Does this medical database look correct?
As a very basic structure it is close.

The one glaring issue is that the relationship between trial and centre is the wrong way around.  You should have a CentreId on the Trial table, as I believe there can by multiple trials from 1 centre and not vice versa.

Also you may want to consider adding some extra details to Centre like name etc.

Lastly, the Patient -> Trial relationship may well be a many-to-many relationship and thus you  would need to add a table to encapsulate this relationship.