21-year-old Stefann Alan Brown was reported missing by staff at York Hospital after he walked out of the hospital without completing his treatment or taking his essential medication with him.
Stefann has now been missing for more than 24 hours and police are becoming increasingly concerned for his safety and wellbeing.
The last sighting of Stefann was on the side of the A19 near Germany Beck, heading out of the city on Tuesday morning.
It is possible that someone travelling along the A19 or the A64 may have given Stefann a lift.
He is described as 5ft 6in tall, of slim build with dark hair. It is believe he was wearing pyjamas bottoms when he left the hospital and may not be wearing any shoes.
Stefann also has contacts in the Cleveland area and officers have extended their enquiries to that area.
Anyone who believes they have seen Stefann since Tuesday morning or knows where he is now, is urged to contact North Yorkshire Police as a matter of urgency.
Please call North Yorkshire Police on 101, select option 1 and pass information to the Force Control Room.