Cancer and heart disease are bigger killers, but Alzheimer’s is the most expensive malady in the U.S., costing families and society $157 billion to $215 billion a year, according to a new study that looked at this in unprecedented detail.

The biggest cost of Alzheimer’s and other types of dementia isn’t drugs or other medical treatments, but the care that’s needed just to get mentally impaired people through daily life, the nonprofit RAND Corp.’s study found.

It also gives what experts say is the most reliable estimate for how many Americans have dementia — around 4.1 million. That’s less than the widely cited 5.2 million estimate from the Alzheimer’s Association, which comes from a study that included people with less severe impairment.

“The bottom line here is the same: Dementia is among the most costly diseases to society, and we need to address this if we’re going to come to terms with the cost to the Medicare and Medicaid system,” said Matthew Baumgart, senior director of public policy at the Alzheimer’s Association.

Dementia’s direct costs, from medicines to nursing homes, are $109 billion a year in 2010 dollars, the new RAND report found. That compares to $102 billion for heart disease and $77 billion for cancer. Informal care by family members and others pushes dementia’s total even higher, depending on how that care and lost wages are valued.

“The informal care costs are substantially higher for dementia than for cancer or heart conditions,” said Michael Hurd, a RAND economist who led the study. It was sponsored by the government’s National Institute on Aging and will be published in Thursday’s New England Journal of Medicine.

Alzheimer’s is the most common form of dementia and the sixth leading cause of death in the United States. Dementia also can result from a stroke or other diseases. It is rapidly growing in prevalence as the population ages. Current treatments only temporarily ease symptoms and don’t slow the disease. Patients live four to eight years on average after an Alzheimer’s diagnosis, but some live 20 years. By age 80, about 75 percent of people with Alzheimer’s will be in a nursing home compared with only 4 percent of the general population, the Alzheimer’s group says.

“Most people have understood the enormous toll in terms of human suffering and cost,” but the new comparisons to heart disease and cancer may surprise some, said Dr. Richard Hodes, director of the Institute on Aging.

“Alzheimer’s disease has a burden that exceeds many of these other illnesses,” especially because of how long people live with it and need care, he said.

For the new study, researchers started with about 11,000 people in a long-running government health survey of a nationally representative sample of the population. They gave 856 of these people extensive tests to determine how many had dementia, and projected that to the larger group to determine a prevalence rate — nearly 15 percent of people over age 70.

Using Medicare and other records, they tallied the cost of purchased care — nursing homes, medicines, other treatments — including out-of-pocket expenses for dementia in 2010. Next, they subtracted spending for other health conditions such as high blood pressure, diabetes or depression so they could isolate the true cost of dementia alone.

“This is an important difference” from other studies that could not determine how much health care cost was attributable just to dementia, said Dr. Kenneth Langa, a University of Michigan researcher who helped lead the work.

Even with that adjustment, dementia topped heart disease and cancer in cost, according to data on spending for those conditions from the federal Agency for Healthcare Research and Quality.

Finally, researchers factored in unpaid care using two different ways to estimate its value — foregone wages for caregivers and what the care would have cost if bought from a provider such as a home health aide. That gave a total annual cost of $41,000 to $56,000 per year for each dementia case, depending on which valuation method was used.

“They did a very careful job,” and the new estimate that dementia affects about 4.1 million Americans seems the most solidly based than any before, Hodes said. The government doesn’t have an official estimate but more recently has been saying “up to 5 million” cases, he said.

The most worrisome part of the report is the trend it portends, with an aging population and fewer younger people “able to take on the informal caregiving role,” Hodes said. “The best hope to change this apparent future is to find a way to intervene” and prevent Alzheimer’s or change its course once it develops, he said.