I also work at a hospital and have a Masters in Healthcare Admin. It sounds like something like data science may be something for you to look in to. At my organization, I work on the business analytics team and we are constantly analyzing operational data in order to help leaders make strategic decisions, arm marketing with data so that they know "who are patients are" and who are target market is”, etc... the possibilities are endless in data science.
I started out in operations and it has been a big help when transitioning over to the analytics team, as I understand the operational workflows more than anyone else. From my experience, understanding the operations is something that can’t be taught – it’s best to have worked in that area. Whereas, if you are an analytical person, you can learn the data science piece.
Data science and analytics is becoming HUGE in healthcare right now. From both a non-clinical (business) perspective, and a clinical perspective. Hope that helps.