Researchers have pondered about how sleep relates to cognitive decline.

Answers have been elusive because it is hard to know if insufficient sleep is a symptom of the brain changes that underlie dementia — or if it can actually help cause those changes.

Now, a large new study reports some of the most persuasive findings yet to suggest that people who don’t get enough sleep in their 50s and 60s may be more likely to develop dementia when they are older.

One theory is that the more people are awake, the longer their neurons are active and the more amyloid (a protein in the brain that clumps into plaques in Alzheimer’s) is produced, Dr. Musiek said. 

Another theory is that during sleep, fluid flowing in the brain helps clear out excess prote...