  Measurement error (ME) and missing values in covariates are often unavoidable
in disciplines that deal with data, and both problems have separately received
considerable attention during the past decades. However, while most researchers
are familiar with methods for treating missing data, accounting for ME in
covariates of regression models is less common. In addition, ME and missing
data are typically treated as two separate problems, despite practical and
theoretical similarities. Here, we exploit the fact that missing data in a
continuous covariate is an extreme case of classical ME, allowing us to use
existing methodology that accounts for ME via a Bayesian framework that employs
integrated nested Laplace approximations (INLA), and thus to simultaneously
account for both ME and missing data in the same covariate. As a useful
by-product, we present an approach to handle missing data in INLA, since this
corresponds to the special case when no ME is present. In addition, we show how
to account for Berkson ME in the same framework. In its broadest generality,
the proposed joint Bayesian framework can thus account for Berkson ME,
classical ME, and missing data, or for any combination of these in the same or
different continuous covariates of the family of regression models that are
feasible with INLA. The approach is exemplified using both simulated and real
data. We provide extensive and fully reproducible Supplementary Material with
thoroughly documented examples using {R-INLA} and {inlabru}.

Methodology