Clinical trials are run by researchers, also called investigators, who could be trained as scientists, medics, nurses, complementary or alternative medicine practitioners, or other health professionals, like physiotherapists.
The researcher with primary responsibility for looking after the trial at a particular centre (called the principal investigator) should have relevant qualifications and experience to run the trial and care for the safety of the people in the trial. Those qualifications will usually be reviewed by the ethics committee and sponsors of the trial before the trial and investigator are approved to start.
The principal investigator is allowed to delegate responsibilities to their research team, but the team must be trained for the tasks they are delegated. The principal investigator will always have the final responsibility for the way the trial is run and the quality of the data collected.