If a CAGE patient wants to leave but is not under an involuntary hold, then one of two things can heppen:
1. He can leave. It may be AMA, but he has the legal right to leave the facility.
2. You can petition to place him under a hold. That would only work if he meets the criteria to be held--if he is not a danger to himself, not a danger to others, or is not gravely disabled, there's no grounds for him to be held and he is free to go.
I know that detox is the grey area of "danger to self" because yes, some detoxes are very dangerous...but at the same time, it's not as though the patient is directly trying to end their life via withdrawal complications that may or may not kill him. I've seen attempts at holds go both ways.
As far as convincing a non-holdable patient to stay, all you and the MD can do is keep educating him on the risks involved with leaving early. Be brutally honest about these risks and the fact that some can be fatal. Encourage him to give it another day or even another shift (start the "One Day at a Time" thinking now) and then decide if he wants to go.
Also, given that he is going through both physical and mental anguish from withdrawal, an increase in medication to get him through the first few days of discomfort may not be a bad idea...but that's a MD call.
Ultimately though, if he's not ready for recovery, he's not ready...and if he's not ready, it doesn't matter if he leaves that day or two weeks from now: he's going to go right back to his addiction. That's one thing you learn in addictions/CD: not every patient is there because they are ready for recovery. They may be there voluntarily, but that doesn't mean they want recovery.