The trimester that the fever hits, as well as multiple fevers, might play a role, too.
For the study, researchers from Columbia University Mailman School of Public Health analyzed information on close to 96,000 children born in Norway between 1999 and 2009. They reported that there were 583 cases of autism spectrum disorder in the group.
They also found that moms of 15,701 children (16 percent of the group) reported one or more fevers during pregnancy. That's similar to rates seen in the U.S.
"We had maternal reports of fever in 4-week intervals throughout the entire pregnancy and we were able to link these data to the autism data we had collected through various methods and also through a patient registry," said Columbia's Dr. Mady Hornig, director of translational research at the Center for Infection and Immunity.
Hornig, who is also an associate professor of epidemiology, told CBS News, "We were interested in trying to understand the role of fever because of prior reports with respect to fever, but there were not many. And there had also been many suggestions over the years that various types of infections in mothers during pregnancy had been associated with autism outcomes."
While they found some patterns in the first trimester, Hornig said, "It was most significant and prominent in the second trimester."
The study found that in pregnant women who came down with a fever in the second trimester, the risk of autism increased by 40 percent. In the third trimester, a fever was linked to a 15 percent higher risk of autism.
But multiple fevers after the first trimester seemed to have an even greater impact on risk. In women who reported three or more fevers after the 12th week of pregnancy, the risk of autism jumped over 300 percent.
The researchers also looked at medications mothers took to reduce fever, specifically acetaminophen (Tylenol) and ibuprofen (Advil, Motrin).
Fifty percent of U.S. women take acetaminophen during pregnancy, Hornig noted, similar to Norwegian women in the study and other Europeans. But fewer women take NSAID painkillers like ibuprofen when expecting a baby.
In the study, acetaminophen didn't seem to "mitigate" the risk for autism, but among the ibuprofen-takers, there were no cases of autism. It's not known why, though.
Still, the study didn't prove that a fever during pregnancy causes autism, and the majority of children whose moms have a fever during pregnancy will not have autism, said Hornig, whose research appears in the journal Molecular Psychiatry.
"We don't want to be alarmist, but certainly we want to know the best way to manage fever should it occur," she said.
Future research will look at ways to better prevent prenatal infections and "draw more solid conclusions and interpretations about what the relationship of fever is to autism," Hornig said.
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