Expectant mothers who have a fever during pregnancy are significantly more likely to have a child with autism, new research suggests.

The odds of a child developing autism increased 34 percent in women who came down with a fever at any time during pregnancy. The risk was greatest during the second trimester when a 40 percent bump was observed.

The findings come from a study published this week in the journal Molecular Psychiatry.

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Researchers looked at data on 95,754 kids born in Norway between 1999 and 2009. About 16 percent of mothers reported having a fever at some point during pregnancy and nearly 600 of the children were ultimately diagnosed with autism.

The risk for autism appeared to increase with the frequency of fevers. Women who experienced fevers three or more times after their 12th week of pregnancy had a 300 percent higher chance of having a child with autism, the study found.

Taking acetaminophen did minimally lessen the risk of autism among those who had a fever during their second trimester, according to the findings. Meanwhile, none of the women studied who took ibuprofen had a child with autism, but it was unclear if that was due to the drug itself or a small sample of people using it.

“Our results suggest a role for gestational maternal infection and innate immune responses to infection in the onset of at least some cases of autism spectrum disorder,” said Mady Hornig of Columbia University’s Mailman School of Public Health who led the study.

Additional research is already underway looking at blood samples taken during pregnancy and at birth to assess if particular infectious agents or certain immune responses are at play, the researchers said.