(CNN) — The US Centers for Disease Control and Prevention on Friday warned people who are immunocompromised that the COVID-19 vaccine may not have been effective for them and encouraged them to take precautions as if they were not vaccinated.

“People who are immunocompromised should be counseled about the potential for reduced immune responses to COVID-19 vaccines and to follow current prevention measures (including wearing a mask, staying 6 feet apart from others staying they don’t live with, and avoiding crowds and poorly ventilated indoor spaces) to protect themselves against COVID-19 until advised otherwise by their healthcare provider,” according to the CDC’s website.

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New numbers from the Massachusetts Department of Health, revealed there are 4,450 breakthrough COVID cases and 79 deaths among the fully vaccinated population in the state. Among the 4,450 cases, there were 4,124 people who did not need hospitalization. There were also 247 people that were hospitalized, but did not die.

Provincetown is asking the state for more COVID testing capacity after reporting 20 to 25 positive COVID cases last week. Of those cases, “the majority were fully vaccinated” people, according to the Barnstable County Department of Health. Most have only experienced mild symptoms.

Those cases may not include individuals who left Massachusetts and tested positive in their home states, according to Barnstable County Public Health Nurse Deirdre Arvidson.

“Over half of those people were short-term visitors and have gone back home,” Arvidson said.

The CDC did not go so far as to tell the millions of immunocompromised people in the U.S. to get an additional shot of a COVID-19 vaccine, noting that “the safety, efficacy and benefit of additional doses for COVID-19 vaccines in immunocompromised persons continues to be evaluated.”

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A federal official told CNN that “CDC is looking into ongoing research exploring the possibility that immunocompromised could benefit from an additional dose.”

Some immunocompromised people have, on their own, received additional doses of the vaccine, and a study last month by Johns Hopkins researchers suggested that an extra shot may help increase COVID-19 antibody levels for some organ transplant recipients who did not have a full response to their original vaccinations.

On Sunday, Dr. Anthony Fauci, President Joe Biden’s chief medical adviser, acknowledged the reality that some people are acting ahead of official recommendations, noting that there are individual physicians “right now that are saying, ‘I want to go the extra mile with someone who might have a lower level of immunity.'”

On Friday, the CDC said data suggest the response to the vaccines might be reduced for several groups, including organ transplant recipients, people who are receiving chemotherapy for cancer, people who have certain blood cancers and people receiving dialysis or taking certain medications that suppress the immune system.

The CDC’s Advisory Committee on Immunization Practices is scheduled to discuss additional doses for immunocompromised individuals during its meeting on July 22.

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© Copyright 2020 CBS Broadcasting Inc. All Rights Reserved. CNN’s Elizabeth Cohen contributed to this report.