Can you submit two different abstracts about the same data to two different conferences?
In most experimental fields (to which I would definitely slot medicine), it's rather common to present results more than once at conferences.  The obvious reasons for doing this are that different conferences hit different audiences.  Also, that the researcher may be going to the conference to hear other talks, or even enjoy some travel (do not bind the mouths of the oxen!), not ONLY to publish his/her results.

Also I strongly advise to publish your results in a "real journal", widely circulated, not a conference proceedings, only.  [In most fields, CS/Math excluded.]  The conference(s) may have some boilerplate about "original research" or "peer reviewed conference proceedings" (the latter often a very poorly distributed set of volumes).  

You have to learn to play the game with that sort of thing (conference proceedings in experimental fields).  Your interests AND the interests of the field are much better served by eventually publishing in JAMA or some lesser but similar "real journal".  Give the conference enough so that it looks good, but not your whole case.  Maybe enough of the problem to flash the motivation (is of interest) and then a subsection of the results.  This is probably enough so that you can still publish the entire study in a real article (or set of them), in real, well-circulated and well-reviewed magazines.  Of course, cite the earlier conference proceedings (gives you as self cite also...woot!), so that you are not covering up doing the earlier publication.  But don't feel bashful about repeating the content from the earlier, page-limited conference proceedings, within your longer "real articles".