The soaring costs of insuring the state’s poorest residents drove health care spending in Massachusetts up 4.8 percent last year, double the rate of growth in 2013, dealing a setback to the state’s efforts to contain medical costs.

The increase far exceeds inflation, which was 1.6 percent last year, and blows past a state goal of holding health care spending growth to 3.6 percent annually, according to a report to be issued Wednesday by the state Center for Health Information and Analysis.