The depth of field on a digital camera is a delicate subject because there are two different approaches.
The first, which has no equivalent in the field of analog photography, corresponds to the best possible image taking into account the characteristics of the sensor, i.e. the optical image on a sensor of a point in the scene must be smaller than the size of a pixel on this sensor.
The second, which is the one that will be discussed next, s related to the perception of a person looking at the image, the observer, looking at the image on a print, or possibly a screen assuming that the definition of this screen is such that the observer does not perceive the pixels of that screen.
Magnification / circle of confusion
On the one hand, an observer has a limited visual acuity, in the sense of his capacity to distinguish two close points. On the other hand, the prints are generally viewed at a distance close to the length of their diagonal.
This makes it possible to define a value for the size of the luminous point on the sensitive surface which can be the sensor of a digital camera or a film for an analog camera. This value is the circle of confusion.
However, this value is necessarily a function of the size of the sensitive surface, when the size of the sensor decreases, the size of the circle of confusion must decrease because to obtain a similar image, the rate of magnification must be increased.
It is generally accepted that a size of the circle of confusion corresponding to d/1500 (with d being the diagonal of the sensitive surface expressed in millimeters) seems to be admissible, but one finds other rules for example d/1750.
Thus it gives for the size of the circleof confusion, approximately, 0.03 mm for a 24 * 36 mm camera and 0.02 mm for an APS-C camera
Depth of field
Now back to the original question.
From the above, we can directly conclude that if for a 50mm lens at f/2.0 and a focus distance of 2m the depth of field (DOF) is equal to 18cm for a 24 x 36mm camera then necessarily it will be 12cm for an APS-C camera given the ratio between the sizes of the circles of confusion.