For the past year, Advocate Health Care, which operates a number of Chicago hospitals and clinics, has cared for more than 200,000 patients insured by Illinois Blue Cross plans, and so far the A.C.O. has managed to reduce hospital stays and overall costs for patients, according to Steve Hamman, vice president for network management at Illinois Blue Cross. Advocate, like other A.C.O.'s, manages to do this in large part by hiring care managers to better coordinate patient care.