Convert research into business
If you want to start a company using data from a source you do not own, and via ideas you developed as part of your research, you have to contact your university’s legal department. 

You are not the only stakeholder here. In addition to the hospital (obviously) who may have a claim to ownership we have


Your university
Your PI
Your funding agency 
Other collaborators 


In addition, medical data is highly sensitive usually and at least in my university more care is needed. Did you obtain IRB approval for example? To illustrate: hospitals have to obtain consent from patients in order to release their data to third parties. If the consent was for research purposes only then you can’t commercialize it. 

Good luck!