Surgery patients had a greater chance of dying after procedures in hospitals where nurses have heavier patient loads, according to a study released yesterday that underscores the importance of the national nurse shortage.

For example, there were 31 percent more patient deaths per month after common types of surgeries, such as gall-bladder removal or hip replacement, at hospitals where each nurse cared for eight patients than when each nurse cared for four patients, according to the University of Pennsylvania study, which was published today in the Journal of the American Medical Association.

The report follows a study published in May by the New England Journal of Medicine saying that patients who received more hours of care from a registered nurse had a lower risk of health complications and were less likely to die than patients who received fewer hours.

The nurse shortage has been attracting the attention of legislators in Washington and in state capitals. Last year about 13 percent of all U.S. nursing jobs went unfilled, in part because of demographic changes. The average hospital nurse is 45 years old, and too few young nurses are entering the pipeline to replace them as they leave the profession. By the year 2020, when many of today's nurses will be retiring, there could be a shortfall of more than 400,000 nurses, according to the Labor Department.

Nurse-retention problems are compounding the shortage, said Linda H. Aiken, director of the Center for Health Outcomes and Policy Research at the University of Pennsylvania School of Nursing, which conducted the study. Aiken said that many nurses report constant overwork and understaffing on hospital wards, prompting many to leave the profession each year.

"Nurses report greater job dissatisfaction and emotional exhaustion when they're responsible for more patients than they can safely care for," Aiken said. "Failure to retain nurses contributes to avoidable patient deaths."

Aiken said that unlike other industries in which businesses have been compelled by market forces to offer benefits such as flexible hours and child-care assistance to keep valued workers, many hospitals have declined to do so. Instead, they have instituted forced overtime and reduced staffing to cut costs, she said.

Richard H. "Rick" Wade, a senior vice president at the American Hospital Association, a trade group representing about 4,600 hospitals nationwide, did not dispute the University of Pennsylvania study, and he described Aiken as a "respected researcher." He said the association's members are acutely aware of the problems posed by inadequate staffing.

"Our number one issue today is the workforce shortage, and when you boil it down, it's recruiting and retaining nurses," Wade said. The industry is taking steps to try to solve the problem, he said, referring to a report recently commissioned by the association that outlines ways hospitals can make themselves more attractive employers.

Wade said the hospital industry is aware that many nurses are working "harder than they should be" and that it has become apparent that some hospitals "have not maintained as attractive a work environment as they should have."

"But it's not the majority," he said.

Meanwhile, Labor Secretary Elaine L. Chao, who has called the nursing shortage a "crisis," plans to use federal job programs to steer would-be nurses into the health-care industry. In July, Congress passed the Nurse Reinvestment Act, which is to provide federal money to help pay for nursing training and forgive education loans for trainees who agree to work in areas with acute shortages. President Bush has signed the law, but Congress has not yet appropriated money to fund the program.

Sen. Barbara A. Mikulski (D-Md.) co-sponsored the legislation, calling it an effort "to deal with the nursing crisis in a serious way." In Maryland about 2,000 nursing jobs, or more than 15 percent, are unfilled, she said.

"For years, they tended to overwork and underpay these women," Mikulski said about the hospital industry. "There was a lack of respect in how they were treated. . . . In some ways, it's a crisis of their own doing."

Many nurses have been urging industry leaders to take steps to make work more attractive to today's nurses rather than focusing on recruiting new nurses, saying that bringing in workers who quickly leave fails to solve the problem. About 500,000 registered nurses have left the field in recent years, according to Susan Bianchi-Sand, director of United American Nurses, the labor arm of the American Nurses Association.

Nurses have taken their concerns to state legislatures. More than 20 states have enacted or seriously considered laws mandating that hospitals maintain certain patient-to-nurse ratios. California, for example, passed legislation last year establishing fixed nurse-patient ratios for hospitals statewide. Public hearings to discuss implementing the law are scheduled to be held over the next three months. Maine and Oregon have banned mandatory overtime for nurses, according to the nurses association, and nursing trends and patterns are the subject of state study in Florida, Mississippi, North Dakota, Tennessee, Texas, Arkansas and Pennsylvania.