Not a guru, but I do know this:
DOF is determined by
1) the aperture - the larger the opening (the lower the f-stop number) the shallower the DOF;
2) the focal length - the longer the focal length, again, the shallower will be the DOF;
3) the object distance - the closer the lens, hence the sensor, the shallower the DOF.
Incidentally, the crop factor on most DSLRs play a secondary role in determining DOF. Basically, what this means is that on a 1.5 or 1.6 crop camera, the camera would have to be placed further away from the subject (as opposed to a FF camera), in order to get the closest approximate equivalent in composition, etc. Of course, all other variables constant between the cropped and FF camera. In a nutshell, because of the increased object distance the DOF also proportionately increases; not directly because of the crop factor, but because of compositional requirements.
Not sure if this answers your question, though.
PoF