As the old song goes, one is the loneliest number. And while old sayings and song lyrics don’t have much scientific basis in fact, recent research indicates chronic loneliness can be bad for the mental health of some older Americans.

A recent study by a team of researchers from Rush University Medical Center in Chicago found that lonely older individuals could in some cases be twice as likely to develop a form of dementia associated with Alzheimer’s disease as those who are not lonely.

Doctors looked at the connection between being lonely and Alzheimer’s among more than eight-hundred study participants whose average age was eighty. At the beginning of the study, participants underwent a series of evaluations that were repeated annually for up to four years. Assessments included questionnaires to gauge loneliness, classifications of dementia and Alzheimer’s disease, and testing of their thinking, learning and memory abilities.

Loneliness was measured on a scale of one to five, with higher scores indicating increased loneliness. The risk of developing Alzheimer’s disease increased with each point on the loneliness score. Loneliness also was linked to more rapid cognitive decline in multiple areas.

The study didn’t determine why loneliness was associated with Alzheimer’s in some patients. But doctors nonetheless recommend that adults strive to have a good circle of friends. That’s in part because strong social networks have been shown to be associated with better overall health.

That could have them singing a whole new tune.