How to become a supervisor? Finding students to supervise
These are the possible approaches in which you can get people (especially students) to know you. Since, you are in a hospital working as a statistician it would be more valuable and increase the chance of getting students.


Deliver talks at local organisations/universities: You should try to meet the head and principal of the university. Discuss with them your profile and eager to talk to the students. If your talk is well accepted by the students, some of those students would surely be interested to work with you. Moreover, professors would also like to collaborate with you.
Visit conferences and present your works: Work on your own and write research papers, visit the conferences or seminars. There you will get to know few aspiring students and people to work with.
Discussion with your own colleagues in the hospital: I am sure you may not be alone and wanting to work on research. There will always be someone. Since, you are new; talk to your colleagues and propose your ideas to work on it. This will help you get the above points (1) and (2) easily.