Should I become first author of a paper for which I did the statistical analysis?
In medicine, as in most biological fields that I know of, the first author is the person who did most of the hands-on work, while the last author is the one who had the idea and planned the project.  From what you've said, then, it would be appropriate for you to be first author and the doctor to be last.

That said, if you don't feel comfortable being first author (and especially in light of your comment that I do not agree fully with all the conclusions) it's also appropriate for you to request to not be first author -- some middle position (second author, or whatever) is also perfectly suitable for your contributions, from the sound of it.