Health officials are concerned fewer children are current on their immunizations. And parents must rely on 2-year-old school vaccination data.

One of the concerned parents is Rebecca Mauldin, who will send her 4-year-old son to a private school that accepts only children who are up to date on immunizations unless they cannot be vaccinated for medical reasons. He falls into that category after battling cancer and undergoing a liver transplant, she said.

His sister, who has no special health concerns, is a third-grader who started at the school last year after attending public school in Edmond f...