In Medicine and in Surgery, the convention is similar to that of the Physical Sciences with the most significant contributor being first or last, or with the owner of the lab equipment or funding getting senior author position as the last author.
However, there is a curve ball in Medical and Surgical Journals in that the first three authors are the ones who gain the most credit. The reason for this is that back in the pre-WWW-historic era, when I wrote papers that went into Surgical journals and when I went through medical school and surgical residency, the medical journal articles were all indexed in the Index Medicus.
The Index Medicus was a hard-copy index prepared at the end of each year and found in every medical library with three sets of listings sorted by Medical E-something Subject Headings (MeSH), title of the journal article, and the last name of the first three authors. This paper index was how people found journal articles of interest and how the authors gained "publication cred." I ended up as third author on many papers giving me a lot of cred even above some grad students and post-docs who helped with experiments but had not supervised or designed (or originally proposed some of, i.e. conception and design, as I had) the experiments in these papers as I had.
Because of the problem with "author inflation" (people being added to author lists as a courtesy or to accomodate seniority), journals in medical fields such as JAMA (Journal of the American Medical Association) now require authors to submit signed Authorship Responsibility Forms which outline specifically what constitutes valid criteria for being listed as an author on a paper:
Obtaining funding is listed as one of the possible criteria, as are administrative, technical, or material support. Some of these criteria surprised me as being rather flimsy in some contexts.