An experimental drug for Alzheimer’s disease sharply slowed the decline in mental function in a small clinical trial, researchers reported Friday, reviving hopes for an approach to therapy that until now has experienced repeated failures.

The drug, being developed by Biogen Idec, could achieve sales of billions of dollars a year if the results from the small trial are replicated in larger trials that Biogen said it hoped to begin this year. Experts say that there are no really good drugs now to treat Alzheimer’s.

Biogen’s stock has risen about 50 percent since early December, when the company first announced that the drug had slowed cognitive decline in the trial, without saying by how much. Analysts and investors had been eagerly awaiting the detailed results, some of them flying to France to hear Biogen researchers present them at a neurology meeting on Friday.

The drug, called aducanumab, met and in some cases greatly exceeded Wall Street expectations in terms of how much the highest dose slowed cognitive decline. However, there was a high incidence of a particular side effect that might make it difficult to use the highest dose.

Still, the net impression was positive. “Out-of-the-ballpark efficacy, acceptable safety,” Ravi Mehrotra, an analyst at Credit Suisse, wrote on Friday. Shares of Biogen rose $42.33, or 10 percent, to $475.98.

Alzheimer’s specialists were impressed, but they cautioned that it was difficult to read much from a small early-stage, or Phase 1, trial that was designed to look at safety, not the effect on cognition. Also, other Alzheimer’s drugs that had looked promising in early studies ended up not working in larger trials.

“It’s certainly encouraging,” said Dr. Samuel Gandy, director of the Center for Cognitive Health at Mount Sinai Hospital in New York, who was not involved in the study. He said the effect of the highest dose was “pretty impressive.”

Aducanumab, which until now has been called BIIB037, is designed to get rid of amyloid plaque in the brain, which is widely believed to be a cause of the dementia in Alzheimer’s disease. However, other drugs designed to prevent or eliminate plaque have failed in large clinical trials, raising questions about what role the plaque really plays.

Johnson & Johnson and Pfizer abandoned a drug they were jointly developing after it showed virtually no effect in large trials. Eli Lilly and Roche are continuing to test their respective drugs despite initial failures. Experts say there is some suggestion the drugs might work if used early enough, when the disease is still mild.

Biogen tried to increase its chances of success by treating patients with either mild disease or so-called prodromal disease, an even earlier stage. It also enrolled only patients shown to have plaque in their brains using a new imaging technique. In some trials of other drugs, some of the patients turned out not to have plaque, which could have been a reason the trials were not successful.

The results reported Friday were for 166 patients, who were randomly assigned to get one of several doses of the drug or a placebo. The drug not only slowed cognitive decline but also substantially reduced plaque in the brain, and higher doses were better than lower doses. Those are signs that the effects seen were from the drug.

“It would be kind of hard to get those kind of results by chance,” said Dr. Rachelle S. Doody, director of the Alzheimer’s Disease and Memory Disorders Center at Baylor College of Medicine, who was not involved in the study but has been a consultant to Biogen and many other companies.

On one measure of cognition, a 30-point scale called the mini-mental state exam or M.M.S.E., those receiving the placebo worsened by an average of 3.14 points over the course of a year. The decline at one year was only 0.58 points for those getting the highest dose and 0.75 points for a middle dose. The difference with a placebo was statistically significant for both doses.

On another measure of both cognition and the ability to function in daily tasks, patients in the placebo group worsened by an average of 2.04 points at one year. Those getting the highest dose of the drug had a decline of only 0.59, a statistically significant difference.

Some analysts said they would have been impressed if the drug had slowed the rate of cognitive decline by 20 or 30 percent. But the actual reduction for the high dose was above 70 percent. They said the drug’s effect was stronger than that of Lilly’s drug.

A major side effect was a localized swelling in the brain, known as A.R.I.A.-E. This has been seen with other drugs in this class, though the rate for aducanumab seems higher.

Among patients with a genetic variant that raises the risk of getting Alzheimer’s, 55 percent of those who got the highest dose suffered this side effect, and about 35 percent of the high-dose patients dropped out of the trial because of this. Among those without the genetic variant, 17 percent of those who got the highest dose suffered the side effect and 8 percent discontinued treatment.

Biogen said the swelling often did not cause symptoms and probably could be managed by watching for it and reducing doses. Dr. Doody and Dr. Gandy agreed.

But Dr. Thomas M. Wisniewski, a professor of neurology at NYU Langone Medical Center, disagreed. “Most clinicians would find that unacceptable,” he said in a conference call hosted by the Wall Street firm Evercore ISI. He said the side effect was “something you definitely don’t want happening in your patients.”

Over all, however, Dr. Wisniewski was enthusiastic, saying the drug looked to be “way better” than Lilly’s.

A lesser dose might suffice. There were no discontinuations from this side effect among patients taking a middle dose. And that middle dose also seemed somewhat effective in slowing cognitive decline.

The results were presented in Nice, France, at the International Conference on Alzheimer’s and Parkinson’s Diseases and Related Neurological Disorders.