  We use a combination of the XMM-Newton serendipitous X-ray survey with the
optical SDSS, and the infrared WISE all-sky survey in order to check the
efficiency of the low X-ray to infrared luminosity selection method in finding
heavily obscured AGN. We select sources in the 2-8 keV X-ray band which have a
redshift determination in the SDSS catalogue. We match this sample with the
WISE catalogue, and fit the SEDs of the 2844 sources which have three, or more,
photometric data-points in the infrared. We then select the heavily obscured
AGN candidates by comparing their 12 micron AGN luminosity to the observed 2-10
keV X-ray luminosity and their expected intrinsic relation. With this approach
we find 20 candidates, and we examine their X-ray and optical spectra. Of the
20 initial candidates, we find nine (64%; out of the 14, for which X-ray
spectra could be fit) based on the X-ray spectra, and seven (78%; out of the
nine detected spectroscopically in the SDSS) based on the [OIII] line fluxes.
Combining all criteria, we determine the final number of heavily obscured AGN
to be 12-19, and the number of Compton-thick AGN to be 2-5, showing that the
method is reliable in finding obscured AGN, but not Compton-thick. However
those numbers are smaller than what would be expected from X-ray background
population synthesis models, which demonstrates how the optical-infrared
selection and the scatter of the L_x-L_MIR relation introduced by observational
constraints limit the efficiency of the method. Finally, we test popular
obscured AGN selection methods based on mid-infrared colours, and find that the
probability of an AGN to be selected by its mid-infrared colours increases with
the X-ray luminosity. However, a selection scheme based on a relatively low
X-ray luminosity and mid-infrared colours characteristic of QSOs would not
select ~25% of the heavily obscured AGN of our sample. (abridged)
