Professional entertainer Donald Trump suggested during a nationally televised Republican debate that vaccines cause autism, a theory that has been massively discredited.

"Autism has become an epidemic. Twenty-five years ago, 35 years ago, you look at the statistics, not even close," Trump said. "I am totally in favor of vaccines but I want smaller doses over a longer period of time."

Trump related the story of an employee's "beautiful child [who] went to have the vaccine and came back and a week later got a tremendous fever, got very, very sick, now is autistic."

All states require certain immunizations in order for children to be admitted to public schools, with limited exceptions for religious or health reasons. Some parents worry vaccines cause autism, a theory supported by less than a shred of evidence. Some other parents favor slowing the schedule of immunizations to reduce the risk of autism, another unsupported theory.

The Centers for Disease Control and Prevention explains the risk of delaying immunizations: "Some vaccine-preventable diseases remain common in the United States, and children may be exposed to these diseases during the time they are not protected by vaccines, placing them at risk for a serious case of the disease that might cause hospitalization or death."

Skipping or delaying vaccinations also weakens herd immunity, which protects people who are too young to have been immunized.

Moderator Jake Tapper invited Dr. Ben Carson to weigh in on Trump's analysis. Carson declined to contradict Trump directly.

"The fact of the matter is, we have extremely well-documented proof that there is no autism associated with vaccinations," Carson said. "But it is true that we are probably giving way too many in too short a period of time."

Rand Paul also joined Trump's call for spacing out vaccines.

"I'm all for vaccines, but i'm also for freedom," Paul said. "I'm also a little concerned about how they're bunched up."

In a September 2011 Republican debate, Rep. Michele Bachmann (R-Minn.) falsely claimed a link between vaccines and neurological problems, and it tanked her campaign.

Read the latest updates on the GOP debate here .

Also on HuffPost: