ATLANTA — A rising number of parents in more than half of the United States are opting out of school shots for their kids. And in eight states, more than 1 in 20 public school kindergartners do not get all the vaccines required for attendance, an Associated Press analysis found.

That has health officials worried about possible new outbreaks of diseases that were all but stamped out.

The AP analysis found more than half of the states have seen at least a slight rise in the rate of exemptions over the past five years. Most states with the highest exemption rates are in the West and Upper Midwest.

Alaska had the highest exemption rate in 2010-11, at nearly 9 percent. Colorado’s rate was 7 percent, Minnesota 6.5 percent, Vermont and Washington 6 percent, and Oregon, Michigan and Illinois were close behind.

It’s “really gotten much worse,” said Mary Selecky, secretary of health for Washington state.

Rules for exemptions vary by state and can include medical, religious or – in some states – philosophical reasons.

Parents’ reasons for skipping the shots vary. Some doubt that vaccines are essential. Others fear that vaccines carry their own risks. And some find it easier to check a box opting out than to get the shots and required paperwork.

Still others are ambivalent, believing in older vaccines but questioning newer shots against, say, chickenpox.

The number of shots is also giving some parents pause. By the time most children are 6, they will have been stuck with a needle about two dozen times. The cumulative effect of all those shots has not been studied enough, some parents say.

“Many of the vaccines are unnecessary, and public health officials don’t honestly know” the effects of giving so many vaccines to such small children, said Jennifer Margulis, a mother of four and parenting writer in Ashland, Ore., a small liberal community with unusually high vaccination exemption rates.

But few serious problems have turned up over years of vaccinations, and several studies have shown no link between vaccines and autism, a theory from the 1990s that has been widely discredited.

Childhood vaccination rates remain high overall, at 90 percent or better for several vaccines, including those for polio, measles, hepatitis B and chickenpox. In many states, exemptions are filed for fewer than 1 percent of children entering school for the first time.

Health officials have not identified an exemption threshold that would likely lead to outbreaks. But they worry when some states have exemption rates climbing beyond 5 percent. The average state exemption rate has been estimated at less than half that.

Even more troubling are pockets in some states where exemption rates are much higher. In some rural counties in northeast Washington, for example, vaccination exemption rates in recent years have been as high as 50 percent.

“Vaccine refusers tend to cluster,” said Saad Omer, an Emory University epidemiologist.

Parents who let their kids skip some vaccines put others at risk, health officials say. Because no vaccine is completely effective, if an outbreak begins in an unvaccinated group of children, a vaccinated child may still be at some risk of getting sick.

Studies have found that measles has re-emerged in some communities with higher exemption rates.

And last year, California had more than 2,100 whooping cough cases, and 10 infants died. Only one had received a first dose of vaccine.

While it seems unlikely that diseases such as polio and diphtheria could make a comeback in the United States, immunization expert Dr. Lance Rodewald says it’s not impossible.

“Polio can come back. China was polio-free for two decades, and just this year, they were infected from Pakistan. And there is a big outbreak of polio in China now. The same could happen here,” said Rodewald, of the federal Centers for Disease Control and Prevention.

He cited outbreaks of Hib, which can lead to meningitis, among the Amish, who don’t consistently vaccinate their children. Russia had a huge diphtheria outbreak in the early to mid-1990s, he said, because vaccine coverage declined.

Exemption seekers are often middle-class, college-educated white people, but there’s a mix of views. Exemption hot spots such as Sedona, Ariz., and rural northeast Washington have concentrations of parents who prefer alternative medicine and libertarians who fear giving government too much authority.

A national survey of roughly 750 parents, published last month in the journal Pediatrics, found that more than 1 in 10 parents said they refused or delayed shots, mainly because of safety concerns.

The dangers of vaccine-preventable diseases are less important than the possible harm from vaccines, many exemption-seeking parents conclude.

Some parent groups and others have pushed legislators to make exemptions easier or do away with vaccination requirements altogether. The number of states allowing philosophical exemptions grew from 15 to 20 in the last decade.

Some in public health are exasperated by the trend.

“Every time we give them evidence (that vaccines are safe), they come back with a new hypothesis” for why vaccines could be dangerous, said University of Arizona researcher. Kacey Ernst.

The exemption increases have come during a time when the government has been raising its estimates of how many children have autism and related disorders. Some parents believe the growing roster of recommended shots must somehow be connected.

“I don’t understand how other people don’t see that these two things are related,” said Stacy Allan of Summit, N.J., who filed religious exemptions and stopped vaccinating her three children.

Several parents said that while they believe many health officials mean well, their distrust of the vaccine-making pharmaceutical industry only continues to grow.

“I wouldn’t be one to say I am absolutely certain these things are hurting our children,” said Michele Pereira, an Ashland mother of two girls who is a registered nurse and is married to an anesthesiologist. While her daughters have had some vaccinations, they have not had the full recommended schedule.

“There are enough questions out there that I don’t want to take the chance,” she said.