It’s only the focal length and f-stop that affect depth of field. Sensor size affects it only indirectly, because you need a different focal length to get the same angle of view.
From an optical point of view, light does not bend differently just because you put a differently-sized rectangle somewhere in its path. Or to put it another way, if you cut the edges off your sensor, that won’t alter the image on the remaining area of the sensor.
