But in the secondary outcome — developing mild cognitive impairment or MCI — results did show a statistically significant difference. In the intensive group, 287 people developed it, compared to 353 people in the standard group, giving the intensive treatment group a 19 percent lower risk of mild cognitive impairment, Dr. Williamson said.

Because dementia often develops over many years, Dr. Williamson said he believes that following the patients for longer would yield enough cases to definitively show whether intensive blood pressure treatment helps prevent dementia too. To find out, the Alzheimer’s Association said Monday it would fund two more years of the study.

“Sprint Mind 2.0 and the work leading up to it offers genuine, concrete hope,” Maria C. Carrillo, the association’s chief science officer, said in a statement. “MCI is a known risk factor for dementia, and everyone who experiences dementia passes through MCI. When you prevent new cases of MCI, you are preventing new cases of dementia.”

Dr. Yaffe said the study had several limitations and left many questions unanswered. It’s unclear how it applies to people with diabetes or other conditions that often accompany high blood pressure. And she said she would like to see data on the participants older than 80, since some studies have suggested that in people that age, hypertension might protect against dementia.

The researchers did not specify which type of medication people took, although Dr. Williamson said they plan to analyze by type to see if any of the drugs produced a stronger cognitive benefit. Side effects of the intensive treatment stopped being monitored after the main trial ended, but Dr. Williamson said the biggest negative effect was dehydration.

Dr. Williamson said the trial has changed how he treats patients, offering those with blood pressure over 130 the intensive treatment. “I’ll tell them it will give you a 19 percent lower chance of developing early memory loss,” he said.

Dr. Yaffe is more cautious about changing her approach. “I don’t think we’re ready to roll it out,” she said. “It’s not like I’m going to see a patient and say ‘Oh my gosh your blood pressure is 140; we need to go to 120.’ We really need to understand much more about how this might differ by your age, by the side effects, by maybe what else you have.”

Still, she said, “I do think the take-home message is that blood pressure and other measures of vascular health have a role in cognitive health,” she said. “And nothing else has worked.”