Children may be at increased risk of autism if their mother had the flu or a prolonged fever during pregnancy, a new study suggests.

Researchers spotted the link in a study of nearly 100,000 kids born in Denmark between 1997 and 2003, about 1 percent of whom were found to have autism. The findings were based on data collected from multiple telephone interviews with the children’s mothers and information from a national database on psychiatric disorders.

Overall, researchers from the University of Aarhus in Denmark and the U.S. Centers for Disease Control and Prevention found that women who had the flu during pregnancy were two times more likely to have a child with autism. Those odds increased to threefold when the mother had a fever for a week or more, according to the report published in the journal Pediatrics Monday.

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But the study carries a note of caution. Researchers behind the report said it is possible that despite the large number of families studied, their conclusions hinge on “chance findings.”

“Ninety-nine percent of women with influenza do not have a child with autism,” the study’s lead author, Dr. Hjordis Osk Atladottir of the University of Aarhus, told Reuters. “If it were me that was pregnant, I wouldn’t do anything different from before, because our research is so early and exploratory.”