Jameson Murapa had been admitted to the University Hospital of North Staffordshire with a bad chest.
But the 44-year-old walked out of ward 70 after three days and lay down on the A34 London Road, in Newcastle.
At least two motorists managed to dodge Zimbabwe-born Mr Murapa before he was killed by a car.
Now Mr Murapa’s family are demanding to know why staff did not know the father-of-three had left the hospital.
North Staffordshire deputy coroner Anthony Curzon yesterday recorded Mr Murapa, of Brittain Avenue, Chesterton, ‘deliberately took his own life’.
Following the inquest, Mr Murapa’s father Israel Murapa told The Sentinel: "Jameson’s death remains a shock.
"We honestly feel that the care of patients at the hospital is questionable.
"Jameson needed oxygen in hospital and it appears nobody monitored his oxygen levels and he got confused as his oxygen levels went down.
"It is not clear how he got out of the hospital. The hospital did not know where Jameson was for almost 90 minutes.
"He died a very painful death and the hospital had to be advised about his death by the police."
The inquest heard care support worker Mr Murapa had come to the UK in 2002.
He was admitted to the University Hospital on September 17, 2009 and his wife Georgina and their three children last saw him during a hospital visit which finished at 8pm on September 20, 2009.
Less than an hour later Mr Murapa was seen running along the A34 wearing no shoes or socks and lying in front of cars at its junction with The Avenue.
Richard Webber, who was travelling in his girlfriend’s car towards The Avenue at about 8.50pm on September 20, told the inquest: "I saw a man running along the pavement as we approached the lights to turn left into The Avenue.
"He lay down in front of the car.
"We managed to stop. He got up and laughed at us. I got out of the car and he ran off so I chased him, but I couldn’t catch him."
Mr Murapa was struck by Rover driver Sharon Lambert.
Police called to the scene found Mr Murapa’s hospital wristbands further along the road.
PC Carl Kelsall said: "Mr Murapa was lying in the carriageway with his head near the kerb.
"It would appear he left the hospital and deliberately attempted to lie in the road in front of cars on several occasions until he was hit by a Rover."
Mr Murapa died from cranial fractures and a traumatic brain injury.
Following the inquest, a hospital spokesman said: "While staff provide a very high level of care, patients are not obliged to stay in hospital and are free to leave if they wish, with the exception of children’s wards."