The death of former Secretary of State Colin Powell on Monday from complications of Covid-19 has provided fuel for vaccine skeptics and opponents, who immediately seized on the news that Mr. Powell had been vaccinated to stoke doubts about the effectiveness of the vaccines.

But Mr. Powell’s immune system had quite likely been weakened by multiple myeloma, a cancer of white blood cells. Both the disease and the treatment can make people more susceptible to infections.

His age, 84, may also have increased his risk, scientists said.

Mr. Powell received his second dose of the Pfizer-BioNTech vaccine in February, said Peggy Cifrino, his longtime aide. He was scheduled for a booster last week but fell ill before he received it, she said. Mr. Powell had also undergone treatment for early stage Parkinson’s disease, she said.

Although Mr. Powell’s death is a high-profile tragedy, scientists emphasized that it should not undermine confidence in the Covid-19 vaccines, which drastically reduce the odds of severe disease and death.

“Nothing is 100 percent effective,” said Dr. Paul A. Offit, the director of the Vaccine Education Center at Children’s Hospital of Philadelphia. “The point of getting a vaccine is that you want to know that the benefits clearly and definitively outweigh the risks. And we know that for this vaccine.”

The vaccines are highly effective, even against the more contagious Delta variant, which is now responsible for nearly all coronavirus infections in the United States. People who are fully vaccinated are roughly one-tenth as likely to be hospitalized and even less likely to die from Covid-19 than those who are unvaccinated, according to a recent study from the Centers for Disease Control and Prevention.

A New York Times analysis of data from 40 states found that fully vaccinated people have accounted for 0.2 to 6 percent of Covid-19 deaths.

Among the more than 187 million Americans who have been fully vaccinated, there have been 7,178 deaths, according to the C.D.C. Eighty-five percent of those deaths have been in people 65 or older.

“Breakthrough deaths with vaccinated individuals do occur,” said Dr. Peter J. Hotez, dean of the National School of Tropical Medicine at Baylor College of Medicine in Houston. “But there are certain groups that are at greater risk.”

Since the beginning of the pandemic, it has been clear that older adults are the most likely to develop severe Covid-19. They also have less robust immune systems in general and mount a weaker immune response to the vaccines.

In one recent study, which has not yet been reviewed by experts, researchers found that residents of Canadian long-term care homes, who had a median age of 88, produced levels of neutralizing antibodies roughly five- to sixfold lower after vaccination than did staff members, who had a median age of 47.

“This puts them at risk for not only getting infected by Covid but also having severe consequences,” said Anne-Claude Gingras, a senior investigator at the Lunenfeld-Tanenbaum Research Institute at Mount Sinai Hospital in Toronto and the lead author of the study.

Mr. Powell had undergone treatment for multiple myeloma, a cancer of plasma cells, which are a type of white blood cell. Plasma cells make antibodies and thus play a critical role in the immune system.

Both the disease and the treatment — which may include chemotherapy, immunotherapy and steroids — can leave patients more vulnerable to infections.

“Colin was undergoing treatment for multiple myeloma but seemed to be responding well,” Kathy Giusti, who founded the Multiple Myeloma Research Foundation and met Mr. Powell when he spoke at a foundation event, said in a statement. “Immunosuppression is a well-known side effect of cancer treatment and a reminder that as patients, we are at high risk, especially if also over 65 years of age.”

Vaccines are also likely to be less effective in people with multiple myeloma.

“The treatments we’re using are indiscriminately knocking off both the malignant and the normal immune cells,” said Dr. James R. Berenson, the medical and scientific director of the Institute for Myeloma and Bone Cancer Research in West Hollywood, Calif.

That puts patients “at double risk for getting no response to a vaccination and also not responding as well once they get the disease,” he added.

What to Know About Covid-19 Booster Shots

The F.D.A. authorized booster shots for a select group of people who received their second doses of the Pfizer-BioNTech vaccine at least six months before. That group includes: vaccine recipients who are 65 or older or who live in long-term care facilities; adults who are at high risk of severe Covid-19 because of an underlying medical condition; health care workers and others whose jobs put them at risk. People with weakened immune systems are eligible for a third dose of either Pfizer or Moderna four weeks after the second shot.

The C.D.C. has said the conditions that qualify a person for a booster shot include: hypertension and heart disease; diabetes or obesity; cancer or blood disorders; weakened immune system; chronic lung, kidney or liver disease; dementia and certain disabilities. Pregnant women and current and former smokers are also eligible.

The F.D.A. authorized boosters for workers whose jobs put them at high risk of exposure to potentially infectious people. The C.D.C. says that group includes: emergency medical workers; education workers; food and agriculture workers; manufacturing workers; corrections workers; U.S. Postal Service workers; public transit workers; grocery store workers.

Yes. The C.D.C. says the Covid vaccine may be administered without regard to the timing of other vaccines, and many pharmacy sites are allowing people to schedule a flu shot at the same time as a booster dose.

In a study published in July, Dr. Berenson and his colleagues found that just 45 percent of those with active multiple myeloma “developed an adequate response” after receiving the Pfizer or Moderna vaccines.

People who received the Pfizer vaccine had lower antibody levels than Moderna recipients, on average, the researchers found. Older patients and those who were not yet in complete remission also had lower antibody levels.

It is unclear what kind of treatment Mr. Powell received for his multiple myeloma or whether he was in full remission. But even patients who are in remission may have compromised immune systems, Dr. Berenson said.

“They usually — not in all cases, but usually — maintain an immune-suppressed state even if they’ve had a good response to their treatment,” Dr. Berenson said. “Their antibody levels in most cases don’t go back up to normal.”

In a new study, scheduled to appear on Monday in the journal Cancer Cell, researchers report that some people with multiple myeloma also have weak T cell responses after vaccination. T cells can help reduce the severity of disease in people who contract the virus.

The study included 44 people with multiple myeloma who were at least two weeks past their second Pfizer or Moderna shot. Seventeen of those people produced no detectable antibodies against the virus after vaccination. These patients had significantly fewer helper T cells, which activate other parts of the immune response, to the virus compared with multiple myeloma patients who had produced antibodies after vaccination.

The good news, said Dr. Samir Parekh, a hematologist at the Icahn School of Medicine at Mount Sinai Hospital in New York who led the research, is that research suggests that booster shots “are looking extremely promising” for people with multiple myeloma.

“Patients who haven’t received them should do that immediately,” he added.

The best way to protect older adults and others with compromised immune systems is for everyone else to be vaccinated, said Dr. Ashish K. Jha, dean of the Brown University School of Public Health.

“When there are large numbers of infections happening in the community, it spills over into vaccinated people,” he said. “And the vulnerable are really at risk.”

Eric Schmitt and Christine Hauser contributed reporting.

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