I would think that your drive shaft diameter is going to be determined more by the torque you are transmitting.
Sprockets aren't usually that heavy. The force exerted on the sprockets to transmit the torque could also be a concern, as it is a cyclic load, so you could have a fatigue failure.
If you know the torque then Torsional Stress=(Torque/Polar Moment of Inertia)*radius
equate this to shear stress of the material, then u can solve the RHS for radius.
Also as Jerry said, the sprockets are usually not heavy, but if you really want take in account their weight then you have to solve this problem using Mohrs Circle Theory. Because now you have bending moment due to sprocket weight and the acting torque.