St. Luke's Health System of Kansas City has entered an alliance with three other hospital systems in the Midwest in a cooperative attempt to rein in health care costs. The other participants are BJC HealthCare of St. Louis; CoxHealth of Springfield, Mo.; and Memorial Health System of Springfield, Ill. The alliance is named The BJC Collaborative LLC. Together, the systems in the alliance represent 31 hospitals in Missouri, Illinois and Kansas with combined annual revenues of nearly $7 billion.