CHICAGO — New research shows another decline in dementia rates, but experts say the rising numbers of older Americans may halt that trend unless better ways are found to keep brains healthy.

The study released Monday shows the rate of Alzheimer’s disease and other dementias in adults age 65 and older dropped to about 9 percent in 2012 from nearly 12 percent in 2000, continuing a decline noted in earlier research.

Older adults with the most schooling had the lowest dementia rates.

Alzheimer’s is the most common form of dementia, which also can be caused by strokes, Parkinson’s disease and other conditions.

Led by University of Michigan researchers, the study was published in JAMA Internal Medicine. The National Institute on Aging paid for the research.

Researchers analyzed nationally representative government surveys of about 10,500 older adults in both years, including some living in nursing homes. They were interviewed and given mental tests by phone or in person; spouses or relatives responded for those impaired by dementia or other illness.

The dementia rate declined amid a rise in diabetes and heart disease. Both increase risks for Alzheimer’s and other dementias but the researchers say better treatment for both diseases may explain the results.

Obesity rates also increased, while dementia was most common among underweight adults. Previous research has shown weight loss may precede dementia by several years.

Dementia was most common in the oldest adults; in 2012 almost 30 percent of adults aged 85 and up were afflicted versus just 3 percent of those 65-74.