Juli Engel was delighted when a neurologist recommended a PET scan to determine whether amyloid — the protein clumps associated with an increased risk of Alzheimer’s disease — was accumulating in her mother’s brain.

“My internal response was, ‘Yay!’” said Ms. Engel, 65, a geriatric care manager in Austin, Tex., who has been making almost monthly trips to help her mother in Florida. “He’s using every tool to try to determine what’s going on.”

Sue Engel, who’s 83 and lives in a retirement community in Leesburg, Fla., has been experiencing memory problems and other signs of cognitive decline for several years. Her daughter checked off the warning signs: her mother has been financially exploited, suffered an insurance scam, caused an auto accident.

Medicare officials decided in 2013, shortly after PET (positron emission tomography) amyloid imaging became available, that they lacked evidence of its health benefits. So outside of research trials, Medicare doesn’t cover the scans’ substantial costs ($5,000 to $7,000, the Alzheimer’s Association says); private insurers don’t, either.