametric model for the unknown joint distribution for the missing data, the observed covariates and the proxy. This nonparametric distribution defines the measurement error component of the model which relates the missing covariates X with a proxy W. The oxymoron 'nonparametric Bayes' refers to a class of flexible mixture distributions. For the likelihood of disease, given covariates, we choose a logistic regression model. By using a parametric disease model and nonparametric exposure model we obtain robust, interpretable results quantifying the effect of exposure.