I can't guarantee that I am totally correct and if someone is positive, please let me know, but as I understand it:
The roan gene could best be described as a 3rd variant in the color scheme, neither dominant or recessive, but rather incomplete (or co dominant I can't remember which is which)
An animal with one copy of the white gene will be roan with the major coat color determined by the other gene
An animal with 2 copies of the white gene will be white, or so appear that way. there will more than likely be some red around the eyes, nose, inside the ears...
A white shorthorn (2 copies of the "white" gene) should ALWAYS throw a roan. The extent and pattern of the roan can be influenced by many factors that I'm sure many, myself included, don't understand. Just remember roan is the presence of white hairs amongst other colors. If you have an animal that "should" be roan but doesn't appear to be look for a few white hairs in the brisket, belly, twist.... or shave their head and what you thought was black might now look silver.
One other thing to keep in mind with all of this is the "white marks" markings are completely different genes. The nice even colored roans and the "rednecks" are still both roan and have a "white" gene but the additive effects of the white marks make the two look totally different.