There are quite a few med students that go through the MD-MPH program at HSPH. I went that route myself a couple years back. Applications are made to specific programs, i.e. MPH international health, MPH health care management, etc. I imagine that in addition to the obvious (reasonable grades, etc) they look for department relevant qualifications / experience. For example, many of the med students in my department (international health) had some prior experience in overseas work.