Depth of Field under the SPECIFIED VIEWING CONDITIONS of any photographic image is actually only dependent on TWO factors. The first is the Absolute Reproduction Ratio, which is the ratio of the size of the subject (at the focused distance) in real life, to the size of the subject in the final image (usually specified as a print). The second dependency is to the absolute effective diameter of the aperture. The effective aperture diameter is the size the aperture appears to be from the sensor side of the lens. The important thing to remember is that we are using the actual physical diameter, not the f/number. In both cases, reproduction ratio, and aperture they are actually inversely proportional. So as both the reproduction ratio, and the aperture diameter get smaller, the DoF will get larger.
It is also important to remember that the specified viewing conditions are very important, probably more so than either of the two variable proportionalities. So changing the viewing conditions is likely to have a far more profound effect on DoF than changing either the reproduction ratio, or the aperture diameter. Also of note is the fact that all of the things that are usually considered when calculating the DoF, such as Sensor size, focal length, focal distance f/number etc, are just convenient ways of pre-defining the reproduction ratio, and aperture diameter, based on the equipment that is in current use.