But APOE is not definitive. Many people with e4 never become demented, and many Alzheimer’s patients have no e4. That uncertainty helped turn the medical profession against testing.

In the past, the Alzheimer’s Association discouraged testing, but it has relaxed its stance in the past few years, largely because of reports from the Reveal study. Even so, William Thies, the association’s chief medical and scientific officer, said that so far there had not been much demand for the test, and that a direct-to-consumer company specializing in it had gone out of business. Two authors of the study, but not Dr. Green, provided consulting services to a company that was marketing APOE testing.

Two study participants, among a half dozen whose telephone numbers were given to reporters by Boston University, said they were pleased that they had joined the study. Amy Sumner, 45, a social worker in Simsbury, Conn., said she had sought out the research because there were several cases of Alzheimer’s in her grandmother’s generation on her mother’s side. Ms. Sumner thought her test results might help her mother and aunts (who do not have dementia) decide whether to be tested. She turned out to have no copies of e4, a relief for her but not much help for her relatives, who could still carry the gene.

She said her mother and aunts were concerned about their risk but did not dwell on it, adding, “All four are very strong, spiritual women and have a lot of peace about it even though they’re concerned.”

Another participant, Robert McKersie, 79, said he wanted the test because his mother died of Alzheimer’s. Dr. McKersie said he thought the test results might help him and his wife decide whether to stay in their house or consider moving to an assisted-living facility, just in case. He learned that he did have a copy of e4  but given his high scores on mental tests and the fact that he has reached 79 with no intellectual decline, the researchers estimated his risk as fairly low. Although is retired, Dr. McKersie is still teaching business courses at the Sloan School of Management at the Massachusetts Institute of Technology.

Despite the study’s reassuring results, Dr. Green said it did not mean that APOE testing was right for everybody. Some people who initially wanted to participate changed their minds after they learned more about the test. Dr. Green also cautioned that the study was small, participants were given extensive talks by genetic counselors and they were followed for only one year. It is too soon to tell whether the knowledge will begin to haunt them later in life. It is also not clear whether being positive for e4 could hurt people financially. Although a law enacted last year forbids health insurers and employers to discriminate based on genetic tests, it does not apply to insurance for long-term care or disabilities.

Some study participants have already bought long-term care insurance specifically because they learned they had an e4 gene, Dr. Green said, adding that this scares long-term-care insurance companies. He said that when he mentioned those purchases in a presentation to insurance executives, whom he described as a staid group, some leapt to their feet and shouted that there would be no more long-term-care insurance if too many people with risky genes started buying policies.