I very much disagree with Mark's assessment. You shouldn't compensate this person for the COO role until they are confirmed into this role and working full-time in this capacity. If they are a part time medical advisor, they should have a very small amount of equity to begin with. It would depend mostly on how much (if any) you've raised to date, but it would be unusual for an advisor to have more than 1% of the Company.

Happy to talk to you about the details of your situation to come up with a fair offer that doesn't hurt your chances of raising capital in the future.