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People with diabetes face an increased risk of Alzheimer’s disease and other forms of dementia, a connection scientists and physicians have worried about for years. They still can’t explain it.

Now comes a novel observational study of patients at a large health care system in Washington State showing that higher blood glucose levels are associated with a greater risk of dementia — even among people who don’t have diabetes. The results, published Thursday in The New England Journal of Medicine, “may have influence on the way we think about blood sugar and the brain,” said Dr. Paul Crane, the lead author and associate professor of medicine at the University of Washington.

The researchers tracked the blood glucose levels of 2,067 members of Group Health, a nonprofit HMO, for nearly seven years on average. Some patients had Type 2 diabetes when the study began, but most didn’t. None had dementia.

Over the years, as they saw doctors at Group Health, the participants received blood glucose tests. “It’s a common test in routine clinical practice,” Dr. Crane said. “We had an amazing opportunity with all this data. All the lab results since 1988 were available to us.”

The participants (average age at the start: 76) also reported to Group Health every other year for cognitive screening and, if their results were below normal, further testing and evaluation. Over the course of the study, about a quarter developed dementia of some kind, primarily Alzheimer’s disease or vascular dementia.

To measure blood sugar levels, the researchers combined glucose measurements, both fasting and nonfasting, with the HbA1c glycated hemoglobin assay, which provides a more accurate long-term picture. They also adjusted the data for other cardiovascular factors already linked to dementia, like high blood pressure and smoking.

“We found a steadily increasing risk associated with ever-higher blood glucose levels, even in people who didn’t have diabetes,” Dr. Crane said. Of particular interest: “There’s no threshold, no place where the risk doesn’t go up any further or down any further.” The association with dementia kept climbing with higher blood sugar levels and, at the other end of the spectrum, continued to decrease with lower levels.

This held true even at glucose levels considered normal. Among those whose blood sugar averaged 115 milligrams per deciliter, the risk of dementia was 18 percent higher than among those at 100 mg/dL, just slightly lower. The effects were also pronounced among those with diabetes: patients with average glucose levels of 190 mg/dL had a 40 percent higher risk of dementia than those whose levels averaged 160 mg/dL.

Though a longitudinal study like this one provides insight into the differences between people, it can’t explain why higher blood glucose might be connected to dementia, or tell individuals whether lower blood glucose is protective.

“People shouldn’t run for the hills or try crazy diets,” Dr. Crane cautioned. While an epidemiological study like this one can guide further exploration, he said, “This doesn’t show that changes in behavior that lower your individual blood sugar would decrease your individual risk of dementia.”

As for the blood glucose levels the study recorded, “clinically, they’re not big differences,” said Dr. Medha Munshi, a geriatrician and endocrinologist who directs the geriatric diabetes program at the Joslin Diabetes Center in Boston, who was not involved in the study. “I wouldn’t change my goals for diabetes management based on this study.” Nor would she warn someone whose blood glucose hits 115 mg/dL that he or she faces a greater risk of dementia.

But because diabetes itself can pose such a threat to health and quality of life, she still urges patients to adopt healthy practices like exercising regularly and maintaining a normal weight to try to avoid the disease. If by doing so they also lower their dementia risk — and knowing that would require a different study, focused on interventions — that would be a bonus.

This research “offers more evidence that the brain is a target organ for damage by high blood sugar,” said Dr. Munshi. “And everyone is still working on the ‘why’.”