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The people most likely to refuse to have their children vaccinated tend to be white, well-educated and affluent, researchers report.

A study published in the January issue of the American Journal of Public Health used California state government data on “personal belief exemptions,” or opting out of vaccinations for nonmedical reasons. From 2007 to 2013, the rate of vaccine refusal for personal belief doubled, to 3.06 percent.

The researchers reviewed data among all kindergarten children in the state during that time. More than 17,000 children, attending 6,911 schools, were exempted.

Exemption percentages were generally higher in regions with higher income, higher levels of education, and predominantly white populations. In private schools, 5.43 percent of children were exempt, compared with 2.88 percent in public schools.

In some suburban areas, rates of exemption were near 50 percent, and more than a quarter of California’s schools have measles immunization rates below the 92 to 94 percent required for herd immunity, the level of vaccination necessary to protect people who are not immune.

The lead author, Y. Tony Yang, an associate professor at George Mason University, said that broader vaccination coverage is critical for public health. The findings “emphasize the importance of a targeted approach, focusing on selected communities,” he said. “And we have to think about communicating with these people effectively without attacking them or making them feel defensive.”