This is a common problem especially in new houses around here (K.C.), and we adjust a whole lot of them during the first year the homeowner has taken possesion. Here's the first thing to try, remove one of the screws in the bottom hinge on the casing side and towards the middle of the casing, replace it with a longer screw (2"-3"). Install the longer screw with a good powered screwgun or a drill with a screw tip. The longer screw will bite into the 2x4 framing behind the casing and draw the door down and in some (also the reverse will work on the top hinge if a door needs to be drawn up and in). Note that this can't be done just by hand screwing, the key is in the power of a screwgun/drill.
If this doesn't correct the problem, then sanding as you mentioned is the other solution.