The authors generalize the linear response theory of magnetoconductivity of disordered two-dimensional electron gases to include the case where a confinement potential is present in one of the two spatial directions. The theory allows studies of the effect of suppression of backscattering due to the existence of spatially separated edge states in high magnetic fields. Explicit calculations of the conductivity are carried out for weak scattering in two limits: the weak and the strong confinement limit.