Medical stations and qualified doctors are few and far between within the outer colonies while most patients can be serviced at the usual medical facility (every station is required to have one), but for more severe cases the patient's would need to be rushed to medical facilities within the inner planets. Stepping into this role is the Medrunners.
Medrunners main job is to: assess, stabilize, and freeze. To do this they serve as EMTs in quickly assessing the patient and doing what they must go stabilize the patient so they can be put in cryosleep for the ride. In this line of work the Medrunners quickly gained the nickname butcher due to the lengths they are willing to go to stabilize a patient (amputations, cauterizing wounds, and in a short span of time).
Now the problem I've run into is team/crew size as well as specific roles/jobs within the team. For sure you have to have more than one, but I personally have no idea what the ideal team size would be.
Medrunners themselves don't go into cryo unless it's a long trip. Ex: Eris to Ceres.