For expecting women, a strong link between acetaminophen and autism would be cause for alarm. But despite a recent flurry of alarmist headlines, the evidence for such an association is still lacking.

Pregnant women generally rely on acetaminophen, a painkiller commonly found in Tylenol, rather than potentially-risky ibuprofen to manage fevers and pain. But after a June study in the International Journal of Epidemiology turned up a link between acetaminophen use during pregnancy and the incidence of autism and ADHD in children, the media was quick to exaggerate the findings.

The biggest offender, of course, was the Daily Mail, which declared in its headline that “women who take paracetamol [acetaminophen] during pregnancy ‘risk having a child with autism or ADHD.’” The words in single-quotes do not appear in the study itself.

As the UK’s National Health Service (NHS) was quick to point out in response, the study “provides no evidence of a direct link to either condition.”

Here’s what the study of over 2,500 mother-child pairs in Spain actually found: Male children who had been exposed to the painkiller in utero experienced symptoms of autism and ADHD in a way that seemed “dependent on the frequency of exposure.” For female children, only the link between acetaminophen and attention-related symptoms could be confirmed.

While that may sound concerning, the study is riddled with methodological holes that should cast doubt on strong claims of a causative relationship between acetaminophen use during pregnancy and autism or ADHD.

For one, the authors could not completely rule out the possibility that the underlying medical conditions which prompt pregnant women to use acetaminophen could account for some of the symptoms experienced by their children down the line. “Since ADHD and ASC [autism spectrum condition] have been associated with maternal infection and inflammation, despite adjustment for reported maternal chronic illness, urinary tract infection and fever, residual confounding by indication could still be a limitation,” the authors noted. In layman’s terms: illness during pregnancy, not painkiller use, could partially account for their findings.

This has been a common problem with previous research examining the potential links between acetaminophen use during pregnancy and developmental problems in children. As FiveThirtyEight contributor Emily Oster pointedly asked when she reported on two such studies in 2014: “Why did the mothers take the Tylenol in the first place?” “People typically take painkillers for fevers, headaches, inflammation, etc.,” she continued. “It remains possible that these symptoms drove the increased risk of behavior problems in their children, not the Tylenol use.” The authors of this latest study controlled for maternal health during pregnancy but due to some severe methodological constraints, they did not know nearly as much about the women as they would have liked.

Their research was performed after the women had given birth, meaning that they had to rely on self-reported data to draw their conclusions. Accordingly, they had no way of measuring exactly how much acetaminophen the women consumed during pregnancy.

“We were unable to evaluate the effects of dosage because of mothers’ difficulties in recalling the dose taken,” the authors admitted.

Instead, they categorized the mothers’ acetaminophen usage as “never,” “sporadic,” or “persistent” based on the number of trimesters in which they had taken the painkiller. Over 40 percent had used it at least once during pregnancy.

And, as the NHS noted, the authors also did not appear to measure other key variables that could potentially affect the children’s health, including “the mother’s alcohol consumption, or whether or not she or anyone else in the home smoked during pregnancy or in the child’s younger years.”

All in all, there is not enough evidence to suggest that acetaminophen used as necessary during pregnancy significantly increases the risk of either autism or ADHD. In fact, a 2012 study from UC Davis even found that the opposite may be true: refusing to use fever-reducing medicine while pregnant could be associated with an increased risk of autism.

“Out study provides strong evidence that controlling fevers while pregnant may be effective in modifying the risk of having a child with autism or developmental delay,” said Dr. Ousseny Zerbo, the lead author on that study. “We recommend that pregnant women who develop fever take anti-pyretic medications and seek medical attention if their fever persists.”