Changes to the Medicaid program backed by the Bush administration could cause New York City's public and private hospitals to lose more than $1 billion in state and federal funds for the training of doctors, according to an analysis. The change would end a revenue stream that the medical residencies rely on, and could have wide ramifications because New York hospitals train a large share of the nation's doctors. The city's Independent Budget Office analysis found that the proposed cut would cost the city's public hospitals about $390 million in federal and state funds, or about 7.5% of their overall budget. It would cost the city's private hospitals about $790 million, 4.4% of their total revenue.