And then there’s some math that’s bothered me about the headlines and some of the quotes in the news articles. Thankfully, Jon Brock, an autism researcher in Australia, nicely sums it up in a comment on Ed Yong’s well-done article at The Scientist on this study. In the article, Yong quotes Van de Water as saying that if a test based on these antibodies were positive, “their risk is virtually 100 percent” that they will have an autistic child (the story has since been updated). Brock commented:
Based on current estimates, you’d expect roughly 1% (100) of (10,000) mums to have kids to have autism (ignoring for now the fact that some mums have more than one kid with autism). The study suggests that 23% of mothers of kids with autism have a “risky” combination of antibodies, so we’d expect roughly 23 of these mums to test positive.
The specificity is 99%. So of the remaining 9,900 mums in our sample, we’d expect 1% (99) to test positive, in this case falsely because their child is not autistic.
Altogether, we’d expect 23+99=122 mums to test positive. Of these, only 23 (19%) will actually have an autistic child.
Phew. Much better.