In my article on Acts and in an earlier blog, I discussed some of the passages in Luke-Acts which suggest that its author was a doctor (such as prefaces showing familiarity with technical treatises, like those of a doctor, as well as greater interest in the details of medical conditions, and an interest in defending the honor of doctors). This is not a revisitation of W.K. Hobart's argument from precise medical language, but does demonstrate a unique interest in medical issues and healings. Said interest, however, is stronger than I had realized:
Luke's interest in healing is evident from the fact that he recorded all the Markan healing accounts, shared with Matthew the healing of the centurion's slave in Luke 7:1-10, and had five healings unique to his Gospel (7:11-17; 13:10-17; 14:1-6; 17:11-19; 22:51).
Robert H. Stein, Luke (TNAC), page 20.
For a point of comparison, I will turn to a my article The Miracles of Jesus: A Historical Inquiry, in which I note that "Not only does [Matthew] tend to shorten Mark's miracle stories, the author of Matthew excludes some of them altogether." Thus, whereas Matthew shows less interest in Mark's miracle accounts and provides only one of his own. Luke, on the other hand, shows much greater interest in miracles and narrates them more extensively than Matthew.
Obviously, this is not determinative. But it is suggestive, especially when viewed in light of the rest of the evidence suggesting authorship by someone familiar with and interested in the medical sciences of his day.