As the global antivaccination movement grows, so has the number of U.S. parents who don’t vaccinate their children on time: As of 2015, an estimated 10% to 15% didn’t follow the recommended schedules for children under 2. Now, a new study shows that at least one of their fears—that vaccines overload the immune system and increase susceptibility to other diseases—is unfounded. Researchers examined the medical records of more than 900 infants from six hospitals and clinics across the western United States between 2003 and 2013. The team compared children who had contracted diseases not covered by vaccinations with those who didn’t—193 children in the first group and 751 in the second. There was no link between vaccines given before the age of 2 and other infections from ages 2 to 4, the team reports today in The Journal of the American Medical Association. Paul Offit, a physician at the Children’s Hospital of Philadelphia in Pennsylvania who was not involved with the study, says the results aren’t surprising. Newborns experience a “tremendous shock of bacteria” when they’re born, having gone from a sterile womb straight into to our bacteria-filled environment. The immune system challenge from vaccines “pales in comparison,” he says. The researchers say that means that following the Centers for Disease Control and Prevention’s recommended childhood immunization schedule is probably in everyone’s best interest.