  Spatial confounding is how is called the confounding between fixed and
spatial random effects. It has been widely studied and it gained attention in
the past years in the spatial statistics literature, as it may generate
unexpected results in modeling. The projection-based approach, also known as
restricted models, appears as a good alternative to overcome the spatial
confounding in generalized linear mixed models. However, when the support of
fixed effects is different from the spatial effect one, this approach can no
longer be applied directly. In this work, we introduce a method to alleviate
the spatial confounding for the spatial frailty models family. This class of
models can incorporate spatially structured effects and it is usual to observe
more than one sample unit per area which means that the support of fixed and
spatial effects differs. In this case, we introduce a two folded
projection-based approach projecting the design matrix to the dimension of the
space and then projecting the random effect to the orthogonal space of the new
design matrix. To provide fast inference in our analysis we employ the
integrated nested Laplace approximation methodology. The method is illustrated
with an application with lung and bronchus cancer in California - US that
confirms that the methodology efficiency.
