Practice in dealing with medical problems is the greatest, but not the only, determinant of competence. Statisticians at present in Public Health Sciences range in years of experience from several to over twenty eight. Therefore there is a good chance that one of us will be able to solve your problem, but as statistics is a relatively young subject there are many 'unsolved problems' around - like in any other interesting subject. A typical medical school statistician will divide his or her time between teaching, consultancy, collaborative research in their own department and with others, and on research in statistical methods. He or she may be school funded, but may be funded primarily for research in the department in which the statistician works.
All schools have at least one medical statistician, and most now have several.
Researchers in small institutions often do not have access to statistical expertise.