That means some fully recovered patients in the adjacent Erie County Medical Center must stay in their hospital rooms, waiting for a bed in the nursing home. Which means some patients in the emergency department, who should be admitted to the hospital, must stay there until a hospital bed opens up. The emergency department becomes stretched so thin that 10 to 20 percent of arrivals leave without seeing a caregiver — after an average wait of six to eight hours, according to the hospital’s data.