Parents often put off getting their children vaccinated for diseases such as measles, mumps, rubella and varicella because the shots carry a small risk for seizures. But a new analysis, published online in Pediatrics, suggests that kids who received vaccinations when they became older were at increased risk of seizure, The New York Times reports.

For the study, scientists nationwide looked at medical data from 5,496 kids born between 2004 and 2008 who had seizures by age 2. Researchers found that kids who got all of their shots before age 1 (the current window doctors recommend children get measles-related vaccines) had no increased risk of seizures.

But kids who waited and got the measles, mumps, rubella (MMR) shot at the age of 16 months doubled their risk of seizures. What’s more, children who got the measles, mumps, rubella and varicella (MMRV) shot after age 1 increased their risk of seizures by almost six times.

In reality, the risk of suffering a seizure caused by the MMR and MMRV vaccines is still incredibly small at any age: about 1 in 3,000 cases for the MMR and 1 in 1,250 for the MMRV shots. But new measles cases in the United States are currently at a 20-year high, with more than 288 confirmed cases so far this year. The entirely preventable disease can lead to pneumonia, brain damage, deafness and even death in children.

Studies also prove that measles vaccines do not cause autism. Click here for more information.