The rate of avoidable complications affecting patients in hospitals leveled off in 2014 after three years of declines, according to a new federal report.

Hospitals have averted many types of injuries where clear preventive steps have been identified, but they still struggle to avert complications with broader causes and less clear-cut solutions, government and hospital officials said.

There were at least 4 million infections and other potentially avoidable injuries in hospitals last year, the study estimated. That translates to about 12 of every 100 hospital stays. Among the most common complications that were measured - each occurring a quarter-million times or more - were bed sores, falls, bad reactions to drugs used to treat diabetes, and kidney damage that develops after contrast dyes are injected through catheters to help radiologists take images of blood vessels.

The frequency of hospital complications last year was 17 percent lower than in 2010 but the same as in 2013, indicating that some patient safety improvements that hospitals and government made are sticking. But the lack of improvement raised concerns that it is becoming harder for hospitals to further reduce the chances that patients may be harmed.

"We are still trying to understand all the factors involved, but I think the improvements we saw from 2010 to 2013 were very likely the low-hanging fruit, the easy problems to solve," said Richard Kronick, director of the federal Agency for Healthcare Research and Quality, which conducted the study.

The Obama administration has been focusing on lowering the rates of medical infections and injuries as it tracks a slew of patient safety initiatives created by the 2010 federal health law. Those include Medicare penalties for poor-performing hospitals, wider use of electronic records to help track patient care and prevent mistakes, and grants to collaborations of medical providers formed to improve the quality of patient care and identify the best ways of addressing each type of problem.

The report calculated national rates for 27 specific complications by extrapolating from 30,000 medical cases officials examined. Decreases in infections, medicine reactions, and other complications since 2010 have resulted in 2.1 million fewer incidents of harm, 87,000 fewer deaths, and $20 billion in health-care savings, the report concluded.

"Those are real people that are not dying, getting infections, or other adverse events in the hospital," said Patrick Conway, chief medical officer of the Centers for Medicare and Medicaid Services.

Some of the most significant progress was made in lowering the number of infections from central lines inserted into veins - down 72 percent from 2010. Medical researchers have proved those infections can be virtually eliminated if doctors and nurses follow a clear set of procedures.

Infections from urinary catheters decreased by 38 percent, and surgical-site infections dropped by 18 percent. In all three cases, the reductions exceeded the goals the administration set. Conway noted that hospitals had a financial motive to cut these infections, which are used to determine whether hospitals get Medicare bonuses and penalties each year.

However, hospitals have not made headway in trimming the number of falls or pneumonia cases in patients breathing through mechanical ventilators, the report found. And the rates of adverse drug reactions and complications during childbirth were higher than the administration estimated they should be for 2014.

Conway said complications were difficult to address because they involve trade-offs that can cause other problems. For instance, he said, hospitals have to balance efforts to reduce falls with the need to help unstable patients improve their ability to walk. "We've got to work with providers to figure out what's the sweet spot that can keep mobilization occurring but decrease the rate of falls," he said.