  We present a toy model for radio emission in HMXBs with strongly magnetized
neutron stars (NS) where a wind-collision region is formed by the NS outflow
and the stellar wind of the massive companion. Radio emission is expected from
the synchrotron radiation of shock-accelerated electrons and the free-free
emission of the stellar wind. We found that the predicted relation between the
GHz luminosity ($L_R$) and the accretion X-ray luminosity ($L_X$) can be
written as $L_R \propto L_X^b$ for most parameters. No correlation with X-rays
is expected ($b=0$) when the thermal emission of the stellar wind dominates in
radio. We typically find a steep correlation ($b=12/7$) for sub-Eddington X-ray
luminosities and a more shallow one ($b=2(p-1)/7$) for super-Eddington X-ray
luminosities, where $p$ is the power-law index of accelerated electrons. The
maximum predicted radio luminosity is independent of the NS properties, while
it depends on the stellar wind momentum, binary separation distance, and the
minimum electron Lorentz factor. Using a Bayesian approach we modelled the
radio observations of \sj that cover a wide range of mass accretion rates. Our
results support a shock origin for the radio detections at sub-Eddington X-ray
luminosities. However, no physically meaningful parameters could be found for
the super-Eddington phase of the outburst, suggesting a different origin.
Future observations with more sensitive instruments might reveal a large number
of HMXBs with strongly magnetized NSs in radio, allowing determination of the
slope in the $L_R-L_X$ relation, and putting the wind-collision scenario into
test.
