  This paper proposes a new approach to address the problem of unmeasured
confounding in spatial designs. Spatial confounding occurs when some
confounding variables are unobserved and not included in the model, leading to
distorted inferential results about the effect of an exposure on an outcome. We
show the relationship existing between the confounding bias of a non-spatial
model and that of a semi-parametric model that includes a basis matrix to
represent the unmeasured confounder conditional on the exposure. This
relationship holds for any basis expansion, however it is shown that using the
semi-parametric approach guarantees a reduction in the confounding bias only
under certain circumstances, which are related to the spatial structures of the
exposure and the unmeasured confounder, the type of basis expansion utilized,
and the regularization mechanism. To adjust for spatial confounding, and
therefore try to recover the effect of interest, we propose a Bayesian
semi-parametric regression model, where an expansion matrix of principal spline
basis functions is used to approximate the unobserved factor, and
spike-and-slab priors are imposed on the respective expansion coefficients in
order to select the most important bases. From the results of an extensive
simulation study, we conclude that our proposal is able to reduce the
confounding bias with respect to the non-spatial model, and it also seems more
robust to bias amplification than competing approaches.
