I think having a clinical background is very useful specially when you are dealing with the patient in clinical trials as a Bio-medical Engineer, I worked as a patient sitter in the hospital for 2 years and I also currently work as an EMT and from that I can say that It requires a lot of Patience and not every person is same you have to deal with every patient differently based on their needs the key is to that is win the patients trust and that will make your life much easier. Their are biomedical companies out in the market who specially hires nurses help in clinical studies where they can deal with the patient and again patient will trust the nurse or doctor(because they are the center of Medical Profession) more than the engineer. And of course it depends on you job description as a Biomedical Engineer as Principal Investigator and CRA I will say you should have some experience how to interact with the patients and most important how address their needs keep in mind the main goal of the study and not catch feelings for them but instead work with them help them and don’t give them wrong hopes but at the same time don’t be rude. On the other side as a monitor and Statistician you don’t interact with the patient directly so I will say you don’t need medical background but it will be good to have it because remember you work as a team in project and your experience might be helpful.
Reference:-
https://www.indeed.com/q-Clinical-Research-Nurse-jobs.html