New York City's Health and Hospitals Corporation has signed a 10-year, $100 million contract with a medical school in the Caribbean to provide clinical training for hundreds of students at the city's 11 public hospitals. The deal was proposed by a member of the corporation's board who has long worked for the Caribbean school, and has been met by an outcry from New York medical schools fearing that clerkship slots will grow scarcer and that they might have to increase tuitions to compete. Critics worry that the hospital corporation is conferring prestige on a foreign school whose curriculum, they say, is more vocational than research-based and often caters to affluent students who could not get into schools in the United States.