Doctor (skill)
This is one of the skills. Unlike medics, doctors take care of diseases and complicated surgeries. If you wish to remove a bullet from a friend's stomach, doctor is the skill that you need. Just like you need it to give sick people the right medicine. You can however apply a simple bandage with doctor, as well.
Bonuses would be applicable if there has been an earlier experience with this type of treatment, especially good equipment or an experienced assistant.
Handicaps for lack of all the above.
If a test on doctor fails, the patient doesn't have to die. They could just as easily get an infection or their situation could improve – but only very slightly – and whatever else you know from House M.D. and Emergency Room.
The starting value is: 15 + P + I
Details to help distinguish between Doctor and First aid can be found here.