I'm sure I remember reading something ages ago about the medical staff onboard a Constitution-Class ship comprising of 30 doctors, nurses, orderlies, etc.
Out of a crew of 430, that would mean one medical specialist for every 14 crewmembers. I have often used this calculation to work out the medical departments on my fanfic ships.
Commander Austin Harris, First Officer, Deep Space Nine (by FltCpt. Bossco)
8.01 - Darkest Before Dawn
(Chapter 8 added, 12/09/2015)