WASHINGTON — For people with Alzheimer’s disease, a hospital stay may prove catastrophic.

People with dementia are far more likely to be hospitalized than other older adults, often for preventable reasons like an infection that wasn’t noticed early enough.

Now a new study highlights the lingering ill effects: Being hospitalized seems to increase the chances of Alzheimer’s patients moving into a nursing home — or even dying — within the next year, Harvard researchers reported Monday. The risk is higher if those patients experience what’s called delirium, a state of extra confusion and agitation, during their stay.

The study can’t explain the link, although specialists say delirium is especially bad for an already damaged brain. But the researchers, and independent Alzheimer’s experts, agree that caregivers need to know the risk so they can help a loved one with dementia avoid the hospital if at all possible.

Some 5.4 million Americans have Alzheimer’s or similar dementias, and the disease is on the rise as the population ages.

The disease will cost Medicare and Medicaid about $140 billion this year alone, according to the Alzheimer’s Association. There is no cure, and much of the cost is from treating other health conditions that dementia can aggravate.

Alzheimer’s patients gradually lose the ability to manage their diabetes, high blood pressure and other chronic ailments, or even to convey that they’re feeling symptoms until an illness becomes serious, said William Thies, the association’s scientific director.

The new study looked at medical records for 771 Alzheimer’s patients who were living at home and fairly high-functioning, to see what happened if they wound up in the hospital.