There usually is no need for them to sign it. They offer, you accept (with your signature as evidence), which is the essence of a contract. There is no need for them to "accept your acceptance".
As you changed the document, it may or may not be binding. Effectively you offered them new terms, and I wouldn't like to speculate as to if they accepted them (e.g. by treating you).
They need to accept the changes, if any. The lack of a place for them to sign is proof that they intended for it to be signed as-is, or not at all.
Contracts aren't valid unless both parties have accepted them. The doctor's office can't accept a contract they haven't read yet, and any changes to a contract make it a new contract.
As you changed the document, it may or may not be binding. Effectively you offered them new terms, and I wouldn't like to speculate as to if they accepted them (e.g. by treating you).