UnitedHealthcare’s decision last fall to drop thousands of doctors from its Medicare Advantage plans in Connecticut and across the country has spurred Medicare officials to improve protections for seniors who lose their doctors. The new measures were announced late Monday along with a slight increase in next year’s payment rates to Medicare Advantage insurers who provide policies as an alternative to the traditional government-run Medicare program. Nearly 16 million older Americans have enrolled in a Medicare Advantage plan, including more than 147,000 in Connecticut, which requires members to get treatment only from a network of health care providers. They cannot change plans during the year if their doctor leaves their network. The new rules require insurers to provide at least 90 days advance notice of significant changes in their provider networks and allow members to switch plans under certain circumstances.