The DOF can certainly change from shot to shot if the format changes. I can change format easily on a large format camera while keeping everything else the same, and the DOF changes by definition when the format changes, because DOF is defined in relation to the print (making certain assumptions about typical print sizes, etc., as described above), not the image on film. If the format is larger, then the acceptable circle of confusion--the diameter of a blur circle that can be resolved as a sharp point on a typical print at a typical viewing distance by a typical human eye--is larger, and DOF values cannot be calculated without plugging in a value for acceptable circle of confusion.