I came across the following paper, which suggests convincing - though perhaps not yet fully conclusive - evidence that the incidence of autism might be greatly increased by acetaminophen (paracetamol) exposure in genetically susceptible children:
Evidence that Increased Acetaminophen use in Genetically Vulnerable Children Appears to be a Major Cause of the Epidemics of Autism, Attention Deficit with Hyperactivity, and Asthma
Cuba has some of the lowest rates of autism in the world. In comparison, vaccination rates are some of the world's highest; but, acetaminophen is not available without prescription. In fact: their medical system hardly ever uses acetaminophen, preferring a different antipyretic to treat fever.
In the US, on the other hand, there are physicians with the bizarre practice of prescribing acetaminophen prophylactically, every day for 5 days prior to a child's immunization.
The following is another paper suggesting that acetaminophen may be a culprit:
Did acetaminophen provoke the autism epidemic?
Article about a related study in TIME, February 2014:
Tylenol During Pregnancy Linked to Higher Risk of ADHD