I am part of the Radiology team. The Radiology team is physically located in the Radiology Department of the Clinic, so there are always patients and doctors passing by my office. Being around patients who are here for a CT scan, MRI, ultrasound, or X-ray helps me appreciate the little things in life and minimize the everyday frustrations and stresses we face. Our work primarily involves helping radiologists with the design and analysis of studies. If the accuracy of an imaging technique, such as an MRI, for diagnosing a torn rotator cuff is not much better than flipping a coin, then MRI is not very useful in making this particular diagnosis.
Diagnostic accuracy is a function of both sensitivity and specificity.
Specialized statistical techniques, such as ROC curves, have been developed to address these types of questions. I consider myself very fortunate to be doing this kind of work. Well, the answer to that is good news-there are jobs of all kinds out there for people with a math background.