“When I was a tenth-grader, there was a boy in my class whose name was Billy Lynn, and he had leukemia,” Dr. Paul Offit, chief of the Division of Infectious Diseases and director of the Vaccine Education Center at the Children’s Hospital of Philadelphia, reminisced at a panel at the Television Critics Association press tour in Los Angeles on Wednesday.

“This was in the 1960s, before we had very much in the way of good therapy to treat leukemia. And, you know, he was at risk. I can’t imagine any of our parents sending us into that classroom and putting that boy at increased risk because we weren’t vaccinated, because we owed him that, because we are all in this together.”

The treatments for leukemia may have been less effective when Offit was a child. But at least Billy Lynn benefited from a consensus about childhood vaccination that has come under threat in recent years.

Offit was at the conference to promote a new movie, “Vaccines: Calling the Shots,” which will air on PBS on September 10. The documentary, directed by Sonya Pemberton, is an attempt to walk viewers through the state of vaccine and autism science. Pemberton and her subjects also have another aim: to demonstrate new ways of talking about vaccines, childhood illness and risk that could help stem a persistent and unscientific tide of anti-vaccine sentiment.

“Of parents who have chosen to delay or withhold or separate or space out vaccines, I would say 15 percent of them are hard-core, which is to say there is no convincing them,” Offit acknowledged. “They believe that vaccines are doing harm. They believe there’s a conspiracy to sell them. And they don’t want to hear what you have to say.”

Alison Singer, co-founder and president of the Autism Science Foundation, said that parents who believe their childrens’ autism was caused by vaccination may be difficult to persuade until research has identified a definitive cause for that spectrum of conditions.

“There are still pockets of parents,” she said, “who don’t care what the data show and state very clearly that they don’t care what the data show because they believe in their heart that their child’s autism was caused by vaccines.”

But the panelists suggested that there is a clear difference between these hard-core holdouts and a more persuadable majority who, as Offit put it, have “smelled the smoke and want to know whether there’s any fire there.”

Because of that, wielding scientific evidence like a club might not help. Paula Apsell, senior executive producer for Nova, said that one of the challenges in science programming and education is that “we need to really be finding ways, probably through tolerance, to be able to present the scientific facts to people in a convincing way that . . . is not so threatening and challenging to them that they can’t accept it.”

Choosing not to vaccinate “is a bad decision that puts their children at risk, but I don’t think that parents are stupid,” Singer said.

Pemberton admitted that finding the right tone was a challenge. She found it helpful to begin by listening rather than making assumptions.

“Once you start having a conversation, you find out that they have all sorts of complex reasons, and most of them actually are not hard-core opposed to vaccines,” she said.” They just have questions and concerns that they want answered.”

Parents also need help assessing the possibilities of different outcomes. One challenge, Offit suggested, is that vaccines have been so successful that they have blunted people’s sense of what the world would be like without them.

“I think that, for the most part, they don’t fear these diseases. You didn’t have to convince my parents to vaccinate. They saw diphtheria as a major killer of children in the 1920s and ’30s,” he said. “You didn’t have to convince me to vaccinate my children, because I had many of these diseases. But my children not only don’t see these diseases now, they didn’t grow up with these diseases.”

In other words, autism may seem more frightening because it is more familiar, while the measles, mumps and rubella may have no specific meaning for contemporary parents. With those fears out of proportion, it becomes difficult for parents to weigh the cost of not vaccinating because they cannot picture what it would be like for a child to become gravely ill or die of a disease with which they have had no experience.

Pemberton included a risk analyst in the film to try to reframe the debate. “He says the question is not, ‘Is this a perfect choice, but is this a better choice than what we face if we do not vaccinate?’ ” she explained. “And I think this is the really big message.”

It may be tempting to shout down or condemn as ignorant or malign people who express concerns about vaccines. Certainly the panelists gave no quarter to Jenny McCarthy, who enhanced her own celebrity by promoting a discredited study suggesting a link between vaccines and autism.

But Pemberton suggested that such an approach may have its own scientific failings.

“People think sometimes that, by acknowledging fear and concern, you make it worse,” she said. “And all the evidence is that how we deal with fear and concern is by talking about it, by processing it and then choosing to overcome it. And so acknowledging fear does not exacerbate fear. It does the opposite.”