Hi Dura,
First off, you can not rely on another project's programme, the best thing you can do is to read all the working documents specially the scope of works, BoQ, Milestones, key dates, access dates, Particular Specifications and Contract.
As Mike said, the complicated part is the MEP works because of the numerous services that needs to be installed. Normally, the integrated MEP working drawings are not yet done at the start of the project, hence, you need to assume the most logical sequence of works to get your programme approved. List down all the MEP services, and get a sequence and cross section arrangement agreed with the MEP construction team. Normally the gravity pipes (plumbing) comes first simply because you can not divert them when there is a clash. Find out which ones are embeded in the structure (normally conduits for Electrical and ELV system), this can be scheduled as part of the structure. The HVAC system in a hospital is also complicated. The remaining services should be installed according to elevations in your agreed sequence and cross section.
Other important interface issues you need to consider, you need a water tight building or at least several floors before you can start your MEP works.
Good Luck
Daniel