BOSTON — Despite exploding costs, most Americans got sizable life-extending bang for their medical bucks over recent decades, one of the most sweeping studies of health-care value suggests.

That might come as a surprise to anyone who has ever shuddered over a medical bill, and the report itself raises doubts over how quickly costs have risen.

However, the study calculated that Americans of all ages spent an average of $19,900 on medical care for each extra year of life expectancy gained over the last four decades of the 20th century. And that cost is worth it, the study authors say.

“On average, the return is very high,” the study’s leader, David Cutler, a Harvard University health economist, concluded. “But it’s getting worse for … in particular, the elderly.”

The federally funded study by researchers at Harvard and the University of Michigan is being published today in the New England Journal of Medicine.

The researchers measured value by the cost of care that extends the average person’s life by one year. The $19,900 spent for each extra year of life — when averaged over 40 years — would be widely considered a reasonable value. Many public and private insurers routinely pay for treatments that cost up to roughly $100,000 for each additional year of life.

The researchers attribute this relatively low cost for longer lifespan to things like cheap blood-pressure drugs that prevent heart attacks.

However, the study also outlines disquieting trends. It finds that inflation-adjusted costs from birth rose fivefold between the 1970s and 1990s, when the cost of an additional year of life span peaked at $36,300. That means each health-care dollar of the 1990s, when expensive drugs made modest impact on cancer, bought a fifth as much real value as 20 years before, when cheaper medicines saved many lives.

Values deteriorated seriously for older people, the study finds. By the 1990s, 65-year-olds paid $145,000 for each additional year of life gained — a value that would be challenged for many individual treatments. These higher costs presumably come largely from end-of-life care that does not extend life very much.

Health policy chief Kathleen Stoll, of the advocacy group Families USA, said she believes the study suggests real value anyway. “Each increment of gain is more expensive now but certainly very valuable to the person involved and their family,” she said.

Others were troubled. “The fact that someone is writing this paper shows how desperate the health-care system is to justify these out-of-control increases in health spending,” a consumer advocate, Dr. Sidney Wolfe, who heads health research at Public Citizen, said.

The researchers say their calculations give only a partial picture of value.They started by calculating average changes in both medical spending and life expectancy for various age groups in each decade. Then they divided changes in spending by changes in life expectancy, yielding the cost a year of life gained.

But many factors extend life apart from medical care, like not smoking or keeping extra weight off. So the researchers turned to previous studies suggesting that about half of all gains in lifetime stem from medical care — and adjusted their findings accordingly.

Even the researchers acknowledge this adjustment could be off. Others familiar with their findings said their calculations — while potentially useful for the big picture — had to overlook other important factors, like the impact of care on quality of life and the amount of waste in the medical system.

“It really doesn’t tell you whether we are spending too much on what doesn’t matter and too little on what does,” a cost-effectiveness specialist at Yale University, Dr. Harlan Krumholz, said. Others worried about future costs, though the study makes no projections. “The growth in medical spending is unsustainable over time — both in terms of absolute dollars and the benefit it yields,” a health-care analyst, Steven Findlay at Consumers Union, said.